AC and DC circuits Presentation

CIRCUITS AND NETWORKS
CIRCUITSCIRCUITS
Parameters
 The various elements of an electric circuit, like resistance, inductance,
and capacitance which may be lumped or distibuted.
Parameters
 The various elements of an electric circuit, like resistance, inductance,
and capacitance which may be lumped or distibuted.
CIRCUITS
 A closed conducting path through which an electric
current flows or is intended to flow
CIRCUITS
 A closed conducting path through which an electric
current flows or is intended to flow

CIRCUITSCIRCUITS
Linear Circuit
 Is one whose parameters are constant (i.e. They do not change with
voltage and current.
Non-Linear Circuit
 Is that circuit whose parameters change with voltage and current.
Bilateral Circuit
 Is one whose properties or characteristics are the same in either
direction.
Unilateral Circuit
 Is that circuit whose properties or characteristics change with the
direction of its operation.
Linear Circuit
 Is one whose parameters are constant (i.e. They do not change with
voltage and current.
Non-Linear Circuit
 Is that circuit whose parameters change with voltage and current.
Bilateral Circuit
 Is one whose properties or characteristics are the same in either
direction.
Unilateral Circuit
 Is that circuit whose properties or characteristics change with the
direction of its operation.
TYPES

ELECTRICAL NETWORKSELECTRICAL NETWORKS
Passive Network
With no source of emf.
Active Network
Contains one or more than one sources of emf.
Passive Network
With no source of emf.
Active Network
Contains one or more than one sources of emf.
ELECTRICAL NETWORK
 Connection of various electric elements in any manner
ELECTRICAL NETWORK
 Connection of various electric elements in any manner
TYPES

ELECTRICAL NETWORKSELECTRICAL NETWORKS
Node
 A junction in a circuit where two or more circuit elements and/or
branches are connected together.
Branch
 Part of a network which lies netween two junctions.
Loop
 A closed path in a circuit in which no element or node is encountered
more than once.
Mesh
 A loop that contains no other loop within it.
Node
 A junction in a circuit where two or more circuit elements and/or
branches are connected together.
Branch
 Part of a network which lies netween two junctions.
Loop
 A closed path in a circuit in which no element or node is encountered
more than once.
Mesh
 A loop that contains no other loop within it.
PART
S

OHM’S LAWOHM’S LAW
OHM’S LAW
 One of the most fundamental law in electrical circuits relating
voltage, current and resistance
 Developed in 1827 by German physicist Georg Simon Ohm
OHM’S LAW
 One of the most fundamental law in electrical circuits relating
voltage, current and resistance
 Developed in 1827 by German physicist Georg Simon Ohm

OHM’S LAWOHM’S LAW
 According to Ohm’s Law, the current (I) flowing in an
electrical circuit is directly is directly proportional to the
applied voltage (E) and inversely proportional to the
equivalent resistance (R) of the circuit and mathematically
expressed as:
 According to Ohm’s Law, the current (I) flowing in an
electrical circuit is directly is directly proportional to the
applied voltage (E) and inversely proportional to the
equivalent resistance (R) of the circuit and mathematically
expressed as:

SERIES CIRCUITSSERIES CIRCUITS
SERIES circuits
 A circuit connection in which the components are
connected to form one conducting path
SERIES circuits
connected to form one conducting path
SERIES/PARALLEL CIRCUITS

SERIES CIRCUITSSERIES CIRCUITS
Where: EX – voltage across the resistor concerned
ET – total voltage across the circuit
RX – the resistor concerned
RT – the sum of all resistances in the circuit
Where: EX – voltage across the resistor concerned
ET – total voltage across the circuit
RX – the resistor concerned
Voltage Division for Series Circuit:
EX = ET • RX
RT

PARALLEL CIRCUITSPARALLEL CIRCUITS
PARALLEL circuits
connected to form more than 1 conducting path
PARALLEL circuits
connected to form more than 1 conducting path

PARALLEL CIRCUITSPARALLEL CIRCUITS
Where: IX – current concerned flowing through resistor Rx
IT – total current of the circuit
Req – equivalent resistance of the parallel circuit except Rx
Where: IX – current concerned flowing through resistor Rx
IT – total current of the circuit
Req – equivalent resistance of the parallel circuit except Rx
Voltage Division for Parallel Circuit:
IX = IT • Req
RT

KIRCHHOFF’S LAWKIRCHHOFF’S LAW
“In any electrical network, the algebraic sum of the current
meeting at a point (or junction) is zero.”
“In any electrical network, the algebraic sum of the current
meeting at a point (or junction) is zero.”
KIRCHHOFF’S LAW
 More comprehensive than Ohm’s Law and is used in solving electrical
 Termed as “Laws of Electric Networks”
 Formulated by German physicist Gustav Robert Kirchhoff
KIRCHHOFF’S LAW
 More comprehensive than Ohm’s Law and is used in solving electrical
 Termed as “Laws of Electric Networks”
 Formulated by German physicist Gustav Robert Kirchhoff
Kirchhoff’s Current Law (KCL)
NETWORK ANALYSIS

KIRCHHOFF’S CURRENT LAWKIRCHHOFF’S CURRENT LAW
 In short the sum of currents entering a node equals the sum
of currents leaving the node
⁻ Current towards the node, positive current
⁻ Current away from the node, negative current
IB + IC + ID = IA
(IB + IC + ID) - IA = 0
 In short the sum of currents entering a node equals the sum
of currents leaving the node
⁻ Current towards the node, positive current
⁻ Current away from the node, negative current
IB + IC + ID = IA
(IB + IC + ID) - IA = 0
NETWORK ANALYSIS

KIRCHHOFF’S VOLTAGE LAWKIRCHHOFF’S VOLTAGE LAW
“The algebraic sum of the products of currents and resistances
in each of thr conductors in any closed path (or mesh) in a
network PLUS the algebraic sum of the emfs in the path is
zero.”
“The algebraic sum of the products of currents and resistances
in each of thr conductors in any closed path (or mesh) in a
network PLUS the algebraic sum of the emfs in the path is
zero.”
Kirchhoff’s Voltage Law (KVL)
NETWORK ANALYSIS

KIRCHHOFF’S VOLTAGE LAWKIRCHHOFF’S VOLTAGE LAW
 In short, the sum of the voltages around the loop is equal to
zero
⁻ For voltage sources, if loops enters on minus and goes out on plus,
positive voltage and if loops enters on plus and goes out on minus,
negative voltage.
⁻ For voltage drops, if the loop direction is the same as current
direction, negative voltage drop and if the loop direction is opposite
to the current direction, positive voltage drop.
 In short, the sum of the voltages around the loop is equal to
zero
⁻ For voltage sources, if loops enters on minus and goes out on plus,
positive voltage and if loops enters on plus and goes out on minus,
negative voltage.
⁻ For voltage drops, if the loop direction is the same as current
direction, negative voltage drop and if the loop direction is opposite
to the current direction, positive voltage drop.
NETWORK ANALYSIS

MESH ANALYSISMESH ANALYSIS
Loop Analysis Procedure:
1. Label each of the loop/mesh currents.
2. Apply KVL to loops/meshes to form
equations with current variables.
a. For N independent loops, we may write
N total equations using KVL around
each loop. Loop currents are those
currents flowing in a loop; they are
used to define branch currents.
b. Current sources provide constraint
equations.
3. Solve the equations to determine the
user defined loop currents.
Loop Analysis Procedure:
1. Label each of the loop/mesh currents.
2. Apply KVL to loops/meshes to form
equations with current variables.
a. For N independent loops, we may write
N total equations using KVL around
each loop. Loop currents are those
currents flowing in a loop; they are
used to define branch currents.
b. Current sources provide constraint
equations.
3. Solve the equations to determine the
user defined loop currents.
NETWORK ANALYSIS
MESH analysis
 A sophisticated application of KVL with mesh currents.
MESH analysis
 A sophisticated application of KVL with mesh currents.

NODAL ANALYSISNODAL ANALYSIS
 Consist of finding the node
voltages at all principal nodes with
respect to the reference node.
PRINCIPAL node – a node with three
or more circuit elements joined
together.
Reference node – the node from
which the unknown voltages are
measured.
 Consist of finding the node
voltages at all principal nodes with
respect to the reference node.
PRINCIPAL node – a node with three
or more circuit elements joined
together.
Reference node – the node from
which the unknown voltages are
measured.
NETWORK ANALYSIS
NODAL analysis
 A systematic application of KCL at a node and after simplifying
the resulting KCL equation, the node voltage can be calculated.
NODAL analysis
 A systematic application of KCL at a node and after simplifying
the resulting KCL equation, the node voltage can be calculated.

SUPERPOSITION THEOREMSUPERPOSITION THEOREM
In general:
 Number of network to analyze is equal to number of independent
sources.
 To consider effects of each source independently, sources must be
removed and replaced without affecting the final result:
 All voltage sources >> short circuited
 All current sources >> open circuited
In general:
 Number of network to analyze is equal to number of independent
sources.
 To consider effects of each source independently, sources must be
removed and replaced without affecting the final result:
 All voltage sources >> short circuited
 All current sources >> open circuited
NETWORK ANALYSIS
SUPERPOSITION theorem
“ The current through or voltage across, an element in a linear
bilateral network is equal to the algebraic sum of the current or
voltages produced independently in each source. ”
SUPERPOSITION theorem
“ The current through or voltage across, an element in a linear
bilateral network is equal to the algebraic sum of the current or
voltages produced independently in each source. ”

COMPENSATION THEOREMCOMPENSATION THEOREM
NETWORK ANALYSIS
COMPENSATION theorem
 If the impedance Z of a branch in a network in which a current I
flows is changed by a finite amount dZ, then the change in the
currents in all other branches of the network may be calculated
by inserting a voltage source of -IdZ into that branch with all
other voltage sources replaced by their internal impedances.
COMPENSATION theorem
 If the impedance Z of a branch in a network in which a current I
flows is changed by a finite amount dZ, then the change in the
currents in all other branches of the network may be calculated
by inserting a voltage source of -IdZ into that branch with all
other voltage sources replaced by their internal impedances.

RECIPROCITY THEOREMRECIPROCITY THEOREM
Simply mean,
 E and I are mutually transferable, or
 The receiving point and the sending point in a network are
interchangeable, or
 Interchange of an IDEAL voltage source and an IDEAL ammeter in any
network will not change the ammeter reading,
 Interchange of an IDEAL current source and an IDEAL voltmeter in any
network will not change the voltmeter reading
Simply mean,
 E and I are mutually transferable, or
 The receiving point and the sending point in a network are
interchangeable, or
 Interchange of an IDEAL voltage source and an IDEAL ammeter in any
network will not change the ammeter reading,
 Interchange of an IDEAL current source and an IDEAL voltmeter in any
network will not change the voltmeter reading
NETWORK ANALYSIS
RECIPROCITY theorem
“If a voltage source E acting in one branch of a network causes a
current I to flow in another branch of the network, then the same
voltage source E acting in the second branch would cause an identical
current I to flow in the first branch. ”
RECIPROCITY theorem
“If a voltage source E acting in one branch of a network causes a
current I to flow in another branch of the network, then the same
voltage source E acting in the second branch would cause an identical
current I to flow in the first branch. ”

MILLMAN’S THEOREMMILLMAN’S THEOREM
 In Millman’s Theorem, the circuit is re-drawn as a parallel
network of branches, each branch containing a resistor or
series battery/resistor combination.
 Millman’s theorem is applicable only to those cicuits which
can be re-drawn accordingly.
 In Millman’s Theorem, the circuit is re-drawn as a parallel
network of branches, each branch containing a resistor or
series battery/resistor combination.
 Millman’s theorem is applicable only to those cicuits which
can be re-drawn accordingly.
NETWORK ANALYSIS
MILLMAN’S theorem
“ A special case of the application of Thevenin’s Theorem/or
Norton’s Theorem used for finding the COMMON voltage (VAB)
across any network which contains a number of parallel voltage
sources. ”
MILLMAN’S theorem
“ A special case of the application of Thevenin’s Theorem/or
Norton’s Theorem used for finding the COMMON voltage (VAB)
across any network which contains a number of parallel voltage
sources. ”

MAXIMUM POWER TRANSFER
THOREM
MAXIMUM POWER TRANSFER
THOREM
NETWORK ANALYSIS
MAXIMUM POWER TRANSFER theorem
 For loads connected directly to a DC voltage supply, maximum
power will be delivered to the load when the resistance is equal
to the internal resistance of the source.
 For maximum power transfer: RS = RL
MAXIMUM POWER TRANSFER theorem
 For loads connected directly to a DC voltage supply, maximum
power will be delivered to the load when the resistance is equal
to the internal resistance of the source.
 For maximum power transfer: RS = RL

THEVENIN’S THEOREMTHEVENIN’S THEOREM
where:
VTH – the open circuit voltage which appears across the two terminals from where
the load resistance has been removed.
RTH – the resistance looking back into the network across the two terminals with all
the voltage sources shorted and replaced by their internal resistances (if any)
and all current sources by infinite resistance.
where:
VTH – the open circuit voltage which appears across the two terminals from where
the load resistance has been removed.
RTH – the resistance looking back into the network across the two terminals with all
the voltage sources shorted and replaced by their internal resistances (if any)
and all current sources by infinite resistance.
NETWORK ANALYSIS
THEVENIN’S theorem
“ Any two-terminal of a linear, active bilateral network of a
fixed resistances and voltage source/s may be replaced by a
single voltage source (VTH) and a series of internal resistance
(RTH). ”
“ Any two-terminal of a linear, active bilateral network of a
fixed resistances and voltage source/s may be replaced by a
single voltage source (VTH) and a series of internal resistance
(RTH). ”

NORTON’S THEOREMNORTON’S THEOREM
where:
IN– the current which would flow in a short circuit placed across the output terminals.
RN – the resistance of the network when viewed from the open circuited terminals after
all voltage sources being replaced by open circuits.
where:
IN– the current which would flow in a short circuit placed across the output terminals.
RN – the resistance of the network when viewed from the open circuited terminals after
all voltage sources being replaced by open circuits.
NETWORK ANALYSIS
“ Any two-terminal active network containing voltage sources
and resistances when viewed from its output terminals, is
equivalent to a constant-current source (IN) and a parallel
internal resistance (RN). ”
“ Any two-terminal active network containing voltage sources
and resistances when viewed from its output terminals, is
equivalent to a constant-current source (IN) and a parallel
internal resistance (RN). ”

THEVENIN-NORTON
TRANSFORMATION
THEVENIN-NORTON
TRANSFORMATION
NETWORK ANALYSIS

NORTON-THEVENIN
TRANSFORMATION
NORTON-THEVENIN
TRANSFORMATION
NETWORK ANALYSIS

EQUIVALENT THREE-TERMINAL
NETWORKS
NETWORKS
NETWORK ANALYSIS
DELTA to WYE
 The equivalent resistance of each arm to the wye is given by the
PRODUCT of the two delta sides that meet at its end divided by the
SUM of the three delta resistances.
DELTA to WYE
 The equivalent resistance of each arm to the wye is given by the
PRODUCT of the two delta sides that meet at its end divided by the
SUM of the three delta resistances.

NETWORKS
NETWORKS
NETWORK ANALYSIS
WYE to DELTA
 The equivalent delta resistance between any two twrminals is given by the
SUM of a star resistance between those terminals PLUS the PRODUCT of
these two star resistances DIVIDED by the third resistance.
WYE to DELTA
 The equivalent delta resistance between any two twrminals is given by the
SUM of a star resistance between those terminals PLUS the PRODUCT of
these two star resistances DIVIDED by the third resistance.

REVIEW QUESTIONSREVIEW QUESTIONS
1. A battery with a rating of 9 volts has an internal resistance of 20 ohms.
What is the expected resistance of the bulb that is connected across the
battery to attain a maximum power transfer?
a. 20 ohms
b. 10 ohms
c. 5 ohms
d. 2 ohms
2. In a sireis ciscuit a resistors 2200 and 4500 with an impressed voltage of
10, what is the circuit current in mA?
a. 1.49
b. 6.67
c. 4.34
d. 1.34
1. A battery with a rating of 9 volts has an internal resistance of 20 ohms.
What is the expected resistance of the bulb that is connected across the
battery to attain a maximum power transfer?
a. 20 ohms
b. 10 ohms
c. 5 ohms
d. 2 ohms
2. In a sireis ciscuit a resistors 2200 and 4500 with an impressed voltage of
10, what is the circuit current in mA?
a. 1.49
b. 6.67
c. 4.34
d. 1.34

3. The current needed to operate a soldering iron which has a rating of
600 watts at 110 volts is.
a. 5.455 A
b. 66,000 A
c. 18,200 A
d. 0.182 A
4. The ammeter reads 230 ampere while the voltmeter is 115 volts.
What is the power inKW at the time of reading
a. 264.5
b. 2645
c. 264500
d.26.45
3. The current needed to operate a soldering iron which has a rating of
600 watts at 110 volts is.
a. 5.455 A
b. 66,000 A
c. 18,200 A
d. 0.182 A
4. The ammeter reads 230 ampere while the voltmeter is 115 volts.
What is the power inKW at the time of reading
a. 264.5
b. 2645
c. 264500
d.26.45

5. What is the type of circuit whose parameters are constant
which do not change with voltage or current?
a. Lumped
b. Tuned
c. Reactive
d. Linear
6. What is the resistance of two equal valued resistor series?
a. Twice as one
b. The sum of their reciprocal
c. The difference of both
b. The product of both
5. What is the type of circuit whose parameters are constant
which do not change with voltage or current?
a. Lumped
b. Tuned
c. Reactive
d. Linear
6. What is the resistance of two equal valued resistor series?
a. Twice as one
b. The sum of their reciprocal
c. The difference of both
b. The product of both

7. What do you expect when you use two 20 kohms, 1 watts resistors
in parallel instead of one 10 kohms, 1 watt?
a. Provide more power
b. Provide lighter current
c. Provide less power
d. Provide wider tolerance
8. The voltage applied in DC circuit having a power of 36 watts and a
total resistance of 4 ohms.
a. 6 V
b. 9V
c. 12 V
d. 24 V
7. What do you expect when you use two 20 kohms, 1 watts resistors
in parallel instead of one 10 kohms, 1 watt?
a. Provide more power
b. Provide lighter current
c. Provide less power
d. Provide wider tolerance
8. The voltage applied in DC circuit having a power of 36 watts and a
total resistance of 4 ohms.
a. 6 V
b. 9V
c. 12 V
d. 24 V

9. When resistor are connected in series, what happens?
a. The effective resistance
b. Nothing
c. The tolerance
d. The effective resistance is increased
10. Find the thevenin’s impedance equivalent across R2 of a linear
close circuit having 10-V supply in series with the resistors (R1=100
ohms and R2=200 ohms)
a. 666 ohms
b. 6.66 ohms
c. 66.6 ohms
d. 6666 ohms
9. When resistor are connected in series, what happens?
a. The effective resistance
b. Nothing
c. The tolerance
d. The effective resistance is increased
10. Find the thevenin’s impedance equivalent across R2 of a linear
close circuit having 10-V supply in series with the resistors (R1=100
ohms and R2=200 ohms)
a. 666 ohms
b. 6.66 ohms
c. 66.6 ohms
d. 6666 ohms

11. How much power does electronic equipment consume, assuming a
5.5A current flowing and a 120-V power source.
a. 60 W
b. 66 W
c. 660 W
d. 125.5 W
12. How many nodes are needed to completely analyze a circuit
according to Kirchoffs Current Law.
a. One
b. Two
c. All nodes in the circuit
d. One less than the total number of nodes in the circuit
11. How much power does electronic equipment consume, assuming a
5.5A current flowing and a 120-V power source.
a. 60 W
b. 66 W
c. 660 W
d. 125.5 W
12. How many nodes are needed to completely analyze a circuit
according to Kirchoffs Current Law.
a. One
b. Two
c. All nodes in the circuit
d. One less than the total number of nodes in the circuit

13. A common connection between circuit elements or conductors
from different branches.
a. Node
b. Junction
c. Ground
d. Mesh
14. It is used to denote a common electrical point of zero potential.
a. Short circuit
b. Reference point
c. Open circuit
d.ground
13. A common connection between circuit elements or conductors
from different branches.
a. Node
b. Junction
c. Ground
d. Mesh
14. It is used to denote a common electrical point of zero potential.
a. Short circuit
b. Reference point
c. Open circuit
d.ground

15. Loop currents should be assumed to flow in which
direction?
a. Straight
b. Clockwise
c. Counterclockwise
d. Either b or c
16. In mesh analysis, we apply:
a. KCL
b. KVL
c. Source
d. Millman’s theorem
15. Loop currents should be assumed to flow in which
direction?
a. Straight
b. Clockwise
c. Counterclockwise
d. Either b or c
16. In mesh analysis, we apply:
a. KCL
b. KVL
c. Source
d. Millman’s theorem

17. Which of the following is not a valid expression of Ohms Law
a. R = PI
b. E = IR
c. I = E/R
d. R = E/I
18. Using ohms Law, what happens to the circuit current if the applied
voltage increases?
a. Current doubles
b. Current increases
c. Current remians constant
d. Current decreases
17. Which of the following is not a valid expression of Ohms Law
a. R = PI
b. E = IR
c. I = E/R
d. R = E/I
18. Using ohms Law, what happens to the circuit current if the applied
voltage increases?
a. Current doubles
b. Current increases
c. Current remians constant
d. Current decreases

19. According to ohms law, what happen to the circuit current if the
circuit resistance increases?
a. Current doubles
b. Current decreases
c. Current increases
d. Current remains constant
20. If the resistance of a circuit is doubled and the applied voltage is
kept constant, the current will be _______ .
a. Be quaddrupled
b. Remains
c. Be cut in half
d. Be doubled
19. According to ohms law, what happen to the circuit current if the
circuit resistance increases?
a. Current doubles
b. Current decreases
c. Current increases
d. Current remains constant
20. If the resistance of a circuit is doubled and the applied voltage is
kept constant, the current will be _______ .
a. Be quaddrupled
b. Remains
c. Be cut in half
d. Be doubled

21. It is an electrical current that flows in one direction only?
a. Normal current
b. Alternating current
c. Direct current
d. Eddy current
22. In Ohms Law, what is E/R?
a. Amperage
b. Voltage
c. Resistance
d. Power
21. It is an electrical current that flows in one direction only?
a. Normal current
b. Alternating current
c. Direct current
d. Eddy current
22. In Ohms Law, what is E/R?
a. Amperage
b. Voltage
c. Resistance
d. Power

23. A 33-Kohm resistor is connected in series with a parallel
combination made up of 56-Kohm resistor and a 7.8-kohm resistor.
What is the total combined reistance of the three resistors?
a. 390667 ohms
b. 49069 ohms
c. 63769 ohms
d. 95000 ohms
24. Which of the following cannot be included in a loop of Kirchoff’s
Volatage Law
a. Current source
b. Voltage source
c. Resistance
d. Reactance
23. A 33-Kohm resistor is connected in series with a parallel
combination made up of 56-Kohm resistor and a 7.8-kohm resistor.
What is the total combined reistance of the three resistors?
a. 390667 ohms
b. 49069 ohms
c. 63769 ohms
d. 95000 ohms
24. Which of the following cannot be included in a loop of Kirchoff’s
Volatage Law
a. Current source
b. Voltage source
c. Resistance
d. Reactance

25. A series connected circuit consists of 3 loads and consume a total power
of 50 Watts. It was reconfigured such that 2 are in parallel and the other
load is in series with a combination. What is the applied expected powers
to be consumed them?
a. 50 watts
b. 25 watts
c. 75 watts
d. 45 watts
26. If the number of valence electrons of an atom is less than 4, the
substance is usually
a. Semiconductor
b. An insulator
c. A conductor
d. None of the above
25. A series connected circuit consists of 3 loads and consume a total power
of 50 Watts. It was reconfigured such that 2 are in parallel and the other
load is in series with a combination. What is the applied expected powers
to be consumed them?
a. 50 watts
b. 25 watts
c. 75 watts
d. 45 watts
26. If the number of valence electrons of an atom is less than 4, the
substance is usually
a. Semiconductor
b. An insulator
c. A conductor

27. Electric current in a wire is the flow of
a. Free electrons
b. Valence electrons
c. Bound electrons
d. Atoms
28. EMF in a circuit is a form
a. Power
b. Energy
c. Charge
d. none
27. Electric current in a wire is the flow of
a. Free electrons
b. Valence electrons
c. Bound electrons
d. Atoms
28. EMF in a circuit is a form
a. Power
b. Energy
c. Charge
d. none

29. The SI unit of specific-resistance is
a. Mho
b. Ohm-n
c. Ohm-sq.-m
d. Ohm-cm
30. The resistance of a material is ___ its area of cross-section
a. Directly proportional
b. Inversely proportional
c. Independent
d. None of these
29. The SI unit of specific-resistance is
a. Mho
b. Ohm-n
c. Ohm-sq.-m
d. Ohm-cm
30. The resistance of a material is ___ its area of cross-section
a. Directly proportional
b. Inversely proportional
c. Independent
d. None of these

31. The value of α, i.e., the temperarure coefficient of resistance
depends upon the ____ of the material.
a. Length
b. Volume
c. X-sectional area
d. Nature and temperature
32. The value of α of a conductor is 1/236 C. The value of a α is
a. 1/218 C
b. 1/272 C
c. 1/254 C
d. 1/265 C
31. The value of α, i.e., the temperarure coefficient of resistance
depends upon the ____ of the material.
a. Length
b. Volume
c. X-sectional area
d. Nature and temperature
32. The value of α of a conductor is 1/236 C. The value of a α is
a. 1/218 C
b. 1/272 C
c. 1/254 C
d. 1/265 C

33. Electrical appliances are not connected in series because
a. Series circuit is complicated
b. Power loss is greater
c. Appliances have different current rating
d. None of these
34. Electrical appliances are connected in parallel because it
a. Is a simple circuit
b. Results in reduced power loss
c. Draw less current
d. Makes the operation of the appliances independent
from each other
33. Electrical appliances are not connected in series because
a. Series circuit is complicated
b. Power loss is greater
c. Appliances have different current rating
d. None of these
34. Electrical appliances are connected in parallel because it
a. Is a simple circuit
b. Results in reduced power loss
c. Draw less current
d. Makes the operation of the appliances independent
from each other

35. The hot resistance of a 100W, 250V incandecent lamp is
a. 2.5 ohms
b. 625 ohms
c. 25 ohms
d. None of these
36. When a number of resistances are connecte in parallel,
the total resistance is
a. Less than the smallest resistance
b. Greater than the smallest resistance
c. Between the smallest and greater resistance
d. None of these
35. The hot resistance of a 100W, 250V incandecent lamp is
a. 2.5 ohms
b. 625 ohms
c. 25 ohms
d. None of these
36. When a number of resistances are connecte in parallel,
a. Less than the smallest resistance
b. Greater than the smallest resistance
c. Between the smallest and greater resistance
d. None of these

37. If the resistances, each of value 36 ohms are connected in parallel,
a. 2 ohms
b. 54 ohms
c. 36 ohms
d. None of these
38. Two incandecent lamps of 100 W, 200V are in parallel across the
200 V. The total resistance will be
a. 800 ohms
b. 200 ohms
c. 400 ohms
d. 600 ohms
37. If the resistances, each of value 36 ohms are connected in parallel,
a. 2 ohms
b. 54 ohms
c. 36 ohms
d. None of these
38. Two incandecent lamps of 100 W, 200V are in parallel across the
200 V. The total resistance will be
a. 800 ohms
b. 200 ohms
c. 400 ohms
d. 600 ohms

39. Three resistors are connected in parallel and draws 1A, 2.5A, and
3.5A, rspectively. If the applied voltage is 210V, what is the total
resistance of the circuit?
a. 5 ohms
b. 147 ohms
c. 3 ohms
d. 73.5 ohms
40. An ordinary dry cell can deliver about ____ continuously.
a. 3 A
b. 2 A
c. 1/8 A
d. None of these
39. Three resistors are connected in parallel and draws 1A, 2.5A, and
3.5A, rspectively. If the applied voltage is 210V, what is the total
resistance of the circuit?
a. 5 ohms
b. 147 ohms
c. 3 ohms
d. 73.5 ohms
40. An ordinary dry cell can deliver about ____ continuously.
a. 3 A
b. 2 A
c. 1/8 A
d. None of these

41. Four cells of internal resistance 1 ohms, are connected in parallel.
The battery resistance will be
a. 4 ohms
b. 0.25 ohms
c. 2 ohms
d. 1 ohms
42. Of the following combination of units, the one that is not equal to
the watt is
a. Joule/sec
b. Ampere-volt
c. Ampere-ohm
d. Ohm/volt
41. Four cells of internal resistance 1 ohms, are connected in parallel.
The battery resistance will be
a. 4 ohms
b. 0.25 ohms
c. 2 ohms
d. 1 ohms
42. Of the following combination of units, the one that is not equal to
the watt is
a. Joule/sec
b. Ampere-volt
c. Ampere-ohm
d. Ohm/volt

43. The power dissipated in a circuit is not equal to
a. VI
b. IR
c. V/R
d. IR/V
44. An electric iron draws a current of 15A when connected to
120V power source. Its resistance is
a. 0.125 ohms
b. 8 ohms
c. 16 ohms
d. 1,800 ohms
43. The power dissipated in a circuit is not equal to
a. VI
b. IR
c. V/R
d. IR/V
44. An electric iron draws a current of 15A when connected to
120V power source. Its resistance is
a. 0.125 ohms
b. 8 ohms
c. 16 ohms
d. 1,800 ohms

45. The power rating of an electric motor which draws a current of 3 A
when operated at 120 V is
a. 40 W
b. 360 W
c. 540 W
d. 1,080 W
46. When a 100W, 240V, light bulb is operated at 200V, the current
that flows in it is
a. 0.35 A
b. 0.42 A
c. 0.5 A
d. 0.58 A
45. The power rating of an electric motor which draws a current of 3 A
when operated at 120 V is
a. 40 W
b. 360 W
c. 540 W
d. 1,080 W
46. When a 100W, 240V, light bulb is operated at 200V, the current
that flows in it is
a. 0.35 A
b. 0.42 A
c. 0.5 A
d. 0.58 A

47. The equivalent resistance of a network of three 2 ohm resistors
cannot be
a. 0.67 ohms
b. 1.5 ohms
c. 3 ohms
d. 6 ohms
48. A 12V potential difference is applied across a series combination of
four six-ohms resistors. The current in each six-ohm resistor will be
a. 0.5 A
b. 2 A
c. 8 A
d. 6 A
47. The equivalent resistance of a network of three 2 ohm resistors
cannot be
a. 0.67 ohms
b. 1.5 ohms
c. 3 ohms
d. 6 ohms
48. A 12V potential difference is applied across a series combination of
four six-ohms resistors. The current in each six-ohm resistor will be
a. 0.5 A
b. 2 A
c. 8 A
d. 6 A

49. A 12V potential difference is applied across a parallel combination
of four six-ohms resistors. The current in each six-ohm resistor will
be
a. 0.5 A
b. 2 A
c. 8 A
d. 6 A
50. The dissipation of energy can cause burns because it proceduces
a. Heat
b. Fire
c. Friction
d. Overload
49. A 12V potential difference is applied across a parallel combination
of four six-ohms resistors. The current in each six-ohm resistor will
be
a. 0.5 A
b. 2 A
c. 8 A
d. 6 A
50. The dissipation of energy can cause burns because it proceduces
a. Heat
b. Fire
c. Friction
d. Overload

51. The rate of expenditure of energy is
a. Voltage
b. Power
c. Current
d. Energy
52. In a simple DC power line, the wire that carries the current
from the generator to the load is called
a. Return wire
b. Feeder
c. Outgoing wire
d. Conductor
51. The rate of expenditure of energy is
a. Voltage
b. Power
c. Current
d. Energy
52. In a simple DC power line, the wire that carries the current
from the generator to the load is called
a. Return wire
b. Feeder
c. Outgoing wire
d. Conductor

53. A circuit in which the resistance are connected in a continuous run,
i.e., end-to-end is a _____ circuit.
a. Saries
b. Parallel
c. Series-parallel
d. None of these
54. A battery is connected to an external circuit. The potential drop
with the battery is proportional to
a. The EMF of the battery
b. The current of the circuit
c. The equivqlent circuit resistance
d. Power dissipated in the circuit
53. A circuit in which the resistance are connected in a continuous run,
i.e., end-to-end is a _____ circuit.
a. Saries
b. Parallel
c. Series-parallel
d. None of these
54. A battery is connected to an external circuit. The potential drop
with the battery is proportional to
a. The EMF of the battery
b. The current of the circuit
c. The equivqlent circuit resistance
d. Power dissipated in the circuit

55. Two wires A and B have the same cross-sectional area and are
made of the same material. Ra = 600 ohms and Rb = 100 ohms. The
number of times A is longer tahn B is
a. 6
b. 2
c. 4
d. 5
56. A coil has a resistance of 100 ohms at 90 C. At 100 C, its resistance
is 101 ohms. The temperature coefficient of the wire is
a. 0.01
b. 0.1
c. 0.0001
d. 0.001
55. Two wires A and B have the same cross-sectional area and are
made of the same material. Ra = 600 ohms and Rb = 100 ohms. The
number of times A is longer tahn B is
a. 6
b. 2
c. 4
d. 5
56. A coil has a resistance of 100 ohms at 90 C. At 100 C, its resistance
is 101 ohms. The temperature coefficient of the wire is
a. 0.01
b. 0.1
c. 0.0001
d. 0.001

57. The resistance of a conductor does not depend on its
a. Resistivity
b. Length
c. Cross-section
d. Mass
58. A material which has a negative temperature coefficient
of resistance is usually a/an
a. Insulator
b. Conductor
c. Semi-conductor
d. All of these
57. The resistance of a conductor does not depend on its
a. Resistivity
b. Length
c. Cross-section
d. Mass
58. A material which has a negative temperature coefficient
of resistance is usually a/an
a. Insulator
b. Conductor
c. Semi-conductor
d. All of these

59. Which of the following statements is true both for a series
and a parallel dc circuit?
a. Power additive
b. Current are additive
c. Voltage are additive
d. All of these
60. Two resistors are said to be in series when
a. Both carry the same value of current
b. Total current equals the sum of the branch current
c. Sum of IR drops equal to EMF
d. Same current phases through both
59. Which of the following statements is true both for a series
and a parallel dc circuit?
a. Power additive
b. Current are additive
c. Voltage are additive
d. All of these
60. Two resistors are said to be in series when
a. Both carry the same value of current
b. Total current equals the sum of the branch current
c. Sum of IR drops equal to EMF
d. Same current phases through both

61. According to KCL as applied to a juction in a network of
conductors.
a. Total sum of currents meeting at the juction is Zero
b. No current can leave the juction without same current passing
throuhg it
c. Net current flow at he juction is positive
d. Algebraic sum of the currents meeting at the juction is zero
62. Kirchoff’s Current Law is applicable only to
a. Closed-loop circuit
b. Electronic circuits
c. Juctions in a network
d. Electric circuit
61. According to KCL as applied to a juction in a network of
conductors.
a. Total sum of currents meeting at the juction is Zero
b. No current can leave the juction without same current passing
throuhg it
c. Net current flow at he juction is positive
d. Algebraic sum of the currents meeting at the juction is zero
62. Kirchoff’s Current Law is applicable only to
a. Closed-loop circuit
b. Electronic circuits
c. Juctions in a network
d. Electric circuit

63. Kirchoff’s Voltage Lasw is concerned with
a. IR drops
b. Battery EMF’s
c. Juction voltages
d. A and b
64. According to KVL, the algebraic sum of all IR drops and
EMF’s in any closed loop of a network is always
a. Zero
b. Negative
c. Positive
d. Determined by battery EMF
63. Kirchoff’s Voltage Lasw is concerned with
a. IR drops
b. Battery EMF’s
c. Juction voltages
d. A and b
64. According to KVL, the algebraic sum of all IR drops and
EMF’s in any closed loop of a network is always
a. Zero
b. Negative
c. Positive
d. Determined by battery EMF

65. The algebraic sign of an IR drops primarily dependent upon
a. The amount of current flowing through it
b. Direction of current
c. The value of the resistance
d. The battery connection
66. Choose the wrong statement. In the node voltage technique of
solvingnetwork parameters, the choice of the reference node does
not
a. Affect the operation of the circuit
b. Change the voltage across the element
c. Alter the potential difference between any pair of nodes
d. Affect the volatge of various nodes
65. The algebraic sign of an IR drops primarily dependent upon
a. The amount of current flowing through it
b. Direction of current
c. The value of the resistance
d. The battery connection
66. Choose the wrong statement. In the node voltage technique of
solvingnetwork parameters, the choice of the reference node does
not
a. Affect the operation of the circuit
b. Change the voltage across the element
c. Alter the potential difference between any pair of nodes
d. Affect the volatge of various nodes

67. The nodal analysis is primarily based on the application of
a. KVL
b. KCL.
c. Ohms Law
d. b and c
68. Superposition theorem can be applied only to circuits
having ____ elements
a. Non-linear
b. Passive
c. Linear bilateral
d. Resistive
67. The nodal analysis is primarily based on the application of
a. KVL
b. KCL.
c. Ohms Law
d. b and c
68. Superposition theorem can be applied only to circuits
having ____ elements
a. Non-linear
b. Passive
c. Linear bilateral
d. Resistive

69. The superposition theorem is essentially based on the
concept of
a. Reciprocity
b. Linearity
c. non-linearity
d. Duality
70. What are the electrons in motion called?
a. Current variation
b. Electric current
c. Electron velocity
d. Dynamic electricity
69. The superposition theorem is essentially based on the
concept of
a. Reciprocity
b. Linearity
c. non-linearity
d. Duality
70. What are the electrons in motion called?
a. Current variation
b. Electric current
c. Electron velocity
d. Dynamic electricity

71. An active element in a circuit is one which _____ .
a. Receives energy
b. Supplies energy
c. a or b
d. None of these
72. The siperposition theorem is used when the circuit
contains
a. A single voltage source
b. A number of voltage source
c. Passive element only
d. None of these
71. An active element in a circuit is one which _____ .
a. Receives energy
b. Supplies energy
c. a or b
d. None of these
72. The siperposition theorem is used when the circuit
contains
a. A single voltage source
b. A number of voltage source
c. Passive element only
d. None of these

73. Thevenin’s theorem is ____ form of equivalent circuit.
a. Voltage
b. Current
c. Both a and b
d. None of these
74. Norton’s theorem is ____ form of an equivalent circuit.
a. Voltage
b. Current
c. Both a and b
d. None of these
73. Thevenin’s theorem is ____ form of equivalent circuit.
a. Voltage
b. Current
c. Both a and b
d. None of these
74. Norton’s theorem is ____ form of an equivalent circuit.
a. Voltage
b. Current
c. Both a and b
d. None of these

75. In the analysis of vacuum tube circuit, we can generally use ____
theorem.
a. Norton’s
b. Thevenin’s
c. Superposition
d. Reciprocity
76. In the analysis of transistor circuits, we generally use _____
theorem.
a. Voltage
b. Current
c. Both a and b
d. None of these
75. In the analysis of vacuum tube circuit, we can generally use ____
theorem.
a. Norton’s
b. Thevenin’s
c. Superposition
d. Reciprocity
76. In the analysis of transistor circuits, we generally use _____
theorem.
a. Voltage
b. Current
c. Both a and b
d. None of these

77. Under the condition of Maximum Power Transfer, the
efficiency is
a. 75 %
b. 100 %
c. 50 %
d. 25 %
78. The maximum power transfer theorem is used in
a. Electronic circuits
b. Home lightning
c. Power sytem
77. Under the condition of Maximum Power Transfer, the
efficiency is
a. 75 %
b. 100 %
c. 50 %
d. 25 %
78. The maximum power transfer theorem is used in
a. Electronic circuits
b. Home lightning
c. Power sytem

79. delta/star or star/delta transformation technique is
applied to
a. One terminal
b. Two terminal
c. Three terminal
d. None of these
80. _____ will be used under elctrostatics.
a. Incandecent lamp
b. Electric motor
c. Electric iron
d. Lightning rod
79. delta/star or star/delta transformation technique is
applied to
a. One terminal
b. Two terminal
c. Three terminal
d. None of these
80. _____ will be used under elctrostatics.
a. Incandecent lamp
b. Electric motor
c. Electric iron
d. Lightning rod

81. The value of the absulute permitivity of air is ______ F/m.
a. 9 x 10
b. 8,854 x 10 ^ -12
c. 5 x 10
d. 9 X 10
82. When two similar charges eaach of 1 coulumb each are
placed 1m apart in air, then the force of repusion is
a. 8 x10 N
b. 10 N
c. 9 x 10^9 N
d. 5 x 10 N
81. The value of the absulute permitivity of air is ______ F/m.
a. 9 x 10
b. 8,854 x 10 ^ -12
c. 5 x 10
d. 9 X 10
82. When two similar charges eaach of 1 coulumb each are
placed 1m apart in air, then the force of repusion is
a. 8 x10 N
b. 10 N
c. 9 x 10^9 N
d. 5 x 10 N

83. Another name for dielectric strength is
a. Potetial gradient
b. Breakdown voltage
c. Dielectric constant
d. Electric intensity
84. A heater connected to a 100 V supply, generates 10,000 J of heat
energy is 10 sec. How much time is needed to generate the same
amount of heat when it is used on 220V line?
a. 5 sec
b. 2.5 sec
c. 7.5 sec
d. 4 sec.
83. Another name for dielectric strength is
a. Potetial gradient
b. Breakdown voltage
c. Dielectric constant
d. Electric intensity
84. A heater connected to a 100 V supply, generates 10,000 J of heat
energy is 10 sec. How much time is needed to generate the same
amount of heat when it is used on 220V line?
a. 5 sec
b. 2.5 sec
c. 7.5 sec
d. 4 sec.

85. Kirchoff’s current law is applied in what type of circuit analysis?
a. Mesh
b. Thevenin’s
c. Superposition
d. Nodal
86. Inductance and capacitance are not relevant in a dc circuit because
a. Frequency of DC is zero
b. It is a simple circuit
c. They do not exist in dc circuit
85. Kirchoff’s current law is applied in what type of circuit analysis?
a. Mesh
b. Thevenin’s
c. Superposition
d. Nodal
86. Inductance and capacitance are not relevant in a dc circuit because
a. Frequency of DC is zero
b. It is a simple circuit
c. They do not exist in dc circuit

87. Three resistors of 3 ohms resistance each are connected in
delta, the equivalent wye-connected resistors will be
a. 1 ohm
b. 3 ohms
c. 9 ohms
d. 0.111 ohm
88. Cells are conneted in series when _____ is required
a. High current
b. High voltage
c. High power
d. All of these
87. Three resistors of 3 ohms resistance each are connected in
delta, the equivalent wye-connected resistors will be
a. 1 ohm
b. 3 ohms
c. 9 ohms
d. 0.111 ohm
88. Cells are conneted in series when _____ is required
a. High current
b. High voltage
c. High power
d. All of these

ALTERNATING CURRENTALTERNATING CURRENT
ALTERNATING CURRENT
 A current that is constantly changing in amplitude and
direction.
ALTERNATING CURRENT
 A current that is constantly changing in amplitude and
direction.
Advantages of AC:
 Magnitude can easily be changed (stepped-up or stepped down) with the use of a
transformer
 Can be produced either single phase for light loads, two phase for control motors,
three phase for power distribution and large motor loads or six phase for large
scale AC to DC conversion.
Advantages of AC:
 Magnitude can easily be changed (stepped-up or stepped down) with the use of a
transformer
 Can be produced either single phase for light loads, two phase for control motors,
three phase for power distribution and large motor loads or six phase for large
scale AC to DC conversion.
BASIC AC THEORY

AC WAVEFORMSAC WAVEFORMS
BASIC AC THEORY

 Period (T) – the time of one complete cycle in seconds
 Frequency (f) – the number of cycles per second (Hertz)
a. 1 cycle/second (cps) = 1 Hertz (Hz)
b. Proper operation of electrical equipmnent requires specific frequency
c. Frequencies lower than 60 Hz would cause flicker when used in lightning
 Wavelength (λ) – the length of one complete cycle
 Propagation Velocity (v) – the speed of the signal
 Phase (Φ) – an angilar measurement that specifies the position of a sine wave
relative to reference
 Period (T) – the time of one complete cycle in seconds
 Frequency (f) – the number of cycles per second (Hertz)
a. 1 cycle/second (cps) = 1 Hertz (Hz)
b. Proper operation of electrical equipmnent requires specific frequency
c. Frequencies lower than 60 Hz would cause flicker when used in lightning
 Wavelength (λ) – the length of one complete cycle
 Propagation Velocity (v) – the speed of the signal
 Phase (Φ) – an angilar measurement that specifies the position of a sine wave
relative to reference
f = 1
T
λ = v
f
Parameters of Alternating Signal
BASIC AC THEORY

THE SINUSOIDAL WAVE
 Is the most common AC waveform that is practically
generated by generators used in household and industries
 General equation for sine wave:
THE SINUSOIDAL WAVE
 Is the most common AC waveform that is practically
generated by generators used in household and industries
 General equation for sine wave:
Where:
a(t) – instantaneous amplitude of voltage or current at a given time (t)
Am – maximum voltage or current amplitude of the signal
ω – angular velocity in rad/sec; ω = 2πf
t – time (sec)
Φ – phase shift ( + or – in degrees)
Where:
a(t) – instantaneous amplitude of voltage or current at a given time (t)
Am – maximum voltage or current amplitude of the signal
ω – angular velocity in rad/sec; ω = 2πf
t – time (sec)
Φ – phase shift ( + or – in degrees)
A(t) = Am sin (ωt + Φ)
BASIC AC THEORY

 PEAK AMPLITUDE – the height of an AC waveform as measured from the
zero mark to the highest positive or lowest negative point on a graph. Also
known as the crest amplitude of a wave.
 PEAK AMPLITUDE – the height of an AC waveform as measured from the
zero mark to the highest positive or lowest negative point on a graph. Also
known as the crest amplitude of a wave.
AMPLITUDE
 It is the height of an AC waveform as depicted on a graph over time
(peak, peak-to-peak, average, or RMS quantity)
AMPLITUDE
 It is the height of an AC waveform as depicted on a graph over time
(peak, peak-to-peak, average, or RMS quantity)
Measurements of AC Magnitude
BASIC AC THEORY

 PEAK-TO-PEAK AMPLITUDE – the total height of an AC waveform as
measured from maximum positive to maximum negative peaks on a
graph. Often abbreviated as “P-P”
 PEAK-TO-PEAK AMPLITUDE – the total height of an AC waveform as
measured from maximum positive to maximum negative peaks on a
graph. Often abbreviated as “P-P”
BASIC AC THEORY

 AVERAGE AMPLITUDE – the mathematical “mean” of all a waveform’s points
over the period of one cycle. Technically, the average amplitude of any
waveform with equal-area portions above and below the “zero” line on a
graph is zero.
 For a sine wave, the average value so calculated is approximately 0.637 of its
peak value.
 AVERAGE AMPLITUDE – the mathematical “mean” of all a waveform’s points
over the period of one cycle. Technically, the average amplitude of any
waveform with equal-area portions above and below the “zero” line on a
graph is zero.
 For a sine wave, the average value so calculated is approximately 0.637 of its
peak value.
BASIC AC THEORY

 RMS AMPLITUDE - “RMS” stands for Root Mean Square, and is a way of
expressing an AC quantity of voltage or current in terms functionally
equivalent to DC. Also known as the “equivalent” or “DC equivalent”
value of an AC voltage or current.
 For a sine wave, the RMS value is approximately 0.707 of its peak value.
 RMS AMPLITUDE - “RMS” stands for Root Mean Square, and is a way of
expressing an AC quantity of voltage or current in terms functionally
equivalent to DC. Also known as the “equivalent” or “DC equivalent”
value of an AC voltage or current.
 For a sine wave, the RMS value is approximately 0.707 of its peak value.
BASIC AC THEORY

 The crest factor of an AC
waveform is the ratio of
its peak (crest) to its RMS
value.
 The form factor of an AC
its RMS value to its
average value.
 The crest factor of an AC
its peak (crest) to its RMS
value.
 The form factor of an AC
its RMS value to its
average value.
BASIC AC THEORY

AC QUANTITIESAC QUANTITIES
BASIC AC THEORY

Inductive Reactance (XL)
• The property of the inductor to oppose the alternating current
Inductive Susceptance (BL)
• Reciprocal of inductive reactance
Capacitive Reactance (XC)
• The property of a capacitor to oppose alternating current
Capacitive Susceptance (BC)
• Reciprocal of capacitive reactance
d
Inductive Reactance (XL)
• The property of the inductor to oppose the alternating current
Inductive Susceptance (BL)
• Reciprocal of inductive reactance
Capacitive Reactance (XC)
• The property of a capacitor to oppose alternating current
Capacitive Susceptance (BC)
• Reciprocal of capacitive reactance
d
XL = 2πfLXL = 2πfL
BL = 1 BL = 1
XL 2πfL
BL = 1 BL = 1
XL 2πfL
XC = 1
2πfC
XC = 1
2πfC
BL = 1 BL = 2πfC
XC
BL = 1 BL = 2πfC
XC
BASIC AC THEORY

IMPEDANCE (Z)
 Total opposition to the flow of Alternating current
 Combination of the resistance in a circuit and the reactances
involved
IMPEDANCE (Z)
 Total opposition to the flow of Alternating current
 Combination of the resistance in a circuit and the reactances
involved
Z = R + jXeq Z = |Z| ∠φ
Where: |Z| = √ R2
+ X2
φ = Arctan Xeq
R
Where: |Z| = √ R2
+ X2
φ = Arctan Xeq
R
BASIC AC THEORY

 If I = Im ∠β is the resulting current drawn by a passive, linear RLC circuit from a
source voltage V = Vm ∠θ, then
Where: Z = Vm = √ R2
+ X2
= magnitude of the impedance
Im
φ = θ – β = tan-1
X = phase angle of the impedance
R
R = Zcos φ = active or real component of the impedance
X = Zsin φ = reactive or quadrature component of impedance
 If I = Im ∠β is the resulting current drawn by a passive, linear RLC circuit from a
source voltage V = Vm ∠θ, then
Where: Z = Vm = √ R2
+ X2
= magnitude of the impedance
Im
φ = θ – β = tan-1
X = phase angle of the impedance
R
R = Zcos φ = active or real component of the impedance
X = Zsin φ = reactive or quadrature component of impedance
Z = V = Vm ∠θ = Z ∠φ
I Im ∠β
Z = V = Vm ∠θ = Z ∠φ
I Im ∠β
Z cosφ + jZsin φ = R + jX = √ R2
+ X2
∠ tan-1
X
R
Z cosφ + jZsin φ = R + jX = √ R2
+ X2
∠ tan-1
X
R
BASIC AC THEORY

ADMITTANCE (Y)
 The reciprocal of impedance
 Expressed in siemens or mho (S)
ADMITTANCE (Y)
 The reciprocal of impedance
 Expressed in siemens or mho (S)
Where: Y = Im = √ G2
+ B2
= 1 = magnitude of the admittance
Z
φy = β – θ = φ = tan-1
B = phase angle of the admittance
G
G = Ycos φy = conductive/conductance component
B = Ysin φy = susceptive/susceptance component
Where: Y = Im = √ G2
+ B2
= 1 = magnitude of the admittance
Z
φy = β – θ = φ = tan-1
B = phase angle of the admittance
G
G = Ycos φy = conductive/conductance component
B = Ysin φy = susceptive/susceptance component
Y = Im ∠ β – θ = Y = Ycos φy + jYsin φy = G + jB
Vm
Y = Im ∠ β – θ = Y = Ycos φy + jYsin φy = G + jB
Vm
Y = √ G2
+ B2
∠ tan-1
B
G
Y = √ G2
+ B2
∠ tan-1
B
G
BASIC AC THEORY

AC RESISTOR CIRCUITAC RESISTOR CIRCUIT
With an AC circuit like this which is purely resistive, the relationship of the voltage
and current is as shown:
 Voltage (e) is in phase with the current (i)
 Power is never a negative value. When the current is positive (above the line),
the voltage is also positive, resulting in a power (p=ie) of a positve value
 This consistent “polarity” of a power tell us that the resistor is always
dissipating power, taking it from the source and releasing it in the form of
heat energy. Whether the current is negative or positive, a resistor still
dissipated energy.
With an AC circuit like this which is purely resistive, the relationship of the voltage
and current is as shown:
 Voltage (e) is in phase with the current (i)
 Power is never a negative value. When the current is positive (above the line),
the voltage is also positive, resulting in a power (p=ie) of a positve value
 This consistent “polarity” of a power tell us that the resistor is always
dissipating power, taking it from the source and releasing it in the form of
heat energy. Whether the current is negative or positive, a resistor still
dissipated energy.
AC CIRCUITS
Impedance (Z) = RImpedance (Z) = R

AC INDUCTOR CIRCUITAC INDUCTOR CIRCUIT
 The most distinguishing electrical characteristics of an L circuit is that current lags
voltage by 90 electrical degrees
 Because the current and voltage waves arae 90o
out of phase, there sre times when
one is positive while the other is negative, resulting in equally frequent occurences of
negative instantaneous power.
 Negative power means that the inductor is releasing power back to the circuit, while a
positive power means that it is absorbing power from the circuit.
 The inductor releases just as much power back to the circuit as it absorbs over the
span of a complete cycle.
 The most distinguishing electrical characteristics of an L circuit is that current lags
voltage by 90 electrical degrees
 Because the current and voltage waves arae 90o
out of phase, there sre times when
one is positive while the other is negative, resulting in equally frequent occurences of
negative instantaneous power.
 Negative power means that the inductor is releasing power back to the circuit, while a
positive power means that it is absorbing power from the circuit.
 The inductor releases just as much power back to the circuit as it absorbs over the
span of a complete cycle.
Impedance (Z) = jXL
Impedance (Z) = jXL
AC CIRCUITS

AC INDUCTOR CIRCUITAC INDUCTOR CIRCUIT
o Inductive reactance is the opposition that an inductor offers to alternating
current due to its phase-shifted storage and release of energy in its
magnetic field. Reactance is symbolized by the capital letter “X” and is
measured in ohms just like resistance (R).
o Inductive reactance can be calculated using this formula: XL = 2πfL
o The angular velocity of an AC circuit is another way of expressing its
frequency, in units of electrical radians per second instead of cycles per
second. It is symbolized by the lowercase Greek letter “omega,” or ω.
o Inductive reactance increases with increasing frequency. In other words,
the higher the frequency, the more it opposes the AC flow of electrons.
o Inductive reactance is the opposition that an inductor offers to alternating
current due to its phase-shifted storage and release of energy in its
magnetic field. Reactance is symbolized by the capital letter “X” and is
o Inductive reactance can be calculated using this formula: XL = 2πfL
o The angular velocity of an AC circuit is another way of expressing its
frequency, in units of electrical radians per second instead of cycles per
second. It is symbolized by the lowercase Greek letter “omega,” or ω.
o Inductive reactance increases with increasing frequency. In other words,
the higher the frequency, the more it opposes the AC flow of electrons.
AC CIRCUITS

AC CAPACITOR CIRCUITAC CAPACITOR CIRCUIT
 The most distinguishing electrical characteristics of an C circuit is that leads the voltage
by 90 electrical degrees
 The current through a capacitor is a reaction against the change in voltage across it
 A capacitor’s opposition to change in voltage translates to an opposition to alternating
voltage in general, which is by definition always changing in instantaneous magnitude
and direction. For any given magnitude of AC voltage at a given frequency, a capacitor
of given size will “conduct” a certain magnitude of AC current.
 The phase angle of a capacitor’s opposition to current is -90o
,meaning that a
capacitor’s opposition to current is a negative imaginary quantity
 The most distinguishing electrical characteristics of an C circuit is that leads the voltage
by 90 electrical degrees
 The current through a capacitor is a reaction against the change in voltage across it
 A capacitor’s opposition to change in voltage translates to an opposition to alternating
voltage in general, which is by definition always changing in instantaneous magnitude
and direction. For any given magnitude of AC voltage at a given frequency, a capacitor
of given size will “conduct” a certain magnitude of AC current.
 The phase angle of a capacitor’s opposition to current is -90o
,meaning that a
capacitor’s opposition to current is a negative imaginary quantity
Impedance (Z) = -jXC
Impedance (Z) = -jXC
AC CIRCUITS

AC CAPACITOR CIRCUITAC CAPACITOR CIRCUIT
o Capacitive reactance is the opposition that a capacitor offers to
alternating current due to its phase-shifted storage and release of energy
in its electric field. Reactance is symbolized by the capital letter “X” and is
o Capacitive reactance can be calculated using this formula: XC = 1/(2πfC)
o Capacitive reactance decreases with increasing frequency. In other words,
the higher the frequency, the less it opposes (the more it “conducts”) the
AC flow of electrons.
o Capacitive reactance is the opposition that a capacitor offers to
alternating current due to its phase-shifted storage and release of energy
in its electric field. Reactance is symbolized by the capital letter “X” and is
o Capacitive reactance can be calculated using this formula: XC = 1/(2πfC)
o Capacitive reactance decreases with increasing frequency. In other words,
the higher the frequency, the less it opposes (the more it “conducts”) the
AC flow of electrons.
AC CIRCUITS

SERIES RESITOR-INDCUTOR CIRCUITSERIES RESITOR-INDCUTOR CIRCUIT
 For a series resistor-inductor circuit, the voltage and current relation is
determined in its phase shift. Thus, current lags voltage by a phase shift
(θ)
 For a series resistor-inductor circuit, the voltage and current relation is
determined in its phase shift. Thus, current lags voltage by a phase shift
(θ)
Impedance (Z) = R + jXL
Impedance (Z) = R + jXL
Admittance (Y) = 1 = R – jXL
R + jXL R2
+ jXL
2
Admittance (Y) = 1 = R – jXL
R + jXL R2
+ jXL
2
AC CIRCUITS

SERIES RESITOR-INDCUTOR CIRCUITSERIES RESITOR-INDCUTOR CIRCUIT
o When resistors and inductors are mixed together in circuits, the total
impedance will have a phase angle somewhere between 0o
and +90o
. The
circuit current will have a phase angle somewhere between 0o
and -90o
.
Series AC circuits exhibit the same fundamental properties as series DC
circuits: current is uniform throughout.
o When resistors and inductors are mixed together in circuits, the total
and +90o
. The
circuit current will have a phase angle somewhere between 0o
and -90o
.
Series AC circuits exhibit the same fundamental properties as series DC
circuits: current is uniform throughout.
Phase shift (θ) = Arctan ( XL ) |Z| = √ R2
+ jXL
2
= e
R i
Phase shift (θ) = Arctan ( XL ) |Z| = √ R2
+ jXL
2
= e
R i
AC CIRCUITS

SERIES RESISTOR-CAPACITOR CIRCUITSERIES RESISTOR-CAPACITOR CIRCUIT
 For a series resistor – capacitor circuit, the voltage and current relation is
determined by the phase shift. Thus the current leads the voltage by an
angle less than 90 degrees but greater than 0 degrees.
 For a series resistor – capacitor circuit, the voltage and current relation is
determined by the phase shift. Thus the current leads the voltage by an
angle less than 90 degrees but greater than 0 degrees.
Impedance (Z) = R – jXC
Impedance (Z) = R – jXC
Admittance (Y) = 1 = R + jXC
R – jXC R2
+ jXC
2
Admittance (Y) = 1 = R + jXC
R – jXC R2
+ jXC
2
AC CIRCUITS

SERIES RESISTOR-CAPACITOR CIRCUITSERIES RESISTOR-CAPACITOR CIRCUIT
Phase shift (θ) = Arctan ( XC ) |Z| = √ R2
+ jXC
2
= e
R i
Phase shift (θ) = Arctan ( XC ) |Z| = √ R2
+ jXC
2
= e
R i
AC CIRCUITS

PARALLEL RESISTOR-INDUCTORPARALLEL RESISTOR-INDUCTOR
Y = G – jβL where: G – conductance = 1/R
βL – susceptance = 1/XL
Z = E , by Ohm’s Law
I
 The basic approachwith regarda to parallel circuits is using admittance
because it is additive
Y = G – jβL where: G – conductance = 1/R
βL – susceptance = 1/XL
Z = E , by Ohm’s Law
I
 The basic approachwith regarda to parallel circuits is using admittance
because it is additive AC CIRCUITS

PARALLEL RESISTOR-INDUCTORPARALLEL RESISTOR-INDUCTOR
o When resistors and inductors are mixed together in parallel circuits (just
like in series cicuits), the total impedance will have a phase angle
somewhere between 0o
and +90o
. The circuit current will have a phase
angle somewhere between 0o
and -90o
.
o Parallel AC circuits exhibit the same fundamental properties as parallel DC
circuits: voltage is uniform throughour the circuit, brach currents add to
form the total current, and impedances diminish (through the reciprocal
formula) to form the total impedance.
o When resistors and inductors are mixed together in parallel circuits (just
like in series cicuits), the total impedance will have a phase angle
somewhere between 0o
and +90o
. The circuit current will have a phase
angle somewhere between 0o
and -90o
.
o Parallel AC circuits exhibit the same fundamental properties as parallel DC
circuits: voltage is uniform throughour the circuit, brach currents add to
form the total current, and impedances diminish (through the reciprocal
formula) to form the total impedance.
AC CIRCUITS

PARALLEL RESISTOR-CAPACITORPARALLEL RESISTOR-CAPACITOR
Y = G + jβC where: G – conductance = 1/R
βC – susceptance = 1/XC
o When resistors and capacitors are mixxed together in circuits, the total
and -90o
.
Y = G + jβC where: G – conductance = 1/R
βC – susceptance = 1/XC
o When resistors and capacitors are mixxed together in circuits, the total
and -90o
.
AC CIRCUITS

APPARENT POWER (S)APPARENT POWER (S)
APPARENT POWER
 Represents the rate at which the total energy is supplied to the
system
 Measured in volt-amperes (VA)
 It has two components, the Real Power and the Capacitive or
Inductive Reactive Power
APPARENT POWER
 Represents the rate at which the total energy is supplied to the
system
 Measured in volt-amperes (VA)
 It has two components, the Real Power and the Capacitive or
Inductive Reactive Power
POWER IN AC CIRCUITS
S = Vrms Irms = Irms
2
|Z|

APPARENT POWER (S)APPARENT POWER (S)
Power Triangle
Complex Power
S = P ± jQ

REAL POWER (R)REAL POWER (R)
REAL POWER
 The power consumed by the resistive component
 Also called True Power, Useful Power and Productive Power
 Measured in Watts (W)
 It is equal to the product of the apparent power and the power factor
REAL POWER
 The power consumed by the resistive component
 Also called True Power, Useful Power and Productive Power
 Measured in Watts (W)
 It is equal to the product of the apparent power and the power factor
 Cosine of the power factor angle (θ)
 Measure of the power that is dissipated by the cicuit in relation to the
apparent power and is usually given as a decimal or percentage
 Cosine of the power factor angle (θ)
 Measure of the power that is dissipated by the cicuit in relation to the
apparent power and is usually given as a decimal or percentage
Pf = cos θ
P = Scos θ
Power Factor

 Ratio of the Real Power to the Apparent Power ( P )
S
when:
Pf = 1.0 I is in phase with V; resistive system
Pf = lagging I lags V by θ; inductive system
Pf = leading I leads V by θ; capacitive system
Pf = 0.0 lag I lags V by 90o; purely inductive
Pf = 0.0 lead I leads V by 90o; purely capacitive
 The angle between the apparent power and the real poweer in the power triangle
Let v(t) = Vm cos(ωt + θv) volts
V = Vrms ∠θv
i(t) = Im cos(ωt + θi) A
I = Irms ∠θi
 Ratio of the Real Power to the Apparent Power ( P )
S
when:
Pf = 1.0 I is in phase with V; resistive system
Pf = lagging I lags V by θ; inductive system
Pf = leading I leads V by θ; capacitive system
Pf = 0.0 lag I lags V by 90o; purely inductive
Pf = 0.0 lead I leads V by 90o; purely capacitive
 The angle between the apparent power and the real poweer in the power triangle
Let v(t) = Vm cos(ωt + θv) volts
V = Vrms ∠θv
i(t) = Im cos(ωt + θi) A
I = Irms ∠θi
Power factor Angle (θ)

Where: θ = phase shfit between v(t) and i(t) or the phase angle of the
equivalent impedance
Where: θ = phase shfit between v(t) and i(t) or the phase angle of the
equivalent impedance
Instantaneous Power (watts)
Average Power (watts)
P(t) = v(t) i(t)P(t) = v(t) i(t)
P(t) = ½ VmIm cos (θv – θi) + ½ VmIm cos (2ωt + θv + θi)P(t) = ½ VmIm cos (θv – θi) + ½ VmIm cos (2ωt + θv + θi)
P(t) = ½ VmIm cos (θv – θi) = VmIm cos θP(t) = ½ VmIm cos (θv – θi) = VmIm cos θ

REACTIVE POWER (QL or QC)REACTIVE POWER (QL or QC)
REACTIVE POWER
 Represents the rate at which energy is stored or released in any of the
energy storing elements (the inductor or the capacitor)
 Also called the imaginary power, non-productive or wattless power
 Measured in volt-ampere reactive (Var)
 When the capacitor and inductor are both present, the reactive power
associated with them take opposite signs since they do not store or
release energy at the same time
 It is positive for inductive power (QL) and negative for capacitive
power (QC)
REACTIVE POWER
 Represents the rate at which energy is stored or released in any of the
energy storing elements (the inductor or the capacitor)
 Also called the imaginary power, non-productive or wattless power
 Measured in volt-ampere reactive (Var)
 When the capacitor and inductor are both present, the reactive power
associated with them take opposite signs since they do not store or
release energy at the same time
 It is positive for inductive power (QL) and negative for capacitive
power (QC)
 Ratio of the Reactive Power to the Apparent Power
 Sine of the power factor angle (θ)
 Ratio of the Reactive Power to the Apparent Power
 Sine of the power factor angle (θ)
Q = VmIm sin θQ = VmIm sin θ
Reactive factor
Rf = sin θRf = sin θ

BALANCED THREE PHASE SYSTEMSBALANCED THREE PHASE SYSTEMS
BALANCED 3-PHASE SYSTEM
 Comprises of three identical single-phase systems operating at a 120o
phase displacement from one another. This means that a balance
three-phase system provides three voltages(and currents) that are
equal in magnitude and separated by 120o
from each other
BALANCED 3-PHASE SYSTEM
 Comprises of three identical single-phase systems operating at a 120o
phase displacement from one another. This means that a balance
three-phase system provides three voltages(and currents) that are
equal in magnitude and separated by 120o
from each other
Three-Phase, 3-wire systems
 Provide only one type of voltage(line to line) both single phase and
three phase loads
 Provide two types of voltages(line to line and line to neutral) to both
single phase and three phase loads
 Provide only one type of voltage(line to line) both single phase and
three phase loads
 Provide two types of voltages(line to line and line to neutral) to both
single phase and three phase loads
BALANCED THREE PHASE SYSTEM
CLASSIFICATION

BALANCED THREE PHASE SYSTEMSBALANCED THREE PHASE SYSTEMS
and
VLL and VLN are out of phase by 30o
and
VLL and VLN are out of phase by 30o
BALANCED Y-system
VLL = √3 VLN
VLL = √3 VLN IL = IP
IL = IP
and
IL and IP are out of phase by 30o
Where: VLL or VL - line to line or line voltage
VLN or VP - line to neutral or phase voltage
IL - line current
IP - phase current
and
IL and IP are out of phase by 30o
Where: VLL or VL - line to line or line voltage
VLN or VP - line to neutral or phase voltage
IL - line current
IP - phase current
BALANCED ∆-system
IL = √3 IP
IL = √3 IP VLL = VLN
VLL = VLN

ALTERNATING CURRENTALTERNATING CURRENT
VJH
watts
vars
va
VJH
watts
vars
va
Note: for balanced 3-phase systems:Note: for balanced 3-phase systems:
IA + IB + IC = 0IA + IB + IC = 0
VAN + VBN + VCN = 0VAN + VBN + VCN = 0
VAB + VBC + VCA = 0VAB + VBC + VCA = 0
P = 3VPIPcos θ = √3 VLIL cos θP = 3VPIPcos θ = √3 VLIL cos θ
Q = 3VPIPsin θ = √3 VLIL sin θQ = 3VPIPsin θ = √3 VLIL sin θ
S = 3VPIP = √3 VLIL
S = 3VPIP = √3 VLIL
THREE-PHASE POWER

1. The description of two sine waves that are in step with each other
going through their maximum and minimum points ate the same
time and in the same direction.
a. Sine waves in phase
b. Stepped sine waves
c. Phased sine waves
d. Sine waves in coordination
2. Term used for the out of phase, non-productive power associated
with inductors and capacitors.
a. Effective power
b. True power
c. Reactive power
d. Peak envelope power
1. The description of two sine waves that are in step with each other
going through their maximum and minimum points ate the same
time and in the same direction.
a. Sine waves in phase
b. Stepped sine waves
c. Phased sine waves
d. Sine waves in coordination
2. Term used for the out of phase, non-productive power associated
with inductors and capacitors.
a. Effective power
b. True power
c. Reactive power
d. Peak envelope power

3. Refers to a reactive power.
a. Wattles, non productive power
b. Power consumed in circuit Q
c. Power loss because of capacitor leakage
d. Power consumed in wire resistance in an inductor
4. Term used for an out-of-phase, non-productive power
associated with inductors and capacitors.
a. Effective power
b. Reactive power
c. Peak envelope power
d. True power
3. Refers to a reactive power.
a. Wattles, non productive power
b. Power consumed in circuit Q
c. Power loss because of capacitor leakage
d. Power consumed in wire resistance in an inductor
4. Term used for an out-of-phase, non-productive power
associated with inductors and capacitors.
a. Effective power
b. Reactive power
c. Peak envelope power
d. True power

5. The product of current and voltage in an AC circuit refers to the
a. Real power
b. Useful power
c. Apparent power
d. DC power
6. The distance covered or traveled by a waveform during the time
interval of one complete cycle.
a. Frequency
b. Wavelength
c. Time slot
d. Wave time
5. The product of current and voltage in an AC circuit refers to the
a. Real power
b. Useful power
c. Apparent power
d. DC power
6. The distance covered or traveled by a waveform during the time
interval of one complete cycle.
a. Frequency
b. Wavelength
c. Time slot
d. Wave time

7. The power dissipated accross the resistance in an AC
circuit.
a. Real power
b. Reactive power
c. Apparent power
d. True power
8. It is the number of complete cycles of alternating voltage or
current complete each second
a. Period
b. Frequency
c. Amplitude
d. Phase
7. The power dissipated accross the resistance in an AC
circuit.
a. Real power
b. Reactive power
c. Apparent power
d. True power
8. It is the number of complete cycles of alternating voltage or
current complete each second
a. Period
b. Frequency
c. Amplitude
d. Phase

9. How many degrees are there in one complete cycle?
a. 720 deg
b. 360 deg
c. 180 deg
d. 90 deg
10. The impedance in the study of electronics is represented
by resistance and ___ .
a. Reactance
b. Inductance and capacitance
c. Inductance
d. capacitance
9. How many degrees are there in one complete cycle?
a. 720 deg
b. 360 deg
c. 180 deg
d. 90 deg
10. The impedance in the study of electronics is represented
by resistance and ___ .
a. Reactance
b. Inductance and capacitance
c. Inductance
d. capacitance

11. It is the current that is eliminated by a synchro capacitor?
a. Magnetizing stator
b. Loss
c. Stator
d. Rotor
12. It is a rotaing sector that represent either current or
voltage in an AC circuit.
a. Resistance
b. Phasor
c. Solar diagram
d. velocity
11. It is the current that is eliminated by a synchro capacitor?
a. Magnetizing stator
b. Loss
c. Stator
d. Rotor
12. It is a rotaing sector that represent either current or
voltage in an AC circuit.
a. Resistance
b. Phasor
c. Solar diagram
d. velocity

13. The relationship of the voltage accros an inductor to its current is
described as
a. Leading the current by 90 deg
b. Lagging the current by 90 deg
c. Leading the current by 180 deg
d. In phase with the current
14. Find the phase angle between the voltage across through the cicuit
when Xc is 25ohms, R is 100 ohms and XL is 50 ohms.
a. 76 deg with the voltage leading the current
b. 24 deg with the voltage lagging the current
c. 14 deg with the voltage lagging the current
d. 76 deg with the voltage lagging the current
13. The relationship of the voltage accros an inductor to its current is
described as
14. Find the phase angle between the voltage across through the cicuit
when Xc is 25ohms, R is 100 ohms and XL is 50 ohms.
a. 76 deg with the voltage leading the current
b. 24 deg with the voltage lagging the current
c. 14 deg with the voltage lagging the current
d. 76 deg with the voltage lagging the current

15. Calculate the period of an alternating current having a equation of
I=20sin 120πt
a. 4.167 ms
b. 8.33 ms
c. 16.67 ms
d. 33.33 ms
16. What do you mean by root-mean-square (rms) value?
a. It is the average value
b. It is the effective value
c. It is the value that causes the same heating effect as the DC
voltage
d. b or c
15. Calculate the period of an alternating current having a equation of
I=20sin 120πt
a. 4.167 ms
b. 8.33 ms
c. 16.67 ms
d. 33.33 ms
16. What do you mean by root-mean-square (rms) value?
a. It is the average value
b. It is the effective value
c. It is the value that causes the same heating effect as the DC
voltage
d. b or c

17. The maximum instances value of a vrying current, voltage or power
equal to 1.414 times the effective value of a sine wave.
a. RMS value
b. Peak value
c. Effective value
d. Peak to Peak value
18. If an AC signal has a peak voltage of 55V, what is the average
value?
a. 34.98 V
b. 61.05V
c. 86.34 V
d. 38.89 V
17. The maximum instances value of a vrying current, voltage or power
equal to 1.414 times the effective value of a sine wave.
a. RMS value
b. Peak value
c. Effective value
d. Peak to Peak value
18. If an AC signal has a peak voltage of 55V, what is the average
value?
a. 34.98 V
b. 61.05V
c. 86.34 V
d. 38.89 V

19. If an AC signal has an average voltage of 18V, what is the rms
voltage?
a. 12.726 V
b. 19.980 V
c. 25.380 V
d. 16.213 V
20. A 220-V, 60Hz is driving a series RL circuit. Determine the current if
R=100 ohms and 20 mH inductance
a. 2.2 A (lagging)
b. 2.0 A (lagging)
c. 2.2 A (leading)
d. 2.0 A (leading)
19. If an AC signal has an average voltage of 18V, what is the rms
voltage?
a. 12.726 V
b. 19.980 V
c. 25.380 V
d. 16.213 V
20. A 220-V, 60Hz is driving a series RL circuit. Determine the current if
R=100 ohms and 20 mH inductance
a. 2.2 A (lagging)
b. 2.0 A (lagging)
c. 2.2 A (leading)
d. 2.0 A (leading)

21. Ignoring any inductive effects, what is the impedance of RC series
capacitor made up of a 56K ohm resistor and a 0.33uF capacitor at
a signal frequency of 4650 Hz.
a. 66730 ohms
b. 57019 ohms
c. 45270 ohms
d. 10730 ohms
22.What is the time constant of a 500mH coil and a 3300 ohm resistor
in series?
a. 0.00015 sec
b. 6.6 sec
c. 0.0015 sec
d. 0.0000015 sec
21. Ignoring any inductive effects, what is the impedance of RC series
capacitor made up of a 56K ohm resistor and a 0.33uF capacitor at
a signal frequency of 4650 Hz.
a. 66730 ohms
b. 57019 ohms
c. 45270 ohms
d. 10730 ohms
22.What is the time constant of a 500mH coil and a 3300 ohm resistor
in series?
a. 0.00015 sec
b. 6.6 sec
c. 0.0015 sec
d. 0.0000015 sec

23. What is the realtionship between frequency and the value of XC ?
a. Frequency has no effect
b. XC varies inversely with frequency
c. XC varies indirectly with frequency
d. XC varies directly with frequency
24. The reactance of a 25mH coil at 5000Hz which of the following?
a. 785 ohms
b. 785000 ohms
c. 13 ohms
d. 0.0012 ohms
23. What is the realtionship between frequency and the value of XC ?
a. Frequency has no effect
b. XC varies inversely with frequency
c. XC varies indirectly with frequency
d. XC varies directly with frequency
24. The reactance of a 25mH coil at 5000Hz which of the following?
a. 785 ohms
b. 785000 ohms
c. 13 ohms
d. 0.0012 ohms

25. There are no transients in pure resistive circuites becaus
they
a. Offer high resistance
b. Obey ohm’s Law
c. Are linear circuits
d. Have no stored energy
26. The reciprocal of capacitance is called
a. Elastance
b. Conductance
c. Permitivity
d. permeability
25. There are no transients in pure resistive circuites becaus
they
a. Offer high resistance
b. Obey ohm’s Law
c. Are linear circuits
d. Have no stored energy
26. The reciprocal of capacitance is called
a. Elastance
b. Conductance
c. Permitivity
d. permeability

27. The AC system is prefered over DC system because
a. Ac voltages can easily changed in amgnitude
b. Dc motors do not have fine speed control
c. High voltage AC transmission is less efficient
d. DC voltage cannot be used for domestic aplliences
28. An altenating voltage is given by v = 20 sin 157 t. The
frequency of the alternating voltage is
a. 50 Hz
b. 25 HZ
c. 100 Hz
d. 75 Hz
27. The AC system is prefered over DC system because
a. Ac voltages can easily changed in amgnitude
b. Dc motors do not have fine speed control
c. High voltage AC transmission is less efficient
d. DC voltage cannot be used for domestic aplliences
28. An altenating voltage is given by v = 20 sin 157 t. The
frequency of the alternating voltage is
a. 50 Hz
b. 25 HZ
c. 100 Hz
d. 75 Hz

29. An alternating current given by i = 10 sin 314 t. The time taken to
generate two cycles of current is
a. 20 ms
b. 10 ms
c. 40 ms
d. 50 ms
30. In a pure resistive circuit, the instantaneous voltage and are current are
given by:
v=250 sin 314t i=10sin314t
The peak power in the circuit is
a.1250 W
b. 25 W
c. 2500 W
d. 250 w
29. An alternating current given by i = 10 sin 314 t. The time taken to
generate two cycles of current is
a. 20 ms
b. 10 ms
c. 40 ms
d. 50 ms
30. In a pure resistive circuit, the instantaneous voltage and are current are
given by:
v=250 sin 314t i=10sin314t
The peak power in the circuit is
a.1250 W
b. 25 W
c. 2500 W
d. 250 w

31. An average value of 6.63 A is _____ the effective value of 7.07 A.
a. The same area
b. Less than
c. Greater than
d. Any of these
32. In an R-L series circuit, the resistance is 10 ohms and the inductive
reactance is 10 ohms. The phase angle between the applied voltage
and circuit current will be
a. 45 deg
b. 30 deg
c. 60 deg
d. 36.8 deg
31. An average value of 6.63 A is _____ the effective value of 7.07 A.
a. The same area
b. Less than
c. Greater than
d. Any of these
32. In an R-L series circuit, the resistance is 10 ohms and the inductive
reactance is 10 ohms. The phase angle between the applied voltage
and circuit current will be
a. 45 deg
b. 30 deg
c. 60 deg
d. 36.8 deg

33.An R-L series ac circuit has 15V across the resistor and 20V across
the inductor. The supply volatge is
a. 35 V
b. 5 V
c. 25 V
d. 175 V
34. The active and reactive powers of an inductive circuit are equal.
The power factor of the circuit is
a. 0.8 lagging
b. 0.707 lagging
c. 0.6 lagging
d. 0.5 lagging
33.An R-L series ac circuit has 15V across the resistor and 20V across
the inductor. The supply volatge is
a. 35 V
b. 5 V
c. 25 V
d. 175 V
34. The active and reactive powers of an inductive circuit are equal.
The power factor of the circuit is
a. 0.8 lagging
b. 0.707 lagging
c. 0.6 lagging
d. 0.5 lagging

35. A circuit when connected to 200V mains takes a current of 20 A, leading
the voltage by one-twelfth of time period. The circuit resistance is
a. 10 ohms
b. 8.66 ohms
c. 20 ohms
d. 17.32 ohms
36. An AC circuit has a resistance of 6 ohms, inductive reactance of 20 ohms,
and capacitive reactance of 12 ohms. The circuit power will be
a. 0.8 lagging
b. 0.8 leading
c. 0.6 lagging
d. 0.6 leading
35. A circuit when connected to 200V mains takes a current of 20 A, leading
the voltage by one-twelfth of time period. The circuit resistance is
a. 10 ohms
b. 8.66 ohms
c. 20 ohms
d. 17.32 ohms
36. An AC circuit has a resistance of 6 ohms, inductive reactance of 20 ohms,
and capacitive reactance of 12 ohms. The circuit power will be
a. 0.8 lagging
b. 0.8 leading
c. 0.6 lagging
d. 0.6 leading

37. An alternating voltage of 80 + j60 V is applied to a circuit and the
current flowing is -40 + j10 A. Find the phase angle.
a. 25 deg
b. 50 deg
c. 75 deg
d. 100 deg
38. A current wave is represented by the equation i = 10 sin 251t. The
average and RMS value of current are
a. 7.07 A; 6.63A
b. 6.36A; 7.07A
c. 10A; 7.07A
d. 6.36A; 10A
37. An alternating voltage of 80 + j60 V is applied to a circuit and the
current flowing is -40 + j10 A. Find the phase angle.
a. 25 deg
b. 50 deg
c. 75 deg
d. 100 deg
38. A current wave is represented by the equation i = 10 sin 251t. The
average and RMS value of current are
a. 7.07 A; 6.63A
b. 6.36A; 7.07A
c. 10A; 7.07A
d. 6.36A; 10A

39. Calculate the susceptance in mho of a circuit consisting of resistor of 10
ohms in series with a conductor of 0.1H, when the frequency is 50Hz.
a. 0.0303
b. 0.0092
c. -0.029
d. 32.95
40. An inductive circuit of resistance 16.5 ohms and inductive of 0.14H takes
a current of 25 A. If the frequency is 50Hz, the supply voltage is
a. 117.4 V
b. 1174 V
c. 1714 V
d. 1471 V
39. Calculate the susceptance in mho of a circuit consisting of resistor of 10
ohms in series with a conductor of 0.1H, when the frequency is 50Hz.
a. 0.0303
b. 0.0092
c. -0.029
d. 32.95
40. An inductive circuit of resistance 16.5 ohms and inductive of 0.14H takes
a current of 25 A. If the frequency is 50Hz, the supply voltage is
a. 117.4 V
b. 1174 V
c. 1714 V
d. 1471 V

41. The current taken by a circuit is 1.2 A when the applied potential
difference is 250 V and the power taken is 135W. The power factor
is
a. 0.35
b. 0.45
c. 0.55
d. 0.65
42. A capacitor has a capacitance of 20uF. The current supplied if it is
placed across a 1100 V, 25 Hz supply.
a. 3.554 A
b. 6.91 A
c. 3.45 A
d. 9.61 A
41. The current taken by a circuit is 1.2 A when the applied potential
difference is 250 V and the power taken is 135W. The power factor
is
a. 0.35
b. 0.45
c. 0.55
d. 0.65
42. A capacitor has a capacitance of 20uF. The current supplied if it is
placed across a 1100 V, 25 Hz supply.
a. 3.554 A
b. 6.91 A
c. 3.45 A
d. 9.61 A

43. A non-inductive load takes a 100A at 100V. Calculate the inductance of
the inductor to be connected in series in order that the same current is
supplied from 220 V, 50 Hz mains.
a. 1.96 ohms
b. 6.91 ohms
c. 19.6 ohms
d. 9.61 ohms
44. An inductor having negligible resistance and an inductance of 0.07H is
connected in series with a resiostor of 20 ohms resitance across a 200, 50
Hz supply. The maximum energy stored in the coil is
a. 3.175 J
b. 1.585 J
c. 0.236 J
d. 0.33 J
43. A non-inductive load takes a 100A at 100V. Calculate the inductance of
the inductor to be connected in series in order that the same current is
supplied from 220 V, 50 Hz mains.
a. 1.96 ohms
b. 6.91 ohms
c. 19.6 ohms
d. 9.61 ohms
44. An inductor having negligible resistance and an inductance of 0.07H is
connected in series with a resiostor of 20 ohms resitance across a 200, 50
Hz supply. The maximum energy stored in the coil is
a. 3.175 J
b. 1.585 J
c. 0.236 J
d. 0.33 J

45. A coil has 1200 turns and procedures 100 uWb mwhen the current
flowing is 1A. The inductance of the coil is
a. 0.21 H
b. 0.12 H
c. 0.31 H
d. 0.41 H
46. A capacitor connected to a 115 V, 25 Hz supply takes 5 A. What
current will it take when the capacitance and frequency are
doubled?
a. 2 A
b. 5 S
c. 10 A
d. 20 A
45. A coil has 1200 turns and procedures 100 uWb mwhen the current
flowing is 1A. The inductance of the coil is
a. 0.21 H
b. 0.12 H
c. 0.31 H
d. 0.41 H
46. A capacitor connected to a 115 V, 25 Hz supply takes 5 A. What
current will it take when the capacitance and frequency are
doubled?
a. 2 A
b. 5 S
c. 10 A
d. 20 A

47. A resistor of 20 ohms is connected in parallel with a capacitor across a
110 V, 40 Hz supply. If the current taken is 6A, what is the capacitance?
a. 88.6 uF
b. 68.8 uF
c. 86.8 uF
d. 76.8 uF
48. What capacitance must be placed in series with an inductance of 0.05H,
so that when the frequency is 100 Hz, the impedance becomes equal to
the ohmic resitance?
a. 70.5 uF
b. 50.7 uF
c. 5.7 uF
d. 7.05 uF
47. A resistor of 20 ohms is connected in parallel with a capacitor across a
110 V, 40 Hz supply. If the current taken is 6A, what is the capacitance?
a. 88.6 uF
b. 68.8 uF
c. 86.8 uF
d. 76.8 uF
48. What capacitance must be placed in series with an inductance of 0.05H,
so that when the frequency is 100 Hz, the impedance becomes equal to
the ohmic resitance?
a. 70.5 uF
b. 50.7 uF
c. 5.7 uF
d. 7.05 uF

49. A reactance of 20 ohms and inductance of 0.1 H is connected in
parallel with a capacitor. The capacitance of the capacitor required
to produce a resonance when connected to a 100V, 50 Hz is
a. 71.2 uF
b. 1.277 uF
c. 17.2 uF
d. 72.1 uF
50. What is the resonant frequency of a circuit when an inductance of
1uH and capacitance of 10 picofarad are in series?
a. 15.9 MHz
b. 50.3 MHz
c. 15.9 kHz
d. 50.3 KHz
49. A reactance of 20 ohms and inductance of 0.1 H is connected in
parallel with a capacitor. The capacitance of the capacitor required
to produce a resonance when connected to a 100V, 50 Hz is
a. 71.2 uF
b. 1.277 uF
c. 17.2 uF
d. 72.1 uF
50. What is the resonant frequency of a circuit when an inductance of
1uH and capacitance of 10 picofarad are in series?
a. 15.9 MHz
b. 50.3 MHz
c. 15.9 kHz
d. 50.3 KHz

51. The _____ the Q of a circuit, the narrower the bandwidth.
a. Lower
b. Higher
c. Broader
d. Selective
52. Find the half power bandwidth of a parallel resonant circuit which
has a resonant frequency of 3.6MHz and Q of 218.
a. 606 kHz
b. 58.7 kHz
c. 16.5 kHz
d. 47.3 kHz
51. The _____ the Q of a circuit, the narrower the bandwidth.
a. Lower
b. Higher
c. Broader
d. Selective
52. Find the half power bandwidth of a parallel resonant circuit which
has a resonant frequency of 3.6MHz and Q of 218.
a. 606 kHz
b. 58.7 kHz
c. 16.5 kHz
d. 47.3 kHz

53. At series resonance _____ .
a. Circuit impedance is very large
b. Cicuit power factor is minimum
c. Voltage across L or C is zero
d. Circuit power factor is unity
54. At series resonance, the voltage across the inductor is
a. Equal to the applied voltage
b. Much more than the apllied voltage
c. Equal to voltage across R
d. Less than the applied voltage
53. At series resonance _____ .
a. Circuit impedance is very large
b. Cicuit power factor is minimum
c. Voltage across L or C is zero
d. Circuit power factor is unity
54. At series resonance, the voltage across the inductor is
a. Equal to the applied voltage
b. Much more than the apllied voltage
c. Equal to voltage across R
d. Less than the applied voltage

55. The Q factor of the coil is _____ the resistance of the coil.
a. Inversely proportional to
b. Directly proportional to
c. Independent of
d. None of these
56. An RLC circuit is connected is connected to 200V AC source. If Q
factor of the coil is 10, then the voltage across the capacitor at
resonance is
a. 200 V
b. 2000 V
c. 20 V
d. 210 V
55. The Q factor of the coil is _____ the resistance of the coil.
a. Inversely proportional to
b. Directly proportional to
c. Independent of
d. None of these
56. An RLC circuit is connected is connected to 200V AC source. If Q
factor of the coil is 10, then the voltage across the capacitor at
resonance is
a. 200 V
b. 2000 V
c. 20 V
d. 210 V

57. At parallel resonance
a. Circuit impedance is minimum
b. Power factor is zero
c. Line current is maximum
d. Power factor is unity
58. The dynamic impedance of parallel resonant circuit is 1 Mohms. If
the capacitance is 1uF, and the resistance is 1ohm, then the value
of the inductance
a. 1 H
b. 10 H
c. 10 pH
d. 10 uH
57. At parallel resonance
a. Circuit impedance is minimum
b. Power factor is zero
c. Line current is maximum
d. Power factor is unity
58. The dynamic impedance of parallel resonant circuit is 1 Mohms. If
the capacitance is 1uF, and the resistance is 1ohm, then the value
of the inductance
a. 1 H
b. 10 H
c. 10 pH
d. 10 uH

59. When supply frequency is less than the resonant frequency in a
parallel ac circuit, then the circuit is
a. Resistive
b. Capacitive
c. Inductive
d. None of these
60. At parallel resonance, the circuit drwas a current of 2mA. If the Q
of the circuit is 100, then the current through the capacitor is
a. 2 mA
b. 1 mA
c. 200 mA
d. None of these
59. When supply frequency is less than the resonant frequency in a
parallel ac circuit, then the circuit is
a. Resistive
b. Capacitive
c. Inductive
d. None of these
60. At parallel resonance, the circuit drwas a current of 2mA. If the Q
of the circuit is 100, then the current through the capacitor is
a. 2 mA
b. 1 mA
c. 200 mA
d. None of these

61. A circuit has an impedance of (1-j2) ohms. The susceptance of the
circuit in mho is
a. 0.1
b. 0.2
c. 0.4
d. None of these
62. If the admittance of a parallel ac circuit increased, the circuit
current
a. Remains constant
b. Is increased
c. Is decreased
d. None of these
61. A circuit has an impedance of (1-j2) ohms. The susceptance of the
circuit in mho is
a. 0.1
b. 0.2
c. 0.4
d. None of these
62. If the admittance of a parallel ac circuit increased, the circuit
current
a. Remains constant
b. Is increased
c. Is decreased
d. None of these

63. The resistance between any pair two terminals of a balanced wye-
connected load is 12 ohms.
a. 6 ohms
b. 18 ohms
c. 24 ohms
d. None of these
64. If an AC circuit contains three nodes, the number of each mesh
equations that can be formulated is
a. 1
b. 2
c. 3
d. 4
63. The resistance between any pair two terminals of a balanced wye-
connected load is 12 ohms.
a. 6 ohms
b. 18 ohms
c. 24 ohms
d. None of these
64. If an AC circuit contains three nodes, the number of each mesh
equations that can be formulated is
a. 1
b. 2
c. 3
d. 4

65. The relation of the voltage across an
inductor to its current is describe as
65. The relation of the voltage across an
inductor to its current is describe as

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