11 - DC Electricity

CURRENT ELECTRICITY
1. Understand the nature of electric current in terms of a flow of moving
charge - applied to both conventional current & electron flow
2. Define electric current as Coulombs per second, I = q/t
3. Understand how an electric current carries energy in terms of potential
difference and emf
4. Understand the nature of resistance in terms of the control of electric
current
5. Understand Ohm’s Law, V = IR and its limitations
6. Calculate electric power as P = VI
7. Understand how voltage and current divide up in series and parallel
8. Calculate total resistance for resistors in series using RT = R1 + R2 + ...
9. Calculate total resistance for resistors in parallel using RT = 1/R1 + 1/R2
+ ...
10. Construct a simple circuit from a simple sketch of the components in the
circuit
11. Draw a circuit diagram from a sketch of the components in the circuit
12. Describe the operation of a diode, a thermistor, an LDR and an LED

Friday, 9 October 2009

Term Definition GLOSSARY
coulomb the unit of charge
joule the unit of work or energy
the difference in the potential energy per coulomb of charge between two
potential difference
points in an electrical circuit
volt the unit for potential difference

electric field a region within which a charge experiences a force
electrical friction or a measure of the ability of a conductor to conduct
resistance
electricity
relationship between resistance, voltage & current where the resistance
Ohm’s law
remains constant.

impede to slow down or resist

the rate at which charge gains potential energy as it passes through a power
power
supply or loses potential energy as it passes through a component

series connected “one after the other” in a circuit

parallel connected “side by side” in a circuit

refers to power supply (current or voltage) that is divided up between the
shared
components in the circuit

constant used to describe quantities that remain the same
light dependent a resistor that shows a decreasing resistance with increasing exposure to
resistor light
thermistor a resistor that shows a decreasing resistance with increasing temperature

GO WITH THE FLOW !!

A SIMPLE CIRCUIT


DEFINING ELECTRIC CURRENT
Electron Flow
Electrons move through a lattice of metal ions as they flow (or bump their way)
towards the positive end of an electric field:

Conventional Current
The direction in which positive charge would flow Positive to Negative
Charges flow through wires under the influence of an electric field.

Note
(i) The electric field in a wire is uniform.
(ii) As charge flows in the field it loses potential energy.
(iii) The minimum potential energy that charge has is at the negative terminal of the
power supply.

http://regentsprep.org/Regents/physics/
phys03/bsimplcir/default.htm

1. What part of the model is like
the power supply?
________________________
2. What part of the model is like
a component?
________________________

3. In the model, what are electric charges being likened to? __________________

Conventional current is considered to be the flow of ____________ charges from
the __________ to the ____________ terminal of the power supply. Charges behave

like particles which have _____. When charge passes through a power supply it
______ electric potential energy in much the same way as particles (with mass) will
______ gravitational potential energy as they make their way up a slope. When
charge passes through a component it _______ electrical potential energy in much
the same way that particles (with mass) ______ gravitational potential energy as they

make their way down a slope. When charge moves around an electrical circuit it must
lose as much energy as it gains.

MATHEMATICALLY SPEAKING

Current - is the rate of flow of electrical charge
- it is the number of coulombs of electrical charge that passes a point in
one second.

where I = electric current (Cs-1 or A)
I=Q
Q = electric charge (C)
t
t = time (s)

Note
Cs-1 reads Coulomb per Second V
+ -
Consider the simple circuit
I
I

When voltage, V is increased the energy difference between a coulomb of charge on
either side of the power supply will increase. This energy difference drives electrons
around the circuit faster.

In other words, as supply voltage increases then current will also increase (provided
that the resistance remains constant)

Voltage - is a measure of the energy used or produced by a component
(Common definition)

- is the energy difference that a coulomb of charge has on either side of
a component (Formal definition)

Eg. Considering the voltage across a lamp:

V
+ -

A B
1A

If V = 6V then a coulomb of charge has 6J more electrical potential energy at
point A than it does at point B

Unit of Voltage: Joule per Coulomb or Volt
(JC-1) or (V)

Note:
Potential Difference, p.d - a difference in voltage between parts of a circuit.
V = ∆Ep/q describes voltage mathematically as “difference in potential energy per unit
charge”

FACTORS THAT AFFECT RESISTANCE

Also, some materials conduct electricity better than others Eg. Copper is better than iron

Do not copy THE VOLTAGE-CURRENT RATIO

1. Consider a lamp in an electrical circuit:
12V

2A

12V represents the energy difference across the lamp. This drives electrons
through the lamp at the rate (or “speed”) of 2A. The voltage:current ratio is
_____

2. Consider a different lamp in an electrical circuit:
12V

1A

This lamp has higher resistance because 12V across this lamp can only drive
electrons through the lamp at a rate of 1A. The voltage:current ratio is _____

This example shows that the greater the voltage:current ratio then the greater the
resistance is. Resistance is the voltage:current ratio


RESISTANCE
Definitions
1. Resistance, R is a measure of the “electrical friction” in a conductor. (the
opposition to the flow of current)
2. It is the ratio of the voltage across a conductor to the current through it.

Resistance = Voltage
Current R=V
Unit of resistance is the ohm, Ω
I

Resistance is given by the slope or gradient of a voltage - current graph

Example
In an experiment, the voltage across a lamp is measured and recorded as the current
is increased 1 A at a time. Calculate the resistance of the lamp.

V (V)
24
20
16
12
8
4

0 1 2 3 4 5 6
I (A)

Example
What does each of the following graphs show about the resistance of the conductor?
24 A conductor that retains a constant
1 V (V) 20 temperature as the current is increased:
16
12
8
4

0 1 2 3 4 5 6 I (A)

A conductor that is allowed to heat
24
2 V (V) up as the current is increased
20
16
12
8
4
I (A)
0 1 2 3 4 5 6

A conductor that is cooled progressively
3 V (V) 24
20 as the current is increased
16
12
8
4
I (A)
0 1 2 3 4 5 6

OHM’S LAW
Ohm’s Law states that the voltage across a resistor is proportional to the current
through it. i.e. V α I

A resistor that obeys Ohm’s Law has a voltage - current graph that is a straight line
so the resistance is always a constant value:

V Vα I

The gradient of the graph is R

So V = RI

or

V = IR

I
Ohm’s law is usually written this way

Note

Ohm’s law allows us to calculate the correct voltage when the current in the circuit
changes. This requires knowledge of the resistance and requires the value of the
resistance to stay the same regardless of the current.

A conductor which obeys Ohm’s Law is called an Ohmic conductor.

LIMITATIONS OF OHM’S LAW
24
V (V) 20
When a temperature of a lamp increases its
16 resistance increases
12
8
4
I (A)
0 1 2 3 4 5 6

For most conductors, as the temperature increases the increased vibration of particles
impedes the flow of electrons. Resistance in the conductor will therefore increase. The
graph slopes upwards.

V (V) 24
The resistance of a thermistor decreases as its
20
16
temperature decreases
12
8
4
I (A)
0 1 2 3 4 5 6

Ex 16A: Q.1 to 4

POWER TO THE PEOPLE

Electrical power is the rate at which electrical work is done.

P = W Where P = Power (W)
t W = Work (J)
Units of power: Joule per second or Watt t = time (s)
(Js-1) (W)

The above expression for power is of limited use in electricity. The commonly used
formula is as follows:

P = VI Where P = Power (W)
V = Voltage (V)
I = Current (A)

Ohm’s Law states that V = I R. Substituting this into P = VI gives: P = I2R

Ohm’s Law also states that I = V . Substituting this into P = VI gives: P = V2
R R

Note: Work is done by a component because it changes electrical energy into other
forms of energy

EXAMPLES p167 ABA Q5 & 6

1. The diagrams opposite show two different heating
circuits for a hot plate. Both circuits use two similar
heating elements, A and B, of equal resistance.
(b) Draw a circuit diagram for each circuit.
240 V

240 V
(b) Consider circuit 1. The current flowing through
element A is measured to be 1.2 A. What is the
current through element B?
_____________________________________
(c) How much current is drawn by circuit 1 from the mains?
_________________________________________________________________
(d) Explain why the voltage across element A is 120 V.
_________________________________________________________________
_________________________________________________________________
(e) Calculate the resistance of each heating element.
_________________________________________________________________
_________________________________________________________________

Consider circuit 2
(h) Explain why the current through element A is 2.4 A.
_________________________________________________________________
_________________________________________________________________
(i) How much current is drawn from the mains?
_________________________________________________________________
(j) Calculate how much electric power is turned to heat by the circuit.
_________________________________________________________________
_________________________________________________________________
(k) How may times more heat is generated in circuit 2 than in circuit 1.
_________________________________________________________________

2. A stereo uses 240 V and the combined resistance of all its internal components is
60Ω.
(c) Calculate the power rating of the stereo.
__________________________________________________________________
(d) Calculate the amount of energy used to operate the stereo for half an hour.
__________________________________________________________________
__________________________________________________________________

Ex 16E: Q.1 to 3

VOLTAGE AND CURRENT IN SERIES CIRCUITS

+ -

VT
A1 A3

I1 I3

I2
A1

V1 V2

Current in series is constant I1 = I2 = I3

Voltage in series is shared VT = V1 + V2

Note
Voltage is shared in proportion to the size of the resistance

PARALLEL CIRCUITS

+ -
Current in parallel is shared
IT VT IT
IT = I1 + I2
I1 R1
in other words “charge splits
up as it enters a junction in
a circuit”
V1

I2 R2
Voltage in parallel is constant

V2 VT = V1 = V2

Note
Current is shared in an inverse proportion to the size of the resistance.

For example:
If R1 = 5 and R2 = 10
and IT = 3
then I1 = 2 and R2 = 1

http://phet.colorado.edu/simulations/ CIRCUIT CONSTRUCTION
sims.php?
sim=Circuit_Construction_Kit_DC_Only

1. Enter the URL (above) into the address bar of your internet browser.
2. Use the simulation tools to construct each of the following 3 circuits (ensure that you use
identical lamps and an the same power supply for each circuit).
3. Record the current in each circuit and explain your observation.
4. Repeat this exercise for the second set of 3 circuits.

1 2 3
+ - + - + -
A A A

3
+ -
2
A
1 + -

+ - A

A


Examples CIRCUIT CALCULATIONS

1 + 9V -

A1 V1 A3

5Ω 10Ω
A2

V2 V3

For the circuit represented by the circuit diagram above, what is the reading on:
(a) V1

(b) A2

(c) V2

(d) V3


2 + 15V -

V1

5Ω A3
V2 A1

V3
R 10Ω
A2

(a) V3 if V2 = 10 V

(b) A1

(c) A2

(d) A3

(e) What is the value of resistor R?


3 + 12V -

V1

2Ω 4.8Ω V3
A1

V2
3Ω
A2


(a) V1

(b) V3

(c) V2

(d) A1

(e) A2

Ex 16B: Q.1 to 3

RESISTANCE CALCULATIONS
Resistors which are connected end to end are in series with one
another
R1 R2

The total resistance of the series combination, Rs is the sum of the
resistances R1 and R2.

For two or more resistors in series: Rs = R1 + R2 + ...........

Resistors which are connected side by side are in parallel with each other.
R1

R2

The total resistance of the parallel combination, Rp is less than any individual
resistor in the combination.

For two or more resistors in parallel 1 1 1 + ....
the total resistance,Rp is given by: RP = R1 + R2

Examples CALCULATING TOTAL RESISTANCE
100 Ω
1 100 Ω
2
100 Ω 100 Ω
100 Ω • •

100 Ω 100 Ω
• •
Total resistance = Total resistance =

3 100 Ω 4 100 Ω 100 Ω

100 Ω
• • • •

100 Ω 100 Ω 100 Ω

Total resistance = Total resistance =

5 100 Ω 100 Ω 100 Ω Total resistance =
• •

Examples APPLIANCES IN THE HOME

1. A set of 10 Christmas tree lights operate from a 20 V supply. They are all similar
1.0 W bulbs, connected in parallel.

(a) Calculate the voltage across each bulb.

(b) Calculate the current through each bulb, in mA.

(c) Calculate the resistance of each bulb.

(d) Calculate the total resistance in the circuit.

2. A 1000 W iron is connected to a 120 V supply. Should the iron need to be used on
a 240V supply calculate the size of the resistance that will need to be added in
series to the iron so that the iron continues to draw the same current.

Ex 16C: Q.3 & Ex 16E: Q.4 to 8

Examples/exercises DRAWING CIRCUIT DIAGRAMS

Draw the following circuit diagrams in the space provided:

1.
+ -

2.
+ -

3. A
V

+ -


SPECIALIZED COMPONENTS

Thermistor

A thermistor is a resistor which is sensitive to heat. Unlike most resistors though its
resistance decreases as its temperature increases. This makes it useful in the circuit in
your car that contains the temperature gauge. The temperature gauge is an ammeter
calibrated to read temperature instead of Amps and the thermistor is in contact with
the engine and connected in series with the gauge. As the engine temperature
increases the resistance of the thermistor decreases thereby allowing the current in
the circuit to increase. This increase in current is reflected in the reading on the
gauge.

Light dependent resistor

An LDR is a resistor which is very sensitive to light. Its resistance decreases with light
intensity. They are useful in light meters where the meter is essentially an ammeter
re-calibrated to read lux instead of Amps.

Diode

Because a diode allows current to flow in one direction only, it is called a
semiconductor. Diodes require only a low voltage (about 0.6 V) and will only allow a
small current to flow through them. They are useful in circuits that convert AC current
to DC.

Light emitting diode

These give off light as they allow current to flow one way through a circuit. They
require about 2 V to function. Because of their low power input they are useful for
lights (eg. they are finding their way into the tail light clusters of motor vehicles)

11 - DC Electricity

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