Module no. 24

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Module # 24
Circuit & Resistance
Circuit
A circuit is a path through which current flows.
Electric Circuit
The path through which an electric current passes is called an
electric circuit.
In a circuit a rise in voltage indicates a positive sign and a drop in
voltage indicates a negative sign.
Consider a bulb connected to a battery with the help of wires. The
resistance of the filament of the bulb is R and V is the potential
difference between the terminals of the battery. There is a switch
inserted between the bulb and battery.
When the switch is on, then the current flows in the circuit and the
electric bulb glows. But, if the switch is off, the bulb does not glow.
This glowing or otherwise of the bulb indicates that the circuit is
complete or not.
Active Circuit
Active circuit has source of energy while passive circuit does not
have.

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Open Circuit
If the path of the current is incomplete, then, current cannot pass
through the circuit. This circuit is called an open circuit.
Close Circuit
If the path of the current is complete and the current passes
through the circuit, then, the circuit is called a close circuit.
Series Circuit
Any circuit in which end of one resister is connected to the end of
another resister in such a way that current gets only one path to
flow through the circuit is called as series circuit.
Series Combination of Resistors
When in an electric circuit, different resistances are connected in
series and the flow of current through them has the same path,
the combination is called series combination of resistances.
In this case, there is a single path for the passage of electric
current and the same quantity of current passes through each
point in the circuit.

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Characteristics of Series Combination
The series combination of resistances has the following
properties:
(1) There is a single path for the passage of electric current.
(2) The same quantity of electric current passes through each
resistance of the combination.
(3) The voltage (potential difference) applied to the circuit is
equal to the sum of voltages across the individual resistors in
series. If voltage of battery is V and V1, V2 and V3 are the voltages
across R1, R2 and R3 respectively then
V = V1+ V2 + V3
For N resistors in series,
V = V1+ V2 + V3 + ………… VN
(4) The resistances R1, R2 and R3 can be replaced by a single
(or equivalent) resistance Re which when joined in place of these
resistances allows the same current to pass through it as in case
of individual resistances.
Re can be obtained by adding individual resistances combined in
series,
As we know that

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V = V1+V2+V3
therefore,
IRe =IR1+IR2+IR3= I (R1+R2+R3)
By dividing both sides by I, we get
Re = R1 + R2 + R3
In case of N resistances, we can write
Re = R1+ R2 + R3 + …....... + RN
Series Parallel Circuit
Series parallel circuits are used where it is necessary to provide
various amounts of current and voltages with single power supply.
Electronic circuits are usually of this type because they generally
use only one voltage source.
A series parallel circuit is composed of both series and parallel
branches.
Parallel Circuit
Practically, most of the circuits used are parallel. The total current
in a parallel circuit is the resultant of the branch currents. When
resistance, inductance and capacitance are connected in parallel
in different combinations then the branch currents are not in
phase with one another.

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When resistors are arranged so that each forms a separate path
for a part of the total current, they are said to be connected in
parallel i.e. the circuit has more than one path for current to flow.
In parallel circuit
1. The voltage across all branches or paths of a parallel circuit
is the same.
2. The total current in the circuit is equal to the sum of all the
currents flowing in the branches of the parallel circuit.
3 If the resistances and total current are only known, the
branch current can be calculated.
4 The total resistance must always be less than the value of
any resistor in the circuit having the least value.
Parallel connections are also called multiple connections or shunt
connections. A very important feature of parallel circuits, as
compared to series circuits, is that in parallel circuits different
branch loads operate independently of each other. Hence, if any
load is disconnected or turned off other branch loads operate
independently of each other.

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Parallel Combination of Resistors
When, in an electric circuit, different resistors are connected in
such a way that the flow of current through them has many paths,
then, the combination is called parallel combination of resistors.
OR
Resistors are said to be connected in parallel when each one of
them is connected across the same two points. In such a
combination, the same potential drop occurs across each of the
resistors.
It is to be noted here that the sum of the electric current flowing
through different resistances is equal to the total current supplied
by the battery. In the following fig. at the junction A, the electric
current in the external circuit divides into three parts and flows
along the three paths. When these currents reach junction B, they
add up into current of the external circuit.

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Parallel combination of Resistances R1, R2 & R3
Properties of Parallel Combination
(1) There are different paths for the conduction of electric
current.
(2) The potential difference across each resistance is the same
and equal to the voltage of the battery.
V = V1 = V2 = V3
(3) The sum of quantities of current I1, I2 and I3 flowing through
different resistances is equal to the total current I supplied by the
battery.
I = I1 +I2 + I3
OR
V V1 V2 V3
----- = ----- + ------ + -----
Re R1 R2 R3
But

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V1 = V2 = V3 = V
and, therefore, we get
V V V V
----- = ----- + ------ + -----
Re R1 R2 R3
By dividing both sides by V, we get
1 1 1 1
----- = ----- + ------ + -----
Re R1 R2 R3
For N resistors, the equivalent resistance of the combination of
a parallel circuit will be as
1 1 1 1 1
----- = ----- + ------ + ----- + ……………… --------
Re R1 R2 R3 RN
Note: The resultant resistance in parallel combination circuit is
always less than least resistance in the combination.
Resonance Frequency & Resonance Circuit

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Resonance Frequency
Resonance is said to occur whenever a particular body or system
is set in oscillation at its own natural frequency as a result of
impulses received from some other system which is vibrating with
the same frequency.
Resonant Circuit
When resistance, inductance and capacitance are combined in a
circuit the circuit responses differently at different frequencies. At
a particular frequency the circuit response is maximum and at that
frequency the circuit is said to be in a state of resonance. The
frequency at which the circuit resonates is called resonant
frequency, denoted by symbol fr, and such a circuit is known as
resonant circuit.
It is necessary for a resonant circuit to have both inductance and
capacitance. Certainly, resistance is always present in an
electrical circuit. When frequency is changed then resonance
occurs at a particular frequency, fr. Under the condition of
resonance, the energy absorbed by one element of the circuit is
equal to the energy released by the other element at any time.
Thus, the circuit at fr needs no more reactive power, and the total
power is equal to the power dissipated in resistance only.
The resonant circuits are of two types:

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(a) Series resonant circuits
(b) Parallel resonant circuits
The purpose of resonant circuits is to select a particular frequency
or a small band of frequencies.
When inductive and capacitive reactances become equal at a
certain frequency, the circuit resonance and the frequency at
resonance is called resonant frequency.
At resonance impedance becomes resistive.
At resonance the power factor is unity.
At resonance series resonant circuit has maximum current and
minimum impedance, and parallel resonant circuit has minimum
current and maximum impedance.
Resonance is a condition that exists when the Inductive reactance
and the capacitive reactance of a circuit are equal.
All examples of tuning in radio and television are applications of
resonance. When we tune a radio to one station, the LC circuits
are tuned to resonance for that particular carrier frequency. Also
when we tune a television receiver to a particular channel, the LC
circuits are tuned to resonance for that station. There are almost
unlimited uses for resonance in ac circuits.

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The circuit in which the values of inductive and capacitive
reactances are equal is known as a TUNED CIRCUIT OR
Resonance Circuit.
Inductive reactance increases as the frequency is increased, but
capacitive reactance decreases with higher frequencies. Because of
these opposite characteristics, for any LC combination there must be
a frequency at which the XL (inductive reactance) equals the Xc
(capacitive reactance) as one increases while the other decreases.
This case of equal and opposite reactances is called resonance and
the ac circuit is then a resonant circuit.
House Circuits
In house circuits, every circuit is connected in parallel with the
supply i.e., across the live wire and neutral wire and receives the
full main potential difference of 220V.
Switches in House Circuits
A switch is used for off and on or to make and break the electric
circuit. It is always in the live wire in series with the circuit. If
switches and fuses were in the neutral side, then, lamps and
power sockets would be live even when switches were off or
fuses blown. A shock (fatal) could then be obtained by a person
who touches the element of an electric wire when it was switched
off.

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There are two copper strips on the branch distribution board.
These two are connected with two-supply wires separately. When
we switch on the current, the current flows and all the electric
devices connected through this switch start working.
Earthing and Safety in House Circuits
A ring main circuit has a third wire which is connected to one part
(E) of the socket. This wire is earthed by being connected either
to a metal water pipe in the house or to an earth connection on
the supply cable. We take the earth itself as being a zero
potential. This is purely a matter of convenience. It does not mean
that the earth has no electrical charge. Actually, the earth has a
negative charge but this is so large that any charge given to or
taken from it has a negligible effect.
This third wire is a safety precaution to prevent an electric shock
should an appliance develop a fault. The earth pin (E) in a plug is
connected to the earth connection through path having almost
zero resistance. If the element of an electric wire breaks or sags
and touches the case, a large current flows to the earth and blows
the fuse. Otherwise, the case becomes live and anyone touching
it will receive a shock which might be fatal, especially, if they were
earthed by standing in a damp environment, e.g. on a wet
concrete floor. Circuit breakers are also used instead of fuses for

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safety. The circuit breakers are connected in series with the wire
entering the house. The circuit breaker is a device which breaks
the circuit when the current exceeds the rated value (5A to 13A).
These are made on the principal of an electromagnet.
Fuse in House Circuits
Fuse is a small piece of wire which allows only a specific amount
of current to pass through the circuit. Fuse is connected in series
with the live wire. It is used to control the flow of electric current.
Fuse wire is mostly made up of lead or tin metals. If the current
exceeds the specific desired limit, the temperature of fuse rises
and it melts. As the switch is on, the current starts flowing and
passes through the fuse. If we switch on quite a few electrical
appliances at the same time, then, a large amount of current may
flow through the circuit. It may damage the electric meter.
Sometimes, due to carelessness or short circuiting, the live and
neutral wires are inter connected, due to which, a large amount of
current may flow and may damage the electric meter. Only fuse
wire acts as safety measures against such damages. If fuse wire
melts, then, it can easily be replaced.
Live and Neutral Wire
Usually, two wires are used for the supply of current. One of these
wires is earthed and is at zero potential. This wire is called neutral

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wire. The neutral wire is connected to the earth about every
100m.
Second wire is at a potential of 220 V with respect to the neutral
wire and is known as live wire. The potential on the live wire is
alternately positive and negative with respect to the neutral wire.
These two wires are connected to the electric meter.
Resistance
The constant ratio of potential difference to current is called the
resistance R of the wire or conductor. Resistance is a measure of
opposition to the regular flow of free electrons due to their
continuous bumping against vibrating atoms of the lattice of the
conductor.
The SI unit of measurement for resistance is the ohm. The unit
symbol is the Greek capital letter omega, Ω. The letter symbol for
resistance is R.
Before the application of a potential at the ends of a wire, the free
electrons in the wire perform haphazard motion and collide with
each other frequently and constantly. The random motion of
electrons means that the number of electrons passing through a
section of the wire towards the left equals the number of electrons
passing through the same section towards right. No charge,

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therefore, appears to flow through the wire in net. However,
application of a certain potential across the ends of the wire
compels the electrons to move along a certain direction. This
forced directional motion of electrons is known as their drift
velocity.
As a result of the drift velocity, the electrons collide with each
other and the cores of the atoms of the body constantly face
hindrance in their regular directional motion. This hindrance in
regular motion is known as the resistance of the conductor.
Electric resistance or simply resistance depends upon the
following factors.
1 Length of Conductor
The longer the length of a conductor, the more will be its
resistance.
2 Cross Section Area of Conductor
If the cross-section area of a conductor is increased, the
resistance will be decreased.
If L is the length of the conductor and A is its area of cross
section, then it is experimentally found that
R  L/A

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OR
R =  L/A
OR
 = R x A/L
Where,  is a constant known as resistivity and its value depends
upon the nature of the material of the conductor.
3 Temperature
The resistance increases with the increase in temperature.
4 Nature of Matter (Metal)
Nature of metal is more important for the resistance. It is known
that different metals have different resistances, e.g. the same size
of the wires of copper and iron have different resistances.
Ohm
Eq. (V = IR) can be used to define the unit of resistance Ohm.
If
V = 1 volt
I = 1 ampere
then

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R = 1 ohm
It means, if the potential difference across the ends of the
conductor is one volt and the resulting current passing through it
is one ampere, then, the resistance offered by the conductor is
one ohm denoted by a Greek letter omega (). The common
multiples and submultiples of ohm are the mega ohm (M), kilo
ohm (k), milli ohm (m) and micro ohm () which are given by:
1M=106
1k = 103
1m = 10-3
1 = 10-6

Ohm’s Law
If a voltage V is applied across a conductor, a current I flows
through it. Early in the nineteenth century, George Ohm
discovered that the magnitude of the current in metals is
proportional to the applied voltage as long as the temperature of
the conductor is kept the same. The relationship is exact within
the accuracy of the measurements.
Mathematically,
V ∝ I

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OR
V = I R
OR
I = V / R----- (1)
where, R is a constant known as the resistance of the conducting
material.
Eq. (1) is known as Ohm's law. Resistance depends upon the
nature, dimension and physical state of the conductor. It is the
measure of the opposition to the motion of free electrons due to
their continuous collisions against the atoms of the lattice. The
unit of electrical resistance is ohm (Ω). The ohm is defined as a
resistance across which when a potential of one volt is applied, a
current of one ampere starts flowing through it.
1Ω = 1 V A-1
This law can be stated as follows: -
"The current passing through a conductor is directly proportional
to the potential difference applied across its ends provided the
temperature and other physical conditions of the conductor
remain unchanged."
Mathematically speaking,

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V  I
OR
V = RI
OR
V = IR
Where, 'R' is a constant called the resistance of the conductor.
This is a physical property of the conductor. The potential
difference - current curve for a given wire at a fixed temperature is
a straight line.
Resistance Temperature Coefficient
The rise in resistance of a particular material per ohm per l°C is
called the temperature coefficient of that material. Symbol is α
(ALPHA).
Non Inductive Resistance
We know that if current in a coil varies due to any reason, an
induced current is produced in the coil. The direction of this
induced current is opposite to the direction of the original current.
Thus the current decreases. In order to maintain steady current a
possible way is that the wire is doubled on itself before being
coiled up. The current passing through the wires lying side by side

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is such that the direction of current in one wire is opposite to the
direction of the current in other wire. In this way the magnetic field
around one wire cancels the magnetic field around the second
wire.
The closer the two wires are the lesser will be the self-inductance.
Such a coil, even if it is wound upon an iron core has very little
self-inductance.
Non inductive resistances are used in electrical measuring
instruments like ammeter, voltmeter, etc. The wire wound
resistances are used in manufacturing resistance boxes, some
telecommunication equipment, etc.
Power Dissipation in Resistance
On applying potential difference across the two ends of a
conductor, a net force acts on the free electrons comprising the
current. During the collisions of the free electrons with the atoms
of the conductor, the kinetic energy acquired by them from the
external field is lost to the conductor lattice and the power
delivered to the conductor is dissipated as thermal energy.
Specific Resistance
The Resistance offered by a rod of a particular material of unit
length and unit cross-sectional area is to be termed as specific

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resistance offered by that material.
In other words, it may be defined as: -
It is the resistance of a rod of a particular material one meter in
length and with a cross-sectional area of 1 sq. mm.
Symbol is  (RHO).
Hence, specific resistance of a material may be defined as the
resistance between the opposite faces of a meter cube of that
material.
The resistance of the conductor having a unit length and unit
sectional area is defined as the specific resistance. It is also
called resistivity.
The unit of length adopted is one meter and the unit of sectional
area is one sq.mm. Resistance “R” will then be in ohms.
The actual value for the specific resistance of conducting
substances is not constant but depends somewhat upon the
working temperature. In addition, its value depends upon the
actual manufacturing processes employed and is very much
affected by the presence of impurities.
The actual value for the specific resistance depends upon the
purity of the substance and is also influenced by the mechanical
processes, etc. to which the metal has been subjected.

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Resistivity
The resistivity of a material is expressed in ohm meter units and is
numerically equal to the resistance of a conductor made of the
material of length 1 meter and area of cross-section 1 metre2
. The
SI unit of resistivity is the ohm meter.
Resistivity and Its Dependence upon Temperature
Let L be the length and A the area of cross section of a wire
(conductor).
It is experimentally observed that in general the resistance R of a
given wire increases with increase in length and decreases with
increase in the area of cross section. Mathematically, it can be
written as:
R  L/A
OR
R = ρ L/A
where, ρ is the resistivity of the material of which the conductor is
made.
As the temperature of the conductor rises, the amplitude of the
vibration of the atoms in the lattice increases and hence the
probability of their collision with free electrons also increases. It

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can be said that at high temperature, the atoms offer a bigger
target area, i.e., the collision cross section of the atoms increases.
This makes the collision between free electrons and the atoms in
the lattice more frequent and hence the resistance of the
conductor increases.
Although values of resistivity are applicable for the comparison of
materials with respect to their relative merits as conductors,
values of conductivity, the reciprocal of resistivity, are sometimes
used for this purpose.
The resistivity of a material is affected by temperature and it is not
a constant factor.
Resistors
Resistors are commercially produced devices that provide specific
amounts of resistance when added to circuits. Manufacturers
generally mark each resistor with its resistance value using a
color code.
The different numerical values of resistors depend on the
amounts of carbon and binder used in their construction.
Fixed resistors vary in make-up.
Wire Wound Resistors
Wire wound resistors are constructed by winding a long length of

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wire round a core. The length of wire, its diameter, and material
from which it is made determine the value of the resistors.
Wire wound resistors are commonly used in circuits where large
amounts of heat must be dissipated (given off) to the surrounding
air. As a result, they usually are made much larger than carbon
resistors. For this reason, they are much more expensive than the
smaller carbon type.
Fusible Resistors
Fusible resistors are sometimes used in amplifiers and TV sets to
protect certain circuits. They have resistance of less than 15
ohms. Their resistance element is quite similar to the fuse link in
a cartridge fuse and is designed to burn out whenever current in
the circuit exceeds a certain predetermined value.
Superconductivity
In 1986, a remarkable discovery has been made in the field of
superconductivity. In a laboratory of Zurich, two scientists
Bednorz and Mueller have observed that certain ceramic
materials exhibit superconductivity at much higher temperatures,
i.e., at T = 30 K, than the previously found highest value of TC =
7.175 K (TC stands for Critical Temperature). In the following
years (1986 - 1990) some new ceramic materials have been
prepared which have been found to be superconductor even at T

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=125 K. Physicists today are working hard to produce compounds
which could show superconductivity even at room temperature.
The virtue of superconductivity is its ability to transport its
electrical energy without loss. This could lead to substantial
energy saving in future.
Resistivity & Superconductors
The resistivity ρ of a conductor is given by the relation ρ = R x A /
L, where A is the area of cross-section and L is the length of the
conductor.
The unit of resistivity is Ω-m. The temperature coefficient α is the
change in resistivity (or resistance) per unit original resistivity (or
resistance) per degree change in temperature. The resistivity (or
resistance) of a conductor decreases due to fall in temperature,
but, it is very difficult to make it exactly equal to zero. The
resistivity (or resistance) of a class of elements at some critical
temperature TC falls to zero. The materials showing such a
property are called "superconductors".

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