CHAPTER-11

ELECTRICITY
TOPIC-1 ELECTRIC CURRENT , OHM’S LAW

Charge :
 Charge is a fundamental particle of matter. It may be positive and negative.
 S.I. unit of charge is Coulomb (C).
18
 1 Coulomb Charge = Charge present on 6 x 10 electrons
-19
 Charge present on 1 electron = 1.6 x 10 C

Electric current :

The electric current is defined as the rate of flow of electric charge through any cross
section of a conductor.
𝐶ℎ𝑎𝑟𝑔𝑒 𝑄
𝐸𝑙𝑒𝑐𝑡𝑟𝑖𝑐 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 = 𝑂𝑅 𝐼 =
𝑇𝑖𝑚𝑒 𝑡
SI unit of electric current = Ampere (A)
1 Ampere = The flow of one coulomb of charge per second
Small quantities of current are expressed in -
–3
 Milliampere =1 mA = 10 A
–6
 Microampere =1  A = 10 A

Exercise : A current of 0.5 A is drawn by a filament of an electric bulb for 10

minutes. Find the amount of electric charge that flows through the circuit.
Solution : We are given, I = 0.5 A , t = 10 min or 10 x 60 = 600 s.
Q=Ixt
= 0.5 A x 600 s

= 300 C

Ammeter : An instrument used to measures electric current in a circuit is called

Ammeter. Ammeter has low resistance and it is always connected in series in a circuit
Electric circuit : The closed path along which an electric current flows is called an
‘electric circuit’.

Potential difference :
The work done to move a unit charge from one point to another is called potential
difference .
It is generally known as ‘Voltage’
𝑊𝑜𝑟𝑘 𝑑𝑜𝑛𝑒(𝑊)
𝑉𝑜𝑙𝑡𝑎𝑔𝑒 𝑉 =
𝐶ℎ𝑎𝑟𝑔𝑒 (𝑄)
Exercise : How much work is done in moving a charge of 2 C across two points
having a potential difference 12 V?
Solution : We are given, V= 12V , Q = 2C
𝑊
𝑉= or W = VQ
𝑄

= 12 V × 2 C
= 24 J.

S.I unit of potential difference is Volt (V).

1 Volt : When 1 Joule of work is done in carrying one Coulomb charge then potential
difference is called 1 Volt.

Voltmeter: It is a device to measure the potential difference. It has a high resistance

and is always connected in parallel to the circuit.

 The chemical action withina cell generates the potential difference across the
terminals of the cell.
 When the cell is connected to a conducting circuit element, the potential
difference sets the charges in motion in the conductor and produces an electric
current.
 OHM’S LAW
The potential difference, V, across the ends of a given metallic wire in an electric
circuit is directly proportional to the current flowing through it, in a constant
temperature. This is called Ohm’s law.

V I
V = IR
R is a constant for the given metallic wire at a given temperature and is called its
resistance.
V-I graph for Ohm’s law : The graph between V and I is always straight line with
slope equals to R.
Resistance :
It is the property of a conductor to resist the flow of charges through it.
SI unit of resistance is Ohm ( Ω )
If the potential difference across the two ends of a conductor is 1 V and the current
through it is 1 A, then the resistance R, of the conductor is 1 Ω.
It is obvious that the current through a resistor is inversely proportional to its resistance.
If the resistance is doubled the current gets halved

A component used to regulate current without changing the voltage source is called
variable resistance. In an electric circuit, a device called rheostat is often used
to change the resistance in the circuit.

Factors on which the resistance of a conductor depends :

(i) Directly proportional to the length of the conductor.
(ii) Inversely proportional to the area of cross-section.
(iii) Directly proportional to the temperature.
(iv) Depends on nature of the material.

Resistance of a uniform metallic conductor is directly proportional to its length (l ) and

inversely proportional to the area of cross-section (A).
1
𝑅 𝛼 𝑙 𝑎𝑛𝑑 𝑅 𝛼
𝐴
Combining these two equations we get -

𝑙 𝑙
𝑅 𝛼 𝑂𝑅 𝑅 = 𝜌
𝐴 𝐴
where (rho) is a constant of proportionality and is called the electrical resistivity of
the material of the conductor.

Resistivity (): The resistance offered by a wire of unit length and unit cross-sectional
area is called resistivity. It is a characteristic property of the material.
The SI unit of resistivity is Ohm-meter ( m).

 Resistivity does not change with change in length or area of cross-section but it
changes with change in temperature.
–8 –6
 Range of resistivity of metals and alloys is 10 to 10 Ωm.
12 17
 Range of resistivity of insulators is 10 to 10 Ωm.
 Resistivity of alloy is generally higher than that of its constituent metals.
 Alloys do not oxidize (burn) readily at high temperature, so they are commonly
used in electrical heating devices.
 Copper and aluminium are used for electrical transmission lines as they have low
resistivity.
TOPIC-2 COMBINATION OF RESISTORS IN A CIRCUIT

Resistances in series:
When two or more resistances are connected end to end they are said to be connected in
series.

 In a series combination of resistors the current is the same in every part of the
circuit or the same current through each resistor
 The potential difference V is equal to the sum of potential differences V1, V2, and
V3.
On applying Ohm’s law to the three resistors separately, we further have
V1 = I R1 , V2 = I R2 , and V3 = I R3
Or I R = I R1 + I R2 + I R3
Or Rs = R1 +R2 + R3

When several resistors are joined in series, the resistance of the combination Rs equals
the sum of their individual resistances, R1, R2, R3, and is thus greater than any
individual resistance.

Exercise :
An electric lamp, whose resistance is 20 , and a conductor of 4 resistance are
connected to a 6 V battery. Calculate
(a) the total resistance of the circuit, (b) the current through the circuit, and
(c) the potential difference across the electric lamp and conductor.
Solution :
The resistance of electric lamp, R1 = 20 ,
The resistance of the conductor connected in series, R2 = 4 .
(a) Then the total resistance in the circuit is
Rs = R1 + R2
Rs = 20  + 4 = 24 
The total potential difference across the two terminals of the battery V = 6 V.
(b) the current through the circuit will be -

𝑉 6𝑉
𝐼= = = 𝟎. 𝟐𝟓 𝑨
𝑅𝑆 24 Ω

(c) The potential difference across the electric lamp,

V1 = 20  × 0.25 A = 5 V
and, that across the conductor, V2 = 4  × 0.25 A = 1 V.

Resistances in parallel :
When two or more resistances are connected across two points so that each one of them
are parallel to each other, they are said to be connected in parallel.

The total current I, is equal to the sum of the

separate currents through each branch of the
combination.
I = I1 + I2 + I3

Voltage (V) across each resistance will be

same.

Let RP be the equivalent resistance of the

parallel combination of resistors.
𝑉
Hence , 𝐼 =
𝑅𝑃

On applying Ohm’s law to each resistor, we have

𝑉 𝑉 𝑉
𝐼1 = , 𝐼2 = 𝑎𝑛𝑑 𝐼3 =
𝑅1 𝑅2 𝑅3
 𝑉 𝑉 𝑉 𝑉
= + +
𝑅𝑃 𝑅1 𝑅2 𝑅3

1 1 1 1
= + +
𝑅𝑃 𝑅1 𝑅2 𝑅3

The reciprocal of the equivalent resistance of a group of resistances joined in parallel is

equal to the sum of the reciprocals of the individual resistances.

Exercise :
Observe the circuit diagram given below and Calculate (a) the current through
each resistor, (b) the total current in the circuit, and (c) the total circuit
resistance.

Solution :
R1 = 5 , R2 = 10 , and R3 = 30 .
Potential difference across the battery, V = 12 V.
𝑉 12 𝑉
The current through R1 is 𝐼1 = = = 2.4 𝐴
𝑅1 5Ω

𝑉 12 𝑉
The current through R2 is 𝐼2 = = = 1.2 𝐴
𝑅2 10Ω
𝑉 12 𝑉
The current through R3 is 𝐼3 = = = 0.4 𝐴
𝑅3 30Ω

The total current in the circuit, I = I1 + I2 + I3

= (2.4 + 1.2 + 0.4) A
=4A

1 1 1 1
The total resistance RP is = + +
𝑅𝑃 𝑅1 𝑅2 𝑅3
1 1 1 6 + 3 + 1 10 1
= + + = = =
5 10 30 30 30 3

Thus, Rp = 3 .
Advantages of Parallel connection
 A parallel circuit divides the current through the electrical gadgets. This is
helpful particularly when each gadget has different resistance and requires
different current to operate properly.
 The total resistance in a parallel circuit is least.
 When one component fails the circuit will not breaks and other components
works.

HEATING EFFECT OF ELECTRIC CURRENT

When an electric current passes through a conductor with a high resistance the
conductor becomes hot after some time and produces heat. This is called heating effect
of Electric Current.
When current I flowing through a resistor of resistance R. Let the potential difference
across it be V and t be the time during which a charge Q flows across.
The work done in moving the charge Q through a potential difference V is VQ.
Therefore, the source must supply energy equal to VQ in time t.
Hence the power input to the circuit by the source is
𝑄 𝑄
𝑃=𝑉 = 𝑉𝑥𝐼 (𝑏𝑒𝑐𝑢𝑎𝑠𝑒 𝐼 = )
𝑡 𝑡

OR For a steady current I, the amount of heat H produced in time t is

H = VIt
Exercise :
An electric iron consumes electric energy at a rate of 880 W when heating is at the
maximum rate and 110 W when heating is at the minimum. The voltage is 220 V. What
are the current and the resistance in each case.

Solution ,
𝑃
We know that P = V x I , Thus, current is 𝐼 =
𝑉

(a) When heating is at the maximum rate

𝑃 880 𝑊
Current 𝐼 = 𝑉 = 220 𝑉
= 4𝐴
𝑉 220 𝑉
Resistance 𝑅 = = = 55 𝛺
𝐼 4𝐴
(a) When heating is at the minimum rate
𝑃 100 𝑊
Current 𝐼 = 𝑉 = 220 𝑉
= 0.5𝐴
𝑉 220 𝑉
Resistance 𝑅 = = = 440 𝛺
𝐼 0.5𝐴
Joule’s law of heating :
The law states that - Heat produced in a resistor is,
(i) directly proportional to the square of current for a given resistance
(ii) directly proportional to resistance for a given current,
(iii) directly proportional to the time for which the current flows through the resistor
2
Mathematically the it is represented as H = I Rt
Exercise :
The conductor having resistance 4Ω is producing 100J heat for every second. Find the
current flowing through the conductor and potential difference across the conductor.
Solution : R = 4 Ω, H = 100 J, t = 1s

H H
Formula : H = I 2 Rt OR I2 = OR I=
Rt Rt

100
I= I= 25 = 5 A
4x1

Potential difference across the conductor. V = R x I

V = 4 Ω x 5 A = 20 V
Practical Applications of Heating Effect
(a) The heating effect of electric current has many useful applications.
The electric laundry iron, electric toaster, electric oven, electric kettle and electric
heater are some devices based on Joule’s heating.
(b) Electric bulb :

 The electric heating is also used to produce light, as in an electric bulb.

 Tungsten is used for making bulb filaments as it is a strong metal with high
melting point
 The bulbs are usually filled with chemically inactive nitrogen and argon gases to
prolong the life of filament
(c) Fuse :
 Another common application of Joule’s heating is the fuse used in electric
circuits. It protects circuits and appliances by stopping the flow of any unduly
high electric current.
 Fuse is always connected in series with live wire.
 If a current larger than the specified value flows through the circuit, the
temperature of the fuse wire increases. This melts the fuse wire and breaks the
circuit.
ELECTRIC POWER
The rate at which electric energy is dissipated or consumed in an electric circuit is
called Electric power.
The power P is given by -
𝐼2 𝑉2
𝑃=𝑉𝑥𝐼 , 𝑃= , 𝑃=
𝑅 𝑅
The SI unit of electric power is watt (W).

Exercise :

An electric bulb is connected to a 220 V generator. The current is 0.50 A. What is the
power of the bulb?
Solution : P=VxI
= 220 V x 0.50 A
= 110 W.
Exercise :

A bulb is rated 40 W; 220 V. Find the current drawn by it, when it is connected to a 220
V supply and also find its resistance.

Solution :
𝑃 40 𝑊
Current drawn by the bulb 𝐼 = = = 𝟎. 𝟏𝟖 𝑨
𝑉 220 𝑉

𝑉2 (220)2
Resistance of the bulb 𝑅 = = = 𝟏𝟐𝟏𝟎 𝜴
𝐼 0.18

The unit ‘watt’ is very small. Therefore, in actual practice we use a much larger unit
called ‘kilowatt’.
1 kW = 1000 watts.
Commercial unit of electric energy = kilo Watt-hour (KWh)
6
1 kWh = 3.6 × 10 J
1 kWh = 1 unit of electric energy

Exercise :
An electric refrigerator rated 400 W operates 8 hour/day. An electric iron box rated 750
W is used for 2 hours a day. Calculate the cost of using these appliances for 30 days, if
the cost of 1 kWh is Rs. 3/-.
Solution
The total energy consumed by the refrigerator in 30 days would be
 = 400 W x 8 hour/day x 30 days
= 96000 W h or = 96 kW h
The total energy consumed by the iron box in 30 days
= 750 W×2 hour/day x 30 days
= 45000 Wh = 45 kWh
The total energy consumed by the refrigerator and iron box is
= 96 kWh + 45 kWh = 141 kWh
The sum of bill amount for 141 kWh at rate of Rs. 3 per 1 kWh is
= 141 × 3
= Rs. 423.
 CHAPTER-12
Magnetic Effects of Electric Current

TOPIC-1 ELECTRIC CURRENT , OHM’S LAW

Magnet :
Magnet is any substance that attracts iron or iron-like substances.
Properties of a magnet -
(i) Every magnet has two poles i.e., North and South.
(ii) Like poles repel each other.
(iii) Unlike poles attract each other.
(iv) A freely suspended bar magnet aligns itself in nearly north-south direction, with its
north pole towards geographical south direction.

Magnetic Field :
It is the area around a magnet in which its magnetic force can be experienced.

Magnetic Field lines :

The imaginary lines of magnetic field around a magnet are called magnetic field lines.

Properties of Magnetic Field lines :

(i) Field lines arise from North pole and end into South pole of the magnet.
(ii) Field lines are closed and continuous curves.
(iii) The density of the magnetic field lines are more in their poles.
(iv) Field lines never intersect each other as for two lines to intersect, there must be two
directions of magnetic field at a point, which is not possible.
(v) Direction of field lines inside a magnet is from South to North.
(vi) The relative strength of magnetic field is shown by degree of closeness of field
lines. Closer the lines, more will be the strength and farther the lines, less will be the
magnetic field strength.
MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR

Right-Hand Thumb Rule

Right hand thumb rule states that, “If you imagine holding a
current carrying wire in your right-hand with your thumb
pointing towards the direction of electric current flow then the
direction in which your fingers curl, gives the direction of
lines of force of the magnetic field”.

Magnetic Field due to a Current through a Straight Conductor

Tracing the pattern of magnetic field -

 Set the instruments as shown in figure .
 Place some iron fillings uniformly on the
card board.
 Then close the key so that current flows
through the wire.
 Gently tap the card board for few times ,
then we will find that the iron filings
align themselves showing a pattern of
concentric circles around the wire. They represent the magnetic field lines.
 The concentric circles representing the magnetic field around it would become
larger and larger as we move away from the wire
 The magnitude of the magnetic field produced at a given point increases as the
current through the wire increases.
 If the direction of current through the straight wire is reversed the direction of
magnetic field lines also get reversed

Magnetic Field due to a Current through a Circular Loop

 The magnetic field pattern due to a circular coil is as shown

in the given figure.
 At every point of current carrying circular loop, the
concentric circles representing the magnetic field around it
becomes larger and larger as we move away from the wire.
 At the center of the loop, the field appears as a straight line.
 The magnetic field produced by current-carrying circular
wire depends on -
(1) Amount of current flowing through the wire,
(2) The number of turns of coil,
Magnetic Field due to a Current in a Solenoid

 A coil of many circular turns of insulated copper wire

wrapped closely in the shape of a cylinder is called a
solenoid.
 The pattern of the magnetic field lines around a current-
carrying solenoid can be compare with the pattern of the
field with the magnetic field around a bar magnet
 One end of the solenoid behaves as a magnetic north
pole, while the other behaves as the south pole.
 The field lines inside the solenoid are in the form of parallel straight lines. This
indicates that the magnetic field is the same at all points inside the solenoid. That
is, the field is uniform inside the solenoid.
 The strength of magnetic field produced by a solenoid can be increased by
(a) Increasing the number of turns of the coil.
(b) Increasing the current flowing through the coil.

A strong magnetic field produced inside a solenoid can be

used to magnetise a piece of magnetic material, like soft
iron, when placed inside the coil. The magnet so formed is
called an electromagnet.

FORCE ON A CURRENT-CARRYING CONDUCTOR IN A MAGNETIC FIELD

 Force is exerted on the current-carrying aluminium

rod when it is placed in a magnetic field.
 The direction of force is reversed when the direction
of current through the conductor is reversed.
 If we interchange the two pole of magnet then the
direction of force acting on the current-carrying rod
gets reversed.
 It shows that the direction of the force on the
conductor depends upon the direction of current and
the direction of the magnetic field.
 The displacement of the rod is largest when the direction of current is at right
angles to the direction of the magnetic field.

Fleming’s Left Hand Rule :

Stretch the thumb, forefinger and middle finger of your left
hand such that they are mutually perpendicular. If
forefinger points in the direction of magnetic field, middle
finger in the direction of current then thumb will point in
the direction of motion or force.
ELECTRIC MOTOR

An electric motor is a rotating device that converts electrical energy to mechanical

energy.
 An electric motor consists of a rectangular coil of insulated copper wire.
 The coil is placed between the two poles of a magnetic field such that the arms
are perpendicular to the direction of the
magnetic field.
 The ends of the coil are connected to the two
halves of a split ring.
 The inner sides of these halves are insulated
and attached to an axle.
 The external conducting edges of split rings
touch two conducting stationary
brushes

A device that reverses the direction of flow of current through a circuit is called a
commutator. In electric motors, the split ring acts as a commutator.
The commercial motors use -
(i) an electromagnet in place of permanent magnet
(ii) large number of turns of the conducting wire in the current carrying coil
(iii) a soft iron core on which the coil is wound.
This enhances the power of the motor.
The soft iron core, on which the coil is wound is called an armature.
ELECTROMAGNETIC INDUCTION

Michael Faraday made an important breakthrough by discovering how a moving

magnet can be used to generate electric currents.
 A coil of wire having a large number of turns
the ends of which are connected to a
galvanometer
 When a strong bar magnet facing north pole
towards the coil is moved inside there is a
momentary deflection in the needle of the
galvanometer, say to the right.
 This indicates the presence of a current in the
coil.
 The deflection becomes zero when the motion of the magnet stops.
 Now withdraw the north pole of the magnet away from the coil. Now the
galvanometer is deflected toward the left, showing that the current is now set up
in the direction opposite to the first.
  The magnet was kept stationary and coil was moved, then also needle of the
galvanometer deflects.
 When the coil and the magnet are both stationary, there is no deflection in the
galvanometer.
 It is, thus, clear from this activity that motion of a magnet with respect to the coil
produces an induced potential difference, which sets up an induced electric
current in the circuit.

Two different coils of copper wire having large number of turns (say 50 and 100 turns
respectively) inserted over a non-conducting cylindrical roll, as shown in Fig.

 When plugged the key, we will observe that the needle of the galvanometer
instantly jumps to one side and just as quickly returns to zero, indicating a
momentary current in coil-2.
 As the current in the first coil changes, the magnetic field associated with it also
changes. Thus the magnetic field lines around the secondary coil also change.
 This process, by which a changing magnetic field in a conductor induces a
current in another conductor, is called electromagnetic induction.

Fleming’s Right hand rule :

Fleming’s Right hand rule states that if we arrange
our thumb, forefinger and middle finger of the right-
hand perpendicular to each other, then the thumb
points towards the direction of the motion of the
conductor relative to the magnetic field, the
forefinger points towards the direction of the
magnetic field and the middle finger points towards
the direction of the induced current.

ELECTRIC GENERATOR

An electric generator is a rotating device that converts mechanical energy to electrical

energy.
 An electric generator consists of a rotating rectangular coil placed between the
two poles of a permanent magnet.
 The two ends of this coil are connected to the two rings R1 and R2.
  The two conducting stationary brushes
B1 and B2 are kept pressed separately
on the rings R1 and R2, respectively.
 The two rings R1 and R2 are internally
attached to an axle.
 The axle may be mechanically rotated
from outside to rotate the coil inside the
magnetic field.
 Outer ends of the two brushes are
connected to the galvanometer to show
the flow of current in the given external
circuit.

In an electric generator, after every half rotation the polarity of the current in the
respective arms changes. Such a current, which changes direction after equal intervals
of time, is called an alternating current (AC).
To get a direct current (DC, which does not change its direction with time), a split-ring
type commutator must be used.

Alternate current (AC) : The current which reverses its direction periodically is called
alternate current.. In India, most of the power stations generate alternate current. The
direction of current changes after every 1/100 second in India. i.e.,
Frequency is 50 Hz

Direct Current (DC) : The current which does not reverse its direction and flows in
one direction is called direct current. Source of DC are cell, battery, and storage cells.
DC can be stored. Loss of energy during transmission over long distance is high.

TOPIC-2 DOMESTIC CIRCUITS

An electric circuit consists of three main wiring components:

(i) Live wire (positive) with red insulation cover.
(ii) Neutral wire (negative) with black insulation cover.
(iii) Earth wire with green insulation cover.
Domestic circuits are of two types -
(i) A circuit with 15 A rating, suitable for appliances with higher power ratings such as
geysers, air coolers, etc.
(ii) A circuit with 5 A rating for bulbs, fans, etc.
Safety devices :
Electric fuse is an important safety device used in domestic circuits. It prevents damage
to the appliances and the circuit due to overloading.
Earth wire is another important safety device used in domestic circuits. It protects us
from electric shock in case of leakage of current especially in metallic body appliances.
It provides a low resistance path for current in case of leakage of current.

Faults in the domestic circuits :

(i) Short-circuit : when the live wire and the neutral wire come into direct contact. In
such a situation, the current in the circuit abruptly increases. This is called short-
circuiting.
(ii) Overloading of an electric circuit : The overheating of electrical wire in any
circuit due to flow of a large current through it is called overloading of the electrical
circuit.
Reasons for the overloading :
 Overloading can occur when the live wire and the neutral wire come into direct
contact.
 Overloading can also occur due to an accidental hike in the supply voltage.
 Overloading is caused by connecting too many appliances to a single socket.