Electricity

Introduction
→ Charge is a fundamental particle in an atom. It may be positive or negative.
→ Like charges repel each other.
→ Unlike charges attract each other.
→ Coulomb (C) : S. I. unit of charge
→ 1 Coulomb charge = Charge present on approx. 6 × 1018 electrons
→ Charge on 1 electron = Negative charge of 1.6 × 10-19 C
i.e. Q = ne
Where, Q = Charge (total)
n = No. of electrons
e = Charge on 1 electron

Current

Current = Charge/Time ⇒ I = Q/T

• Current (I): The rate of flow of charge is called current.

⇒ 1 A = 1 Cs-1
S. I. unit of current = Ampere (A)

⇒ 1 mA = 10-3 A
⇒ 1 µA = 10-6 A

→ Current is measured by Ammeter. Its symbol is

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 1

 Electricity

→ Ammeter has low resistance and always connected in series.

→ Direction of current is taken opposite to flow of electrons as electrons were

not known at the time when the phenomenon of electricity was discovered
first and current was considered to be flow of positive charge.

Potential Difference

• Potential Difference (V): Work done to move a unit charge from one point to
another.
V = W/Q

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

→ S. I. unit of Potential difference = Volt (V)

1 V = 1 JC-1

1 Volt: When 1 joule work is done in carrying one Coulomb charge then
potential difference is called 1 volt.
V = W/Q

Voltmeter: It is an instrument to measure the potential difference.

→ It has high resistance and always connected in parallel. Symbol is

→ Cell is the simplest device to maintain potential difference.

→ Current always flow from higher potential to lower potential.

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 2

 Electricity

Ohm’s Law

Potential difference across the two points of a metallic conductor is directly

proportional to current passing through the circuit provided that temperature
remains constant.

V∝I
Mathematical expression for Ohm’s law

⇒ V = IR

→ R is a constant called resistance for a given metal.

V-I graph for Ohm’s law

Resistance (R): It is the property of a conductor to resist the flow of

charges through it.

Ohm (Ω): S. I. unit of resistance.

1 ohm = 1 volt/1ampere

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 3

 Electricity

→ When potential difference is 1 V and current through the circuit is 1 A, then

resistance is 1 ohm.

Rheostat: Variable resistance is a component used to regulate current

without changing the source of voltage.

Factors on which the Resistance of a Conductor depends

Resistance of a uniform metallic conductor is:

directly proportional to the length of conductor,

inversely proportional to the area of cross-section,
directly proportional to the temperature and
depend on nature of material.

Resistivity (P): It is defined as the resistance offered by a cube of a

material of side 1m when current flows perpendicular to its opposite
faces.

Its S.I. unit is ohm-metre (Ωm).

→ Resistivity does not change with change in length or area of cross-section

but it changes with change in temperature.

→ Range of resistivity of metals and alloys is 10-8 to 10-6 Ωm.

→ Range of resistivity of insulators is 1012 to 1017 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.

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 4

 Electricity

→ Copper and aluminium are used for electrical transmission lines as they
have low
resistivity.

Resistors in Series

→ When two or more resistors are connected end to end, the arrangement is
called series
combination.

Total/resultant/overall/effective resistance in series

Rs = R 1 + R 2 + R 3

→ Current through each resistor is same.

→ Equivalent resistance is larger than the largest individual resistance.

→ Total voltage = Sum of voltage drops

V = V1 + V2 + V3

Voltage across each resistor

V1 = IR1

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 5

 Electricity

V2 = IR2 [V1 + V2 + V3 = V]
V3 = IR3V = IR

⇒ V = IR1 + IR2 + IR3

∝ IR = I(R1 + R2 + R3)
∝ R = R 1 + R2 + R3

Resistors in Parallel

→ Voltage across each resistor is same and equal to the applied voltage.

→ Total current is equal to sum of currents through the individual reistances.

⇒ V/R = V/R1 + V/R2 + V/R3

I = I1 + I2 + I3

→ Reciprocal of equivalent resistance is equal to sum of reciprocals of

individual resistances.
1/Rp = 1/R1 + 1/R2 + 1/R3

→ Equivalent resistance is less than the value of the smallest individual

resistance in the combination.

Advantages of Parallel Combination over Series Combination

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 6

 Electricity

In series circuit, when one component fails, the circuit is broken

and none of the component works.

Different appliances have different requirement of current. This

cannot be satisfied in series as current remains same.

The total resistance in a parallel circuit is decreased.

Heating Effect of Electric Circuit

→ If an electric circuit is purely resistive, the source of energy continually get

dissipated entirely in form of heat. This is known as heating effect of electric
current.

As E = P×T ∝ VIt {E = H}
Heat produced, H = VIt {V = IR}
Or, Heat produced, H = I2Rt

Joule’s Law of Heating Effect of Electric Current

square of current, H ∝ I2
→ It states that the heat produced in a resistor is (i) directly proportional to

→ It is directly proportional to resistance for a given current, H ∝ R

conductor, H ∝ t.
→ It is directly proportional to time for which current flows through the

So, H = I2Rt

→ Heating effect is desirable in devices like electric heater, electric iron,

electric bulb, electric fuse, etc.

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 7

 Electricity

→ Heating effect is undesirable in devices like computers, computer monitors

(CRT), TV, refrigerators etc.

→ In electric bulb, most of the power consumed by the filament appears a

heat and a small part of it is radiated in form of light.

Filament of electric bulb is made up of tungsten because:

it does not oxidise readily at high temperature.

it has high melting point (3380º C).

→ The bulbs are filled with chemically inactive gases like nitrogen and argon to
prolong the life of filament.

Electric Fuse: It is a safety device that protects our electrical appliances

in case of short circuit or overloading.

→ Fuse is made up of pure tin or alloy of copper and tin.

→ Fuse is always connected in series with live wire.

→ Fuse has low melting point.

→ Current capacity of fuse is slightly higher than that of the appliance.

Electric Power: The rate at which electric energy is consumed or

dissipated in an electric circuit.

⇒ P = I2R = V2/R
P = VI

⇒ 1 Watt = 1 volt × 1 ampere

S.I. unit of power = Watt (W)

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 8

 Electricity

⇒ 1 KWh = 3.6 × 106 J

→ Commercial unit of electric energy = Kilo Watt hour (KWh)

⇒ 1 KWh = 1 unit of electric energy

MATH TUTOR , H.NO. 12 Deen Dayal Nagar,Bharatpur (9610062196) Page 9