Electricity class 10 - Notes, Solved Numerical

Introduction

Definition of Electricity

Electricity is a form of energy that is produced due to the movement of electric charges (electrons) in a conductor.
In simple terms, electricity is the flow of electric charge through a closed path or circuit.

Electricity = Flow of electrons through a conductor.

Origin of Electricity

When free electrons in a conductor move due to the application of potential difference, an electric current is produced.
Electricity originates because of the movement of these electrons in response to a voltage applied across the conductor.

Types of Electricity

1. Static Electricity – charges at rest (e.g., lightning, rubbed balloon)

2. Current Electricity – charges in motion (used in circuits and devices)

Electric Charge

Definition:

Electric charge is a fundamental property of matter due to which materials experience electric force when placed near other charged materials.

Concept:

Every substance is made up of atoms that contain electrons and protons, both of which carry charge.

                        Electrons (e–) → carry negative charge
                        Protons (p⁺) → carry positive charge
                        Neutrons (n⁰) → have no charge (neutral)

Types of Electric Charges
1. Positive charge (+): carried by protons
2. Negative charge (–): carried by electrons
like charges repel each other, unlike charges attract each other.

Unit and Symbol of Charge:
Symbol: Q or q
SI Unit: Coulomb (C)
Other Units: μC (microcoulomb), nC (nanocoulomb)
Define1 coulomb (C): 1Coulomb is the charge transferred when 1 ampere current flows for 1 second.
                        1 C = 1 A × 1 s

Quantization of Charge:
Electric charge is quantized, which means:
                        Q = n × e
where Q = total charge

n = number of electrons

e = charge of one electron = 1.6 × 10^-19 C.

Example:
If 1 million (10⁶) electrons are removed from a body, the charge on it will be:
Q = 10⁶ × 1.6 × 10^-19 = 1.6 × 10⁻¹³ C

Electric Current

Definition:

·         The rate of flow of electric charge through a conductor is known as electric current.

Formula:

                       I = Q / t

Where:
I = Current (Ampere)
Q = Charge (Coulomb)
t = Time (seconds)

SI Unit of Electric current: Ampere (A)

Definition: 1 Ampere
1 ampere is the current when 1 coulomb of charge flows through a conductor in 1 second.

Other units:

Milliampere (mA) → 1 A = 1000 mA

Microampere (µA) → 1 A = 10⁶ µA

Concept:

Electric current is the flow of electric charges (electrons) through a conductor like a copper wire.

How do charges flow:

In metals, current flows due to movement of electrons from the negative terminal to the positive terminal of the battery.
But, conventional direction of current is positive to negative.

Ammeter – Instrument to Measure Current

How to connect an ammeter?

1.     Always connected in series with the circuit.
(So that the entire current flows through it.)

2.     Has very low resistance,
so it does not reduce the current flowing in the circuit.

3.     The positive terminal ( + ) of the ammeter
is connected to the positive terminal of the battery.

4.     The negative terminal ( – )
is connected towards the negative terminal of the battery.

Why Ammeter in Series?

In series, the same current passes through every component of circuit.

To measure that current accurately, ammeter must be in the same path.

If you connect ammeter in parallel, it may get damaged because of its low resistance.

Potential Difference (Voltage)

Definition:

The potential difference between two points is the work done to move one coulomb of charge from one point to another.

Formula:

           V=W/Q

Where:

V = Potential Difference (Volt)

W = Work done (Joule)

Q = Charge (Coulomb)

Unit of Potential Difference:

SI Unit of Potential Difference: Volt (V)

Definition: 1 Volt
If 1 joule of work is needed to move 1 coulomb of charge, then the potential difference is 1 volt.

Other units used:

millivolt (mV)

kilovolt (kV)

Concept:

Potential Difference (P.D.) is the work done in moving a unit positive charge between two points in an electric circuit.

Why Does Potential Difference Occur?

A battery or cell has two terminals: positive (+) and negative (–).

Inside the cell, chemical reactions create an electric pressure that pushes charges.

This electric pressure causes charges to flow, just like water flows due to pressure difference.

This electric pressure is the potential difference.

How is Potential Difference Created?

A cell or battery maintains potential difference by:

Pulling electrons towards the positive terminal

Pushing electrons away from the negative terminal

           This creates a difference in energy levels between the two terminals.

How Do We Measure Potential Difference?

Using a Voltmeter:

Always connected in parallel across the component.

Has high resistance so that it does not draw current.

Why parallel?

Because potential difference across two points is same only when connected in parallel.

Ohms Law:

Statement of Ohm’s Law

"At constant temperature, the electric current (I) flowing through a conductor is directly proportional to the potential difference (V) across its ends."

Mathematically:

V∝I

To remove proportionality:

V = IR

Where:

V = Potential difference (Volt)

I = Current (Ampere)

R = Resistance (Ohm, Ω)

Meaning of Ohm’s Law

If you increase the voltage, the current increases.
If voltage decreases, current decreases.
The ratio V/I is constant for a given conductor at constant temperature.
This constant is called Resistance (R).

Resistance (R)

Resistance is the opposition offered by a material to the flow of electric current.

Formula:

R=V/I

Unit: Ohm (Ω)

Definition: 1 ohm

1 ohm is the resistance when 1 volt produces 1 ampere of current.

Conditions for Ohm’s Law to Hold True

Temperature must remain constant.
Physical conditions (length, shape, material) must remain unchanged.
Applicable mainly to metallic conductors.
If temperature rises → resistance increases → Ohm’s law may not hold.

V–I Graph for Ohmic Conductors

When voltage is increased and current is measured:

The graph of Voltage (V) vs Current (I) is a straight line.
The straight line shows direct proportionality.
Slope of the graph = Resistance (R)
A steeper line → more resistance.

Numerical 1

Question:
Find the current flowing through a conductor of resistance 10 Ω when a potential difference of 5 V is applied.

Solution:
Given:
R = 10 Ω, V = 5V

Using Ohm’s law:

I = V/R = 5/10 = 0.5 A

Answer:

I = 0.5 A

Factors Affecting Resistance

Resistance is the property of a conductor that opposes the flow of electric current. It is denoted by R and its SI unit is ohm (Ω).
The resistance of a conductor depends on the following four main factors:

1. Length of the Conductor (L)

Resistance is directly proportional to the length of the conductor.
Longer wire → more resistance
Shorter wire → less resistance

Reason:

Electrons collide more with atoms in a longer wire, which opposes current flow.

Relation:

R ∝ L

Example:

A long electric wire used in heaters has more resistance than a short wire of the same material.

2. Area of Cross-Section (A)

Resistance is inversely proportional to the area of cross-section.
Thicker wire → less resistance
Thinner wire → more resistance

Reason:

A thick wire provides more space for electrons to move, reducing opposition.

Relation:

R ∝ 1 / A

Example:

House wiring uses thick copper wires to reduce resistance.

3. Nature of Material

Different materials have different resistances.

Good conductors (Copper, Silver, Aluminium) → low resistance
Insulators (Rubber, Glass, Plastic) → very high resistance

This property is also described using resistivity (ρ).

Relation:

R ∝ ρ

Example:

Copper wire has less resistance than iron wire of the same length and thickness.

4. Temperature of the Conductor

For metallic conductors, resistance increases with increase in temperature.
For semiconductors, resistance decreases with increase in temperature.

Reason:

At higher temperature, atoms vibrate more, increasing collisions with electrons.

Example:

The filament of an electric bulb offers more resistance when it becomes hot.

Combined Formula (Very Important for Exams)

All factors together give:

R = ρ L / A

Where:

R = resistance

ρ = resistivity of material

L = length of conductor

A = area of cross-section

Combination of Resistance

When two or more resistors are connected in a circuit, they form a combination of resistances. There are two main types:

1. Series Combination of Resistance

Definition

When resistors are connected end to end, so that same current flows through each resistor, it is called series combination.

Equivalent Resistance:

R = R₁+ R₂ + R₃

Characteristics

Same current flows through all resistors
Total resistance is more than the largest resistance
If one resistor breaks, entire circuit stops

Example

If R₁=2Ω, R₂=3Ω, R₃=5Ω

R = R₁+ R₂ + R₃

R = 2 + 3 + 5

R = 10Ω

Uses

Electric heaters
Fuse wire circuits

2. Parallel Combination of Resistance

Definition

When resistors are connected between same two points, so that same voltage appears across each resistor, it is called parallel combination.

Equivalent Resistance

1 / R =1 / R₁ +1 / R₂+1 / R₃

Characteristics

Same voltage across each resistor
Total resistance is less than the smallest resistance
If one resistor fails, others continue to work

Example

If R₁= 6Ω, R₂= 3Ω, R₃= 2Ω

1 / R =1 / R₁ +1 / R₂+1 / R₃

1 / R = 1 / 6 + 1 / 3 + 1 / 2

1 / R = 11 / 6

R = 0.54 Ω

Uses

Household wiring
Electrical appliances

Comparison: Series vs Parallel

Features	Series	Parallel
*Current*	Same	Divided
*Voltage*	Divided	Same
*Equivalent Resistance*	High	Low
*Appliance Failure*	Whole circuit stops	Others work
*Household use*	No	Yes

Heating Effect of Electric Current

What is Heating Effect of Electric Current?

When an electric current flows through a conductor, the conductor becomes hot.
This phenomenon is called the heating effect of electric current.

Reason:

Electrical energy is converted into heat energy due to the resistance of the conductor.

Joule’s Law of Heating

According to Joule’s law, the heat produced in a conductor depends on:

1. Square of current (I²)

2. Resistance of the conductor (R)

3. Time for which current flows (t)

Mathematical Expression

H = I²Rt

Where:

H = heat produced (joule)

I = current (ampere)

R = resistance (ohm)

t = time (second)

Derivation of Joule’s Law (Board-Oriented)

We know from Ohm’s law:

V=IR

Electrical energy consumed:

E=VIt

Substitute V=IR:

E = (IR)It

E = I²Rt

Since electrical energy is converted into heat:

H = I²Rt

Factors Affecting Heat Produced:

1. Current (I)
More current → More heat

2. Resistance (R)
More resistance → More heat

3. Time (t)
Longer time → More heat

Applications of Heating Effect

1. Electric Heater

Uses high resistance wire (nichrome)
Produces large amount of heat

2. Electric Iron

Converts electrical energy into heat
Used for ironing clothes

3. Electric Bulb

Tungsten filament becomes white-hot and glows

4. Electric Fuse

Protects appliances
Melts when excess current flows

Why Nichrome is Used as Heating Element?

Nichrome is used because:

High resistivity
High melting point
Does not oxidize easily
Can withstand high temperature

Disadvantages of Heating Effect

Wastage of electrical energy.
Can damage appliances if current is too high.
Risk of fire due to overheating.

​

Numerical 1 (Basic)

A current of 2 A flows through a resistor of 5 Ω for 10 seconds. Find the heat produced.

Solution:

Given:
I = 2 A, R =5 Ω, t = 10 s

H = I²R t

H = (2)² x 5 x 10

H = 200 J

Answer: 200 J

Numerical 2 (Board Level)

An electric iron of resistance 20 Ω draws a current of 5 A. Calculate the heat produced in 1 minute.

Solution:

Given:
R = 20 Ω, I = 5 A, t = 1 minute = 60 s

H = I²R t

H = (5)² x 20 x 60

H = 25 x 20 x 60

H = 30000 J

Answer: 30 kJ

Numerical 3 (Using Ohm’s Law)

A resistor of 10 Ω is connected to a 20 V battery. Find the heat produced in 5 minutes.

Solution:

Given:
R = 10 Ω, V = 20 V, t = 5 minute = 300 second

First find current:

V = IR

I = V / R

I = 20 / 10

I = 2 A

Now heat:

H = I²R t

H = (2)² x 10 x 300

H = 12000 J

Answer: 12 kJ

Numerical 4 (Conceptual)

Why do electric heaters use nichrome wire?

Answer:
Nichrome has:

· High resistivity

· High melting point

· Does not oxidize easily

Hence, it produces more heat without burning.

Numerical 5 (Appliance Based)

A bulb draws a current of 0.5 A when connected to a 220 V supply. Find the heat produced in 10 seconds.

Solution:

Given:
I = 0.5 A, V = 220 V, t = 10 second

First find resistance:

V = IR

R = V / I

R = 220 / 0.5

R = 440 Ω

Now heat:

H = I²R t

H = (0.5)² x 440 x 10

H = 1100 J

Answer: 1100 J

Numerical 6 (Power Relation)

An electric heater works on 1000 W at 220 V. Find the heat produced in 5 minutes.

Solution:

Given:
P = 1000 W, V = 220 V, t = 5 minute = 300 second

H = P x t

H = 1000 x 300

H = 300000 J

Answer: 300 kJ

Numerical 7 (Comparative Question)

Two resistors R₁ and R₂ produce heat in the ratio 1:4. If current is same, find the ratio of resistances.

Solution:

Given:

H₁ : H₂ = 1 : 4
H₁ / H₂ = 1 / 4

As, H ∝ R

So, R₁ : R₂ = 1 : 4

Download: Electricity worksheet Numerical pdf download

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