Electricity | Class 10 Science

1. Electric Current and Circuit Dynamics

Fundamental Definition

Electric current is the rate of flow of electric charges through a specific area in unit time.

Charge Carriers and Direction

In metallic wires, electrons are the charge carriers.
Conventional current was defined before electrons were discovered.
Conventional current is considered to flow from the positive terminal to the negative terminal of a cell through the external circuit.
The actual flow of electrons is in the opposite direction.

Electric Circuit

An electric circuit is a continuous and closed path through which electric current can flow.

A switch acts as a conducting link between the cell and an electrical component such as a bulb.

When the switch is open or the conducting path is broken, current stops flowing.

Quantitative Measures of Current

SI unit of charge = Coulomb (C)
Charge of one electron = −1.6 × 10⁻¹⁹ C
1 C corresponds to approximately 6 × 10¹⁸ electrons in magnitude of charge.

I = Q / t

Where:

I = electric current
Q = net charge flowing through the conductor
t = time taken

1 Ampere

One ampere is the current produced when 1 coulomb of charge flows through a conductor in 1 second.

1 A = 1 C / 1 s

Smaller Units

1 mA = 10⁻³ A
1 μA = 10⁻⁶ A

Measurement of Current

An ammeter is used to measure electric current.

It is always connected in series with the circuit.

2. Electric Potential and Potential Difference

Electric Pressure

Just as water flows through a pipe because of a pressure difference, electric charges require a difference in electric pressure to move through a conductor.

Source of Potential Difference

A battery, consisting of one or more cells, produces potential difference through chemical action.

The cell uses its stored chemical energy to maintain the potential difference and drive charges through an external circuit.

Definition

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

V = W / Q

V = potential difference
W = work done
Q = charge

One Volt

A potential difference of 1 volt exists when 1 joule of work is required to move 1 coulomb of charge.

1 V = 1 J / 1 C

Measurement of Potential Difference

A voltmeter measures potential difference.

It is always connected in parallel across the two points whose potential difference is being measured.

3. Circuit Diagram Symbols

Component	Representation / Function
Electric Cell	A long line represents the positive terminal and a short line represents the negative terminal.
Battery	Combination of multiple cells.
Open Switch	Circuit is broken and current cannot flow.
Closed Switch	Circuit is complete and current can flow.
Wire Joint	Indicates that wires are electrically connected.
Crossing Wires	Wires crossing without a joint are not electrically connected.
Electric Bulb	Converts electrical energy mainly into light and heat.
Resistor	A component having resistance R.
Rheostat	Variable resistance used to regulate current.
Ammeter	Measures current and is connected in series.
Voltmeter	Measures potential difference and is connected in parallel.

4. Ohm's Law and Resistance

Ohm's Law

At constant temperature, the potential difference across a metallic conductor is directly proportional to the current flowing through it.

V ∝ I

V = IR

V-I Graph

For an ohmic metallic conductor at constant temperature, a graph of potential difference V against current I is a straight line passing through the origin.

Resistance

Resistance is the property of a conductor that opposes the flow of electric charges.

One Ohm

The resistance of a conductor is 1 Ω when a potential difference of 1 V produces a current of 1 A.

1 Ω = 1 V / 1 A

Conductors and Resistance

Good conductors: Offer relatively low resistance.
Resistors: Components designed to provide appreciable resistance.
Poor conductors: Offer greater resistance than good conductors of comparable dimensions.
Insulators: Offer very high resistance.

5. Detailed Factors Affecting Resistance

Experimental observations show that the resistance of a uniform metallic conductor depends on its length, cross-sectional area, and the nature of the material.

1. Length

Resistance is directly proportional to the length of the conductor.

R ∝ l

Therefore, if the length of a wire is doubled, its resistance also doubles, provided other factors remain unchanged.

2. Area of Cross-section

Resistance is inversely proportional to the cross-sectional area.

R ∝ 1 / A

Therefore, a thicker wire offers less resistance than a thinner wire of the same material and length.

3. Nature of Material

Different materials possess different electrical resistive properties.

Electrical Resistivity

Combining the dependence on length and area gives:

R = ρl / A

Here, ρ (rho) is called the resistivity of the material.

SI unit of resistivity = Ω m
Resistivity is a characteristic property of the material.

Typical Resistivity Ranges

Material Type	Approximate Resistivity
Conductors	10⁻⁸ to 10⁻⁶ Ω m
Insulators	10¹² to 10¹⁷ Ω m
Silver	Approximately 1.60 × 10⁻⁸ Ω m

Alloys

Alloys generally have higher resistivity than their constituent metals and do not oxidise readily at high temperatures.

Because of these properties, alloys are commonly used in heating devices such as irons and toasters.

Transmission Lines

Copper and aluminium are commonly used in electrical transmission because they have relatively low resistivity.

6. Resistance of Resistor Systems

A. Resistors in Series

In a series combination, resistors are connected one after another.

Current in Series

The same current flows through every resistor.

Potential Difference

V = V₁ + V₂ + V₃

Derivation of Equivalent Resistance

Series Combination Derivation

From Ohm's Law: V = IR

Total voltage: V = V₁ + V₂ + V₃

Therefore: IR_s = IR₁ + IR₂ + IR₃

Dividing by I: R_s = R₁ + R₂ + R₃

R_s = R₁ + R₂ + R₃

Key Fact

Equivalent resistance in series is greater than any individual resistance.

B. Resistors in Parallel

In a parallel combination, resistors are connected between the same two points.

Potential Difference in Parallel

The potential difference across each resistor is the same.

Current

I = I₁ + I₂ + I₃

Derivation of Equivalent Resistance

Parallel Combination Derivation

From Ohm's Law: I = V / R

Total current: I = I₁ + I₂ + I₃

Therefore: V/R_p = V/R₁ + V/R₂ + V/R₃

Dividing by V: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃

1/R_p = 1/R₁ + 1/R₂ + 1/R₃

Key Fact

Equivalent resistance in parallel is lower than the smallest individual resistance.

C. Practical Comparison

Series

Same current through all components.
Total resistance increases.
Failure of one component can break the entire circuit.
Components requiring different currents cannot operate independently.

Parallel

Same potential difference across each branch.
Total resistance decreases.
Branches can operate independently.
Current divides according to the resistance of each branch.

7. Heating Effect of Electric Current

Concept

When current flows through a resistor, electrical energy can be converted into heat energy.

In a purely resistive circuit, the electrical energy supplied by the source is entirely dissipated as heat.

Energy Input and Power

Derivation

Power = Energy / Time

P = VQ / t

Since Q/t = I

P = VI

Therefore, energy consumed in time t: E = VIt

Joule's Law of Heating

H = I²Rt

According to Joule's law, the heat produced is:

Directly proportional to I².
Directly proportional to R.
Directly proportional to t.

Practical Applications

Electric irons
Toasters
Electric heaters
Heating coils

Electric Bulb

The filament of an electric bulb becomes extremely hot and emits visible light.

Tungsten is used because it has a very high melting point of approximately 3380°C.

Bulbs are filled with inactive gases such as nitrogen or argon to reduce degradation of the filament.

Electric Fuse

An electric fuse is a safety device connected in series with a circuit.

If the current exceeds the safe limit, the fuse wire heats up, melts and breaks the circuit.

Fuse ratings may include values such as 1 A, 5 A and 10 A, depending on the intended circuit.

8. Electric Power

Electric power is the rate at which electrical energy is consumed or dissipated.

Important Formulae

P = VI

P = I²R

P = V²/R

SI Unit

The SI unit of electric power is the watt (W).

One Watt

A device consumes one watt of power when it operates with a potential difference of 1 V and current of 1 A.

1 W = 1 V × 1 A

Commercial Unit of Electrical Energy

The commercial unit of electrical energy is the kilowatt-hour (kWh).

It is commonly called one "unit" of electricity.

1 kWh = 3.6 × 10⁶ J

Important Concept

Electrons are not consumed by electrical appliances.

What we pay for is the electrical energy transferred or consumed by the appliances.

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