NCERT Class 10 Science Chapter 12: Electricity - Master Concepts and Formulas

Introduction to Electricity

Electricity plays a pivotal role in modern civilization. It is a controllable and convenient form of energy used in homes, schools, hospitals, and industries. Understanding the nature of electricity involves investigating what constitutes electric current, how it flows through a circuit, and the factors that control or regulate its flow. In this chapter, we explore electric current, electric potential difference, Ohm's law, resistance, combination of resistors, heating effects of electric current, and electric power in full alignment with the CBSE Class 10 Science curriculum.

Electric Current and Circuit

An electric current is expressed by the amount of charge flowing through a particular area in unit time. In other words, it is the rate of flow of electric charges. In circuits using metallic wires, electrons constitute the flow of charges. However, electrons were not known at the time when the phenomenon of electricity was first observed. Therefore, electric current was considered to be the flow of positive charges and the direction of flow of positive charges was taken to be the direction of electric current.

Understanding Electric Charge

Electric charge is a fundamental property of matter. It can be either positive or negative. The SI unit of electric charge is the Coulomb (C). One Coulomb is equivalent to the charge contained in nearly 6 × 10¹⁸ electrons. An electron possesses a negative charge of 1.6 × 10^-19 C.

Definition of Electric Current

If a net charge Q flows across any cross-section of a conductor in time t, then the current I through the cross-section is given by:

I = Q / t

The SI unit of electric current is the Ampere (A), named after the French scientist André-Marie Ampère. One Ampere is defined as the flow of one Coulomb of charge per second:

1 A = 1 C / 1 s

Small quantities of current are expressed in milliampere (1 mA = 10^-3 A) or microampere (1 μA = 10^-6 A). An instrument called an ammeter measures electric current in a circuit. It is always connected in series in a circuit through which the current is to be measured.

Electric Circuit Diagram

A continuous and closed path of an electric current is called an electric circuit. A schematic diagram representing different components connected in a circuit using standard symbols is called a circuit diagram.

Electric Potential and Potential Difference

Electrons do not move in a copper wire by themselves. For charges to flow in a conducting metallic wire, there must be a difference of electric pressure—called the electric potential difference—along the conductor.

Concept of Electric Potential Difference

The electric potential difference between two points in an electric circuit carrying some current is defined as the work done to move a unit charge from one point to the other.

Potential Difference (V) = Work done (W) / Charge (Q)

V = W / Q

The SI unit of electric potential difference is the Volt (V), named in honour of Alessandro Volta. One Volt is defined as the potential difference between two points in a current-carrying conductor when 1 Joule of work is done to move a charge of 1 Coulomb from one point to another.

1 V = 1 J / 1 C = 1 J C^-1

Measuring Potential Difference

The potential difference is measured by means of an instrument called the voltmeter. The voltmeter is always connected in parallel across the points between which the potential difference is to be measured, because it has a very high resistance and draws negligible current from the main circuit.

Ohm's Law

In 1827, German physicist Georg Simon Ohm discovered the relationship between the current flowing through a metallic wire and the potential difference across its terminals.

Statement and Mathematical Expression

Ohm's Law states that the electric current flowing through a metallic conductor is directly proportional to the potential difference applied across its ends, provided its temperature and other physical conditions remain constant.

V ∝ I

V = R × I

where R is a constant for the given metallic wire at a given temperature and is called its resistance.

Resistance and Factors Affecting Resistance

Resistance is that property of a conductor by virtue of which it opposes the flow of charges through it. Its SI unit is the Ohm (Ω).

1 Ohm (Ω) = 1 Volt / 1 Ampere

The resistance of a uniform metallic conductor depends on the following factors:

• Length of the Conductor (l): Resistance is directly proportional to the length of the conductor (R ∝ l). Doubling the length doubles the resistance.
• Area of Cross-Section (A): Resistance is inversely proportional to the area of cross-section (R ∝ 1/A). A thicker wire offers less resistance than a thinner wire.
• Nature of the Material: Different materials offer different resistances depending on their atomic structure and electron density.
• Temperature: For pure metals, resistance increases with an increase in temperature.

Resistivity

Combining the proportionalities, we get:

R ∝ l / A ⇒ R = ρ (l / A)

where ρ (rho) is a constant of proportionality called the electrical resistivity of the material of the conductor.

• The SI unit of resistivity is Ohm-metre (Ω·m).
• Resistivity is a characteristic property of the material and does not depend on the length or thickness of the wire.
• Conductors like copper and aluminium have very low resistivities (10^-8 Ω·m to 10^-6 Ω·m).
• Insulators like rubber and glass have \textremely high resistivities (10¹² Ω·m to 10¹⁷ Ω·m).
• Alloys such as Nichrome, Manganin, and Constantan have higher resistivity than their constituent metals and do not oxidize readily at high temperatures, making them ideal for heating element applications.

System of Resistors

In practical circuits, combinations of resistors are used to achieve desired current levels or total resistance values. There are two primary modes of combining resistors: series and parallel.

Resistors in Series

When two or more resistors are connected end-to-end consecutively, they are said to be connected in series.

• Current: The current passing through each resistor in a series circuit is the same (I_total = I₁ = I₂ = I₃).
• Voltage: The total potential difference across the combination equals the sum of potential differences across individual resistors (V_total = V₁ + V₂ + V₃).
• Equivalent Resistance (R_s): Applying Ohm's law, V = IR, we get IR_s = IR₁ + IR₂ + IR₃, which yields:

R_s = R₁ + R₂ + R₃ + ... + R_n

Thus, when several resistors are connected in series, the equivalent resistance is equal to the sum of individual resistances, and is greater than the highest individual resistance.

Resistors in Parallel

When two or more resistors are connected across two common points, they are said to be connected in parallel.

• Voltage: The potential difference across each resistor is equal to the voltage applied across the parallel combination (V_total = V₁ = V₂ = V₃).
• Current: The total current entering the combination divides among the branches such that the total current is the sum of currents in individual branches (I_total = I₁ + I₂ + I₃).
• Equivalent Resistance (R_p): Using I = V / R, we obtain V / R_p = V / R₁ + V / R₂ + V / R₃, leading to:

1 / R_p = 1 / R₁ + 1 / R₂ + 1 / R₃ + ... + 1 / R_n

Thus, the reciprocal of the total equivalent resistance of a parallel combination is equal to the sum of the reciprocals of the individual resistances.

Heating Effect of Electric Current

When an electric current flows through a purely resistive conductor, the electrical energy supplied by the source is continuously dissipated entirely in the form of heat. This phenomenon is known as the heating effect of electric current.

Joule's Law of Heating

Consider a current I flowing through a resistor of resistance R for time t when potential difference V is applied.

Work done, W = Q × V

Since Q = I × t and V = I × R, substituting these values gives:

H = I² R t

This relationship is known as Joule's Law of Heating. It states that heat produced in a resistor is:

• Directly proportional to the square of current for a given resistance.
• Directly proportional to resistance for a given current.
• Directly proportional to the time for which current flows through the resistor.

Practical Applications of Heating Effect

The heating effect of electric current has several indispensable domestic and industrial applications:

• Electric Heating Appliances: Electric irons, toasters, ovens, kettles, and room heaters utilize elements made of high-resistivity alloys like Nichrome.
• Electric Bulb: The filament of an electric lamp is made of tungsten (melting point 3380 °C) because it can retain heat at high temperatures and emit light without melting. Bulbs are filled with chemically inactive gases like nitrogen and argon to prolong filament life.
• Electric Fuse: A safety device connected in series in domestic circuits to protect appliances from overcurrent and short-circuits. It consists of a wire made of an alloy of low melting point (e.g., tin-lead alloy). When excess current flows, heat melts the fuse wire and breaks the circuit.

Electric Power

Power is defined as the rate at which electrical energy is consumed or dissipated in an electric circuit.

Definition and Formulas

Power (P) = Work done (W) / Time (t) = Energy consumed / Time

Since W = V × I × t, we have:

P = V × I

Using Ohm's law (V = IR), electric power can also be expressed as:

P = I² R = V² / R

The SI unit of electric power is the Watt (W). One Watt is the power consumed by a device that carries 1 Ampere of current when operated at a potential difference of 1 Volt.

Commercial Unit of Electrical Energy

The SI unit Joule is very small, so a larger commercial unit called the kilowatt-hour (kWh), commonly known as a 'unit', is used for commercial energy consumption.

1 kWh = 1 kW × 1 hour = 1000 W × 3600 s = 3.6 × 10⁶ Joules (J)

Important Questions and Answers

Q1: Define 1 Ohm resistance and state Ohm's law.

Answer: Ohm's Law states that at constant temperature, the electric current flowing through a conductor is directly proportional to the potential difference across its ends (V = IR).
1 Ohm Resistance: The resistance of a conductor is said to be 1 Ohm if a current of 1 Ampere flows through it when a potential difference of 1 Volt is applied across its ends (1 Ω = 1 V / 1 A).

Q2: Why are copper and aluminium wires usually employed for electricity transmission?

Answer: Copper and aluminium possess \textremely low electrical resistivity (ρ ~ 10^-8 Ω·m). Consequently, they offer very minimal opposition to the flow of electric current, minimizing energy loss in the form of heat during long-distance transmission.

Q3: An electric iron consumes energy at a rate of 840 W when heating is at the maximum rate and 360 W when the heating is at the minimum. The voltage is 220 V. Calculate the current and resistance in each case.

Answer:
Case 1 (Maximum Heating, P = 840 W, V = 220 V):
Current, I = P / V = 840 / 220 = 3.82 A
Resistance, R = V / I = 220 / 3.82 = 57.60 Ω

Case 2 (Minimum Heating, P = 360 W, V = 220 V):
Current, I = P / V = 360 / 220 = 1.64 A
Resistance, R = V / I = 220 / 1.64 = 134.15 Ω

Q4: Why is a parallel arrangement used for domestic wiring instead of a series arrangement?

Answer: A parallel arrangement is preferred in household circuits for the following reasons:

• In parallel, each appliance receives the full mains voltage (220 V in India).
• If one appliance breaks down or is switched off, other appliances continue to operate independently.
• Total circuit resistance decreases, allowing each appliance to draw the required current according to its individual power rating.

Q5: An electric refrigerator rated 400 W operates 8 hours/day. What is the cost of energy to operate it for 30 days at ₹ 3.00 per kWh?

Answer:
Total energy consumed in 1 day = 400 W × 8 h = 3200 Wh = 3.2 kWh
Total energy consumed in 30 days = 3.2 kWh × 30 = 96 kWh
Cost of energy = 96 kWh × ₹ 3.00 = ₹ 288.00

Chapter Summary

• Electric Current (I): The rate of flow of electric charges; measured in Amperes (A) using an ammeter connected in series (I = Q / t).
• Potential Difference (V): Work done per unit charge in moving it between two points; measured in Volts (V) using a voltmeter connected in parallel (V = W / Q).
• Ohm's Law: V = IR at constant temperature. Resistance (R) depends on length (l), area (A), material (ρ), and temperature.
• Resistivity (ρ): Material property measured in Ω·m; low for conductors, high for insulators/alloys.
• Series Combination: R_s = R₁ + R₂ + ... + R_n; current remains constant, voltage divides.
• Parallel Combination: 1/R_p = 1/R₁ + 1/R₂ + ... + 1/R_n; voltage remains constant, current divides.
• Joule's Law of Heating: Heat generated, H = I²Rt; applied in fuses, electric bulbs, irons, and heaters.
• Electric Power (P): P = VI = I²R = V²/R; SI unit is Watt (W).
• Commercial Energy Unit: 1 kWh = 3.6 × 10⁶ J.