Electricity Class 10 Chapter 12 Notes

Key Terms and Definitions

Electric Current (I)

The rate of flow of electric charge through a conductor. Its SI unit is Ampere (A). I = Q/t, where Q is charge and t is time.

Potential Difference (V)

The work done to move a unit charge from one point to another. Its SI unit is Volt (V). V = W/Q, where W is work done.

Resistance (R)

The property of a conductor to resist the flow of charges through it. Its SI unit is Ohm (Ω).

Ohm's Law

At a constant temperature, the current flowing through a conductor is directly proportional to the potential difference across its ends. V ∝ I or V = IR.

Resistivity (ρ)

The resistance offered by a cube of a material of side 1m when current flows perpendicular to its opposite faces. It is a characteristic property of the material. Its SI unit is Ohm-meter (Ωm).

Electric Power (P)

The rate at which electric energy is consumed or dissipated in an electric circuit. Its SI unit is Watt (W). P = VI.

Joule's Law of Heating

The heat produced in a resistor is directly proportional to (i) the square of the current, (ii) the resistance, and (iii) the time for which the current flows. H = I²Rt.

Must-Remember Formulas & Concepts

• {"point":"Electric Current: I = Q/t (Charge/time)"}
• {"point":"Potential Difference: V = W/Q (Work/Charge)"}
• {"point":"Ohm's Law: V = IR"}
• {"point":"Resistance Formula: R = ρ (L/A), where ρ is resistivity, L is length, A is area of cross-section."}
• {"point":"Resistors in Series: R_s = R₁ + R₂ + R₃ + ..."}
• {"point":"Resistors in Parallel: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃ + ..."}
• {"point":"Electric Power Formulas: P = VI = I²R = V²/R"}
• {"point":"Joule's Law of Heating: H = I²Rt"}
• {"point":"Commercial Unit of Energy: 1 kilowatt-hour (kWh) = 3.6 x 10⁶ Joules."}
• {"point":"Charge of one electron = 1.6 x 10⁻¹⁹ C."}

Understanding Ohm's Law and Resistance

Ohm's Law is a cornerstone of electricity. It describes the relationship between potential difference (V), current (I), and resistance (R). The law states that if the physical conditions (like temperature) of a conductor remain constant, the electric current flowing through it is directly proportional to the potential difference applied across its ends. Mathematically, this is written as V ∝ I. To turn this proportionality into an equation, we introduce a constant, 'R', which is called the resistance of the conductor. This gives us the famous formula: V = IR.

Resistance is essentially the 'opposition' a material offers to the flow of electric current. But what determines this resistance? Four main factors:

1. Length of the Conductor (L): Resistance is directly proportional to the length. A longer wire has more resistance than a shorter one (R ∝ L).
2. Area of Cross-section (A): Resistance is inversely proportional to the area of cross-section. A thicker wire has less resistance than a thinner one (R ∝ 1/A).
3. Nature of the Material: Different materials have different inherent abilities to resist current. This property is quantified by resistivity (ρ).
4. Temperature: For most conductors, resistance increases with an increase in temperature.

Combining the first three factors, we get the formula for resistance: R = ρ(L/A). It's crucial to distinguish between resistance and resistivity. Resistance is a property of a specific object (like a 2m long copper wire), while resistivity is a property of the material itself (copper).

Series vs. Parallel Circuits

Solved Numerical Examples

• {"item":"Ohm's Law Calculation","details":"Problem: An electric iron draws a current of 4 A when connected to a 220 V source. What is its resistance?\nSolution:\nGiven: I = 4 A, V = 220 V\nUsing Ohm's Law, V = IR\nSo, R = V / I = 220 V / 4 A = 55 Ω.\nThe resistance of the electric iron is 55 Ω."}
• {"item":"Equivalent Resistance","details":"Problem: Three resistors of 2 Ω, 3 Ω, and 6 Ω are connected in parallel. Find the equivalent resistance of the combination.\nSolution:\nGiven: R₁ = 2 Ω, R₂ = 3 Ω, R₃ = 6 Ω\nFor parallel combination: 1/R_p = 1/R₁ + 1/R₂ + 1/R₃\n1/R_p = 1/2 + 1/3 + 1/6\n1/R_p = (3 + 2 + 1) / 6 = 6/6 = 1\nSo, R_p = 1 Ω.\nThe equivalent resistance is 1 Ω."}
• {"item":"Electric Power & Cost","details":"Problem: An electric bulb rated 100 W is used for 5 hours a day. Calculate the energy consumed in 30 days and its cost if the rate is ₹4 per unit.\nSolution:\nPower, P = 100 W = 0.1 kW\nTime per day, t = 5 h\nTotal time in 30 days = 5 h/day * 30 days = 150 h\nEnergy consumed, E = P × t = 0.1 kW × 150 h = 15 kWh\n1 unit = 1 kWh\nTotal Cost = Energy consumed (in kWh) × Rate = 15 × ₹4 = ₹60."}

Common Exam Mistakes to Avoid

In electricity numericals, silly mistakes can cost you marks. Here's what to watch out for:

• Mixing up Series and Parallel Formulas: This is the most common error. Remember: Series is a simple sum (R_s = R₁ + R₂), Parallel is the sum of reciprocals (1/R_p = 1/R₁ + 1/R₂). After calculating 1/R_p, don't forget to invert the result to find R_p!
• Unit Conversion: Always convert quantities to their SI units before calculation. Time should be in seconds (for H = I²Rt), power in Watts, length in meters, etc. Check the question carefully.
• Distinguishing V, I, R in complex circuits: When resistors are in series, 'I' is constant. When in parallel, 'V' is constant. Use this to find the unknown quantity for each component.
• Forgetting to Draw a Diagram: For circuit problems, always draw a neat, labeled diagram first. It helps you visualize the problem and reduces the chance of errors.

Practice Questions with Solutions

• What is the SI unit of resistivity? The SI unit of resistivity (ρ) is the Ohm-meter (Ωm).
• Why are the heating elements of electric toasters and irons made of an alloy rather than a pure metal? Alloys have a much higher resistivity than pure metals, so they produce more heat (H ∝ R). They also have a high melting point and do not oxidize (burn) easily at high temperatures.
• Two resistors of resistance R are connected first in parallel and then in series. What is the ratio of the equivalent resistance in the parallel combination to that in the series combination? In parallel, R_p = R/2. In series, R_s = 2R. The ratio R_p / R_s = (R/2) / (2R) = 1/4. So the ratio is 1:4.
• What is meant by saying that the potential difference between two points is 1 V? It means that 1 Joule of work is done to move a charge of 1 Coulomb from one point to the other.

Frequently Asked Questions