Chapter 8 · ICSE Class 10 Physics (Selina Concise)

Current Electricity

Ohm's law, resistors in series and parallel, resistivity, electrical power and the kilowatt-hour.

⚡ Chapter 8

Two resistors in series 20 V across 4 ohm and 6 ohm in series gives 2 A, with drops 8 V and 12 V. 20 V R₁ = 4 Ω V₁ = 8 V R₂ = 6 Ω V₂ = 12 V Same current I = 2 A in both (R = 10 Ω) 8 V + 12 V = 20 V
8.1

Ohm's law and resistance

At constant temperature, the current through a conductor is proportional to the potential difference across it: V = I R. Resistance of a wire is R = ρL/A, where ρ is the resistivity of its material.

1

A wire of copper (ρ = 1.7 × 10⁻⁸ Ω m), length 10 m and cross-section 1 mm² = 10⁻⁶ m². Find its resistance.

R = ρL/A = 1.7×10⁻⁸ × 10 / 10⁻⁶ = 0.17 Ω.

2

A 12 V battery drives a current of 3 A through a resistor. Find R.

R = V/I = 12/3 = 4 Ω.

8.2

Combination of resistors

In series: R = R₁ + R₂, the same current flows through each, and voltages add. In parallel: 1/R = 1/R₁ + 1/R₂, the same voltage is across each, and currents add; the total is less than the smallest resistor.

1

4 Ω and 6 Ω are in series across 20 V. Find the total resistance, the current and each voltage drop.

R = 4 + 6 = 10 Ω. I = 20/10 = 2 A. V₁ = 2 × 4 = 8 V, V₂ = 2 × 6 = 12 V. Check: 8 + 12 = 20 V.

2

Find the equivalent resistance of 6 Ω and 3 Ω in parallel.

R = (6×3)/(6+3) = 18/9 = 2 Ω.

3

Find the equivalent resistance of 12 Ω and 4 Ω in parallel.

R = (12×4)/(12+4) = 48/16 = 3 Ω.

8.3

Electrical power and energy

Power P = VI = I²R = V²/R, measured in watts. Energy = power × time. The commercial unit is the kilowatt-hour: 1 kWh = 1000 W × 3600 s = 3.6 × 10⁶ J.

1

An iron draws 5 A from a 220 V supply. Find its power.

P = VI = 220 × 5 = 1100 W.

2

A 220 V, 100 W bulb: find its resistance.

R = V²/P = 220²/100 = 484 Ω.

3

A 2 kW heater runs 5 h. Energy used and cost at ₹6 per unit?

E = 2 × 5 = 10 kWh. Cost = 10 × 6 = ₹60.

Practice

Exercises

1. State Ohm's law and the condition for it to hold.

2. Name the SI unit of resistance and of resistivity.

3. Three resistors of 2 Ω, 3 Ω and 5 Ω are in series. Total resistance?

4. A 5 Ω resistor and a 20 Ω resistor are in parallel. Equivalent resistance?

5. Why is the equivalent resistance in parallel smaller than the smallest resistor?

6. A bulb is rated 60 W, 220 V. Find the current it draws.

7. How many joules are in 1 kWh?

8. A 1 kW heater runs 3 h daily for 30 days. Units used?

9. If the length of a wire is doubled, what happens to its resistance (same material and area)?

10. Does a household appliance connect in series or parallel? Why?

Next chapter — Household Circuits →