Ans: Ohm's Law: At constant temperature, the current through a conductor is directly proportional to the potential difference across it. V = IR. In parallel combination: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃. Given: R₁ = 100Ω, R₂ = 50Ω, R₃ = 500Ω. 1/R_total = 1/100 + 1/50 + 1/500 = 5/500 + 10/500 + 1/500 = 16/500. R_total = 500/16 = 31.25 Ω. Total current = V/R = 220/31.25 = 7.04 A. Note: In parallel, total resistance is always less than the smallest individual resistance (50Ω here).

Ans: Series circuit: components connected end to end; same current through all; voltages add up; total resistance = sum of all resistances; if one component fails, circuit breaks. Parallel circuit: components connected between same two points; same voltage across all; currents add up; total resistance is less than smallest resistor; failure of one component does not affect others. Household wiring is parallel because: (1) Each appliance gets full supply voltage (220V). (2) Each can be switched on/off independently. (3) If one appliance fails, others continue working. (4) More appliances can be added without affecting others.

Ans: When current flows through a resistor, electrical energy is converted to heat energy. Joule's Law: H = I²Rt (heat produced is proportional to square of current, resistance, and time). Applications: (1) Electric heaters and room heaters — nichrome wire (high resistance, high melting point) converts electricity to heat. (2) Electric iron — uses heating coil to heat the base plate for pressing clothes. (3) Electric fuse — thin wire of specific resistance that melts when current exceeds safe limit, protecting the circuit. (4) Incandescent bulb — tungsten filament heats to ~3000°C, producing light (less efficient than LEDs). (5) Electric toaster, geyser, electric kettle.

Ans: Electric power is the rate at which electrical energy is consumed: P = VI = I²R = V²/R. SI unit: Watt (W). Given: P = 60W, V = 220V. Resistance R = V²/P = (220)²/60 = 48400/60 = 806.7 Ω. Current I = P/V = 60/220 = 0.27 A (or using I = V/R = 220/806.7 = 0.27 A). Commercial unit of energy: 1 kWh = 1 unit of electricity = 3.6 × 10⁶ J. A 60W bulb running for 1 hour consumes 0.06 kWh = 0.06 units.

Ans: A fuse is a safety device with a thin wire of specific resistance and low melting point. It is connected in the live wire (high potential) so that if current exceeds safe limits (due to short circuit or overloading), the fuse wire melts and breaks the circuit, preventing fire or damage to appliances. If connected in neutral wire, current would still flow through appliances even after fuse blows. MCB (Miniature Circuit Breaker): a modern alternative to fuses. It automatically trips (switches off) when current is too high; can be reset manually unlike fuses which must be replaced.

Ans: One volt is the potential difference between two points when 1 joule of work is done in moving 1 coulomb of charge from one point to the other: 1 V = 1 J/C.

Ans: Ohm-metre (Ω m).

Ans: A voltmeter, connected in parallel across the component whose potential difference is to be measured.

Ans: They have very low resistivity, so they are good conductors, and they lose little energy as heat.

Ans: 1 kWh = 3.6 × 10⁶ J.

Ans: Charge of one electron = 1.6 × 10⁻¹⁹ C. Number of electrons = 1 ÷ (1.6 × 10⁻¹⁹) = 6.25 × 10¹⁸.

Ans: Tungsten has a very high melting point (about 3380°C) and high resistivity, so the filament can become white-hot and give light without melting.

Ans: R = ρl/A. New R' = ρ(2l)/(A/2) = 4ρl/A = 4R = 4 × 20 = 80 Ω.

Ans: In parallel, each appliance gets the same full voltage, can be switched on and off independently, and if one fails the others keep working. In series, the same current passes through all, the voltage is divided and failure of one breaks the circuit.

Ans: R = V²/P = (220)²/100 = 48400/100 = 484 Ω.

Ans: (a) Series: R = 4 + 6 + 12 = 22 Ω. (b) Parallel: 1/R = 1/4 + 1/6 + 1/12 = (3 + 2 + 1)/12 = 6/12 = 1/2, so R = 2 Ω.

Ans: Energy = power × time = 1 kW × 2 h × 30 = 60 kWh. Cost = 60 × 5 = ₹300.

Ans: H = I²Rt = (2)² × 10 × (5 × 60) = 4 × 10 × 300 = 12,000 J (12 kJ).

Ans: (a) Series: the same current I flows through R₁, R₂, R₃. Total voltage V = V₁ + V₂ + V₃ = IR₁ + IR₂ + IR₃. If R is the equivalent resistance, V = IR, so R = R₁ + R₂ + R₃. (b) Parallel: the voltage V is the same across each resistor, and the total current I = I₁ + I₂ + I₃ = V/R₁ + V/R₂ + V/R₃. Since I = V/R, 1/R = 1/R₁ + 1/R₂ + 1/R₃.

Ans: Resistance depends on (1) length (directly proportional), (2) area of cross-section (inversely proportional), (3) the material, and (4) the temperature. R = ρl/A. Here l = 2 m, A = 1 mm² = 1 × 10⁻⁶ m², ρ = 1.6 × 10⁻⁸ Ω m. R = (1.6 × 10⁻⁸ × 2) ÷ 10⁻⁶ = 3.2 × 10⁻² Ω = 0.032 Ω.