The current flowing through a conductor connected across a source is 2 A and 1.2 A at 0° C and 100° C respectively. The current flowing through the conductor at 50° C will be ___________ × 10² mA.

Solution

Physics sir · 4 steps

Resistance, not current, grows linearly with temperature, so average the resistances and not the currents.

1. What stays fixed. The source voltage V is the same at every temperature, so R = V/I. Resistance changes with temperature as R_T = R₀(1 + α T), which is a straight line in T.
2. Linear means midpoint. Since 50°C is exactly halfway between 0°C and 100°C, R₅₀ is the average of R₀ and R₁₀₀. Because R = V/I, the average is taken of 1/I.

   1/I₅₀ = 1/2(1/2 + 1/1.2) = 1/2(3/6 + 5/6) = 2/3 A⁻¹

3. Check with alpha. R₁₀₀/R₀ = 2/1.2 = 5/3 = 1 + 100α, so α = 1/150 °C⁻¹. Then R₅₀ = R₀(1 + 50/150) = 4/3R₀, giving I₅₀ = 3/4 × 2 = 1.5 A.
4. So. I₅₀ = 1.5 A = 1500 mA = 15 × 10² mA, so the answer is 15.

The common slip: 16. Averaging the two currents, (2 + 1.2)/2 = 1.6 A, gives 16. Current is not linear in temperature. Resistance is.

The idea to keep. Find the quantity that is truly linear in temperature. Here it is resistance, R₀(1 + α T). Current is V/R, so it does not change linearly and you cannot average it directly.

Answer from the NTA final answer key. Solution by PrepWiser.