JEE Main 2020 · 5 September · morning · Single correct · +4 / −1

An electrical power line, having a total resistance of 2 Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately :

  1. (a) 85%
  2. (b) 96%
  3. (c) 72%
  4. (d) 91%
Answer and solution

Answer (b) 96%

Solution

Physics sir · 3 steps

Find the current from the delivered power, then the line wastes I²R on the way.

  1. Current in the line. The load gets 1 kW at 220 V, so I = P/V = 1000/220 = 50/11 ≈ 4.55 A. The same current flows through the line.
  2. Power lost. The line resistance heats up: Pₗₒₛₛ = I² R = 2500/121 × 2 ≈ 41.3 W.

    η = P_(delivered)/(P_(delivered) + I²R) = 1000/(1000 + 41.3) ≈ 0.96

  3. So. The power station must supply about 1041 W to deliver 1000 W, so the efficiency is about 96%, option (b).

The idea to keep. In transmission, the delivered power and voltage give the line current. The line loses I²R, and efficiency is useful power over useful plus lost.

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

Study Current Electricity

Asked about 250 times in JEE Main since 2020. This question is from 2020.