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

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Current Electricity

An electrical power line, having a total resistance of

2Ω

, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Answer: (A)

The line must carry

I = \frac{P}{V} = \frac{1000}{220} = \frac{50}{11}

A to deliver

1

kW at

220

V. The power dissipated in its

2 Ω

resistance is

I^{2} R = (\frac{50}{11})^{2} \times 2 \approx 41

W. The source therefore supplies

1000 + 41 \approx 1041

W, and the transmission efficiency is

\frac{1000}{1041} \times 100 \approx 96%

JEE Main · 2020 · 05 Sep 2020 · Shift 1 · Single correct option