An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line i $s ____$ .
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Question

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line i s ____ .

G1 Physics · Accepted Answer

The delivered output power is P(out) = 1000 W. The receiving-end voltage is V = 250 V. Therefore, P(out) = VI, so I = 1000/250 = 4 A. Power lost in the transmission line is P(loss) = I²R = 4²×2 = 32 W. Hence the input power is P(in) = P(out)+P(loss) = 1000+32 = 1032 W. Transmission efficiency is η = [P(out)/P(in)]×100 = (1000/1032)×100 ≈ 96.9%. Correct option: A.