An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 V . The

Question

An electric power line having total resistance of $2 \Omega$, delivers 1 kW of power at 250 V . The percentage efficiency of transmission line is $\_\_\_\_$ .

Professor PC Thomas Classes · Answer

The power delivered to the load is $P_{out} = 1 	ext{ kW} = 1000 	ext{ W}$ at a voltage $V = 250 	ext{ V}$. The current in the line is $I = \frac{P_{out}}{V} = \frac{1000}{250} = 4 	ext{ A}$. The power lost as heat in the transmission line is $P_{loss} = I^2 R = (4)^2 	imes 2 = 32 	ext{ W}$. The total power generated is $P_{in} = P_{out} + P_{loss} = 1000 + 32 = 1032 	ext{ W}$. The efficiency is $\eta = \frac{P_{out}}{P_{in}} 	imes 100\% = \frac{1000}{1032} 	imes 100\% \approx 96.9\%$.