Explanation

Power delivered to the load is given as

$$ P_{\text{load}} = 1000\ \text{W} $$

Voltage at the load end is

$$ V = 250\ \text{V} $$

Current flowing through the transmission line,

$$ I = \frac{P}{V} = \frac{1000}{250} = 4\ \text{A} $$

Power loss in the transmission line due to its resistance is

$$ P_{\text{loss}} = I^2 R = (4)^2 \times 2 = 32\ \text{W} $$

Total power supplied by the source is

$$ P_{\text{total}} = P_{\text{load}} + P_{\text{loss}} = 1000 + 32 = 1032\ \text{W} $$

Efficiency of transmission line is defined as

$$ \eta = \frac{P_{\text{load}}}{P_{\text{total}}} \times 100 $$

$$ \eta = \frac{1000}{1032} \times 100 \approx 96.9\% $$

Hence, the percentage efficiency of the transmission line is

96.9%

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