Question

An electric power line having total resistance of \(2\,\Omega\), delivers \(1\,\text{kW}\) of power at \(250\ \text{V}\). The percentage efficiency of the transmission line is _________.

• A. 92.5
• B. 96.9
• C. 86.5
• D. 100

Hint:

Transmission efficiency improves when current is low, which reduces \(I^2R\) losses.

Answer 1

The Correct Option is B

Step 1: Calculate the current in the transmission line. 
\[ I = \frac{P}{V} = \frac{1000}{250} = 4\ \text{A} \] 
Step 2: Find power loss in the transmission line. 
\[ P_{\text{loss}} = I^2R = 4^2 \times 2 = 32\ \text{W} \] 
Step 3: Calculate efficiency of transmission. 
\[ \eta = \frac{P_{\text{output}}}{P_{\text{input}}}\times 100 = \frac{1000}{1000+32}\times100 \approx 96.9% \] 
Final Answer: 

\[\boxed{96.9\%}\]