# An electrical power line, having a total resistance

Question:

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

1. (1) $72 \%$

2. (2) $91 \%$

3. (3) $85 \%$

4. (4) $96 \%$

Correct Option: 4,

Solution:

(2) Given : Power, $P=1 \mathrm{~kW}=1000 \mathrm{~W}$

$R=2 \Omega, V=220 \mathrm{~V}$

Current, $I=\frac{P}{V}=\frac{1000}{220}$

$P_{\text {loss }}=I^{2} R=\left(\frac{1000}{220}\right)^{2} \times 2$

$\therefore$ Efficiency $=\frac{1000}{1000+P_{\text {loss }}} \times 100=96 \%$