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

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