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. $72 \%$

  2. $96 \%$

  3. $91 \%$

  4. $85 \%$


Correct Option: , 2

Solution:

$\mathrm{vi}=10^{3}$

$\mathrm{i}=\frac{1000}{220}$

loss $=\mathrm{i}^{2} \mathrm{R}=\left(\frac{50}{11}\right)^{2} \times 2$

efficiency $=\frac{1000}{1000+\mathrm{i}^{2} \mathrm{R}} \times 100=96 \%$

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