Question

A small town with a demand of $800\,kW$ of electric power at $220\,V$ is situated $15\,km$ away from an electric plant generating power at $440\,V$. The resistance of the two wire line carrying power is $0.5\,\Omega$. per $km$. The town, gets power from the line through a $4000-220\,V$ step down transformer at a substation in the town. The line power loss in the form of heat is

• A. $400\,kW$
• B. $600\,kW$
• C. $300\,kW$
• D. $800\,kW$

Answer 1

Answer: (B)

Here, $P = 800\,kW = 800 \times 10^3\, W$
Total resistance of two wire line
$R = 2 \times 15 \times 0.5 = 15\,\Omega$
As supply is through $4000-220\,V$ transformer
$\therefore V_{rms}=4000\,V$
$\therefore I_{rms}=\frac{P}{V_{rms}}$
$=\frac{800\times10^{3}}{4000}$
$=200\,A$
Line power loss $=I^{2}_{rms}\,R=\left(200\right)^{2}\times 15$
$=60\times 10^{4}\,W=600\,kW$