Question

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

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

Answer 1

Answer: (B)

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