Question

An electrical cable having a resistance of $0.2\Omega$ delivers $10kW$ at $200V$ dc to a factory. What is the efficiency of transmission?

• A. $65\%$
• B. $75\%$
• C. $85\%$
• D. $95\%$

Answer 1

Answer: (D)

Let $x$ watt be the power loss in transmission line in the form of heat.
$\therefore x={\left(\frac{P}{V}\right)}^{2}R={\left(\frac{10\times 1000}{200}\right)}^2\times 0.2=500W=0.5kW$
Efficiency of transmission
$=\frac{\text{power delivered by line}}{\text{power supplied to line}}=\frac{10kW}{10kW+xkW}$
$=\frac{10}{10+0.5}=\frac{10}{10.5}=0.95=95\%$