Question

An electrical cable having a resistance of $0.4\Omega$ delivers $20kW$ at $4000VDC$ to a factory.
What is the efficiency of transformer?

• A. $89.5$%
• B. $99.5$%
• C. $79.5$%
• D. $90.5$%

Answer 1

The correct option is B $99.5$%

Let $x$ want be the power loss in transmission line in the form of heat
$\therefore x={\left(\frac{P}{V}\right)}^{2}R={\left(\frac{20\times 1000}{400}\right)}^2\times 0.4$
$={\left(\frac{200}{4}\right)}^2\times 0.4=50\times 50\times 0.4$
$=25\times 4=100W=0.1kW$
Efficiency of transmission $=\frac{Powerdelivered}{Powersupplied}$
$=\frac{20kW}{20kW+0.1kW}=\frac{20kW}{20.1kW}$
$=\frac{20}{20.1}=99.5$%.