Question

$1\,MW$ power is to be delivered from a power station to a town $10\, km$ away. One uses a pair of $Cu$ wires of radius $0.5\,cm$ for this purpose. Calculate the fraction of ohmic losses to power transmitted if a step-up transformer is used to boost the voltage to $11000\,V$, power transmitted, then a step-down transformer is used to bring voltage to $220\,V$.
($\rho_{Cu}= 1.7 \times 10^{-8}\, SI$ unit)

• A. $1.8\%$
• B. $1.5\%$
• C. $3.6\%$
• D. $7.2\%$

Answer 1

Answer: (C)

Given, $l = 20\,km = 20 \times 10^3\, m$
$r = 0.5 \,cm = 0.5 \times 10^{-2}\, m$,
$\rho = 1.7 \times 10^{-8}\,\Omega m$
$R=\frac{\rho l}{A}=\frac{1.7 \times 10^{-8} \times20 \times 10^{3}}{3.14 \times \left(0.5 \times10^{-2}\right)^{2}}$
$=4.3\,\Omega$
$P=10^{6}\,W$,
$V = 11000 \,V$
$I=\frac{P}{V}$
$=\frac{10^{6}}{11000}$
$=\frac{10^{3}}{11}A$
Power loss, $I^{2}R=\left(\frac{10^{3}}{11}\right)^2 \times 4.3$
$=3.6 \times 10^{4}\,W$
$\frac{P_{LOST}}{P_{TRANSMITTED}} \times100\%$
$=\frac{3.6 \times10^{4}}{10^{6}} \times100$
$=3.6\%$