Question

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

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

Answer 1

Answer: (C)

Given, $l=20km=20\times 10^{3}m$
$r=0.5cm=0.5\times 10^{-2}m$,
$\rho =1.7\times 10^{-8}\Omega m$
$R=\frac{\rho l}{A}=\frac{1.7\times 10^{-8}\times 20\times 10^3}{3.14\times {\left(0.5\times 10^{-2}\right)}^2}$
$=4.3\Omega$
$P=10^{6}W$,
$V=11000V$
$I=\frac{P}{V}$
$=\frac{10^6}{11000}$
$=\frac{10^3}{11}A$
Power loss, $I^{2}R={\left(\frac{10^3}{11}\right)}^2\times 4.3$
$=3.6\times 10^{4}W$
$\frac{P_{LOST}}{P_{TRANSMITTED}}\times 100\%$
$=\frac{3.6\times 10^4}{10^6}\times 100$
$=3.6\%$