Question

An electric power station transmits $100MW$ power through long and thin cable. If the transmission is at
(i) $20000V$,
(ii) $200V$,
in which case would be less power loss?

• A. In (i) only
• B. In (ii) only
• C. In each case, power loss is zero
• D. Data is insufficient

Answer 1

Answer: (A)

Power dissipated is given by $P=VI$
where $V$ is voltage and $I$ is current.
First case, $I_1=\frac{P}{V_1}=\frac{100\times 10^6}{20000}=5000A$
Second case, $I_2=\frac{P}{V_2}=\frac{100\times 10^6}{200}=500000A$
Also, power dissipated is given by $P=I^{2}R$
where $R$ is resistance of the cable.
$\therefore P_1=(5000{)}^{2}R=25\times 10^{6}R$
$P_2=(500000{)}^{2}R=25\times 10^{10}R$
$\Rightarrow P_1<P_2$