Electromagnetic Induction and Alternating Current 7 Question 17
17. If the direct transmission method with a cable of resistance $0.4 \Omega km^{-1}$ is used, the power dissipation (in %) during transmission is
(a) 20
(b) 30
(c) 40
(d) 50
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Answer:
Correct Answer: 17. (b)
Solution:
$$ \begin{array}{rlrl} P & =V i \\ \therefore \quad & i & =\frac{P}{V}=\frac{600 \times 10^{3}}{4000}=150 A \end{array} $$
Total resistance of cables, $R=0.4 \times 20=8 \Omega$
$\therefore$ Power loss in cables $=i^{2} R=(150)^{2}(8)$
$$ =180000 W=180 kW $$
This loss is $30 %$ of $600 kW$.
