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 $600 kW$.



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