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A power P is to be delivered to a device through transmission cables of fixed resistance $R_c$, at a line voltage V. The power wasted in the cables is
Adirectly proportional to $V^2$
Bindependent of V
Cinversely proportional to $V^2$
Dinversely proportional to $R_c$
Answer & Solution
Correct answer: C. inversely proportional to $V^2$
1. The line current carrying power P at voltage V is $I = P/V$.
2. Power lost in the cables is $P_c = I^2 R_c = P^2 R_c / V^2$.
3. For fixed P and $R_c$, $P_c \propto 1/V^2$.
4. This is why transmission uses high voltage; A and B contradict the inverse-square dependence.
_Source: NCERT Class 12 Physics Ch 3 "Current Electricity", p.12_
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