Current Electricity Ques 97
97. Three equal resistors connected across a source of e.m.f. together dissipate 10 watt of power. What will be the power dissipated in watts if the same resistors are connected in parallel across the same source of e.m.f.?
[1998]
(a) 10
(b) $\frac{10}{3}$
(c) 30
(d) 90
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Answer:
Correct Answer: 97.(d)
Solution:
- (d) In series, Equivalent resistance $=3 R$
Power $=\frac{V^{2}}{3 R} \Rightarrow 10=\frac{V^{2}}{3 R} \Rightarrow V^{2}=30 R$
In parallel, $\frac{1}{R^{\prime}}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}=\frac{3}{R}$
$\therefore$ Equivalent resistance $R^{\prime}=\frac{R}{3}$
$\therefore$ Power $=\frac{V^{2}}{R^{\prime}}=\frac{30 R}{R / 3}=90 W$
If voltage $V$ remains same, then power consumed by a $n$ equal resistors in parallel is $n^{2}$ times that of power consumed in series.
BETA
