Current Electricity - Result Question 81
86. 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
Show Answer
Answer:
Correct Answer: 86. (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.
