Question

Three equal resistors connected in series across a source of e.m.f. dissipate $10$watts 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.?

• A. $10W$
• B. $30W$
• C. $90W$
• D. $\frac{10}{3}W$

Answer 1

The correct option is C $90W$

Let the resistance of each resistor be $R$

In series combination:
$R_1=3R,P=10W$,

$P=\frac{V^2}{R_{series}}\Rightarrow 10=\frac{V^2}{3R}\Rightarrow \frac{V^2}{R}=30$

In parallel combination:
$P^{\prime }=\frac{V^2}{R/3}=3\frac{V^2}{R}=3\times 30=90W$