Question

Three equal resistors connected in series across a source of emf together dissipate $10\text{W}$ of power. What would be the power dissipated if the same resistors are connected in parallel across the same source of emf?

• A. $50\text{W}$
• B. $70\text{W}$
• C. $90\text{W}$
• D. $110\text{W}$

Answer 1

The correct option is C $90\text{W}$

When resistors are in series,


So, total power developed in circuit will be

$P_1=\frac{V^2}{R_{eq}}=\frac{E^2}{3R}=10\text{W}........\left(1\right)$

When resistors are in parallel,


Similarly, for parallel combination,

$P_2=\frac{E^2}{R/3}=\frac{3E^2}{R}........\left(2\right)$

Using value of $\frac{E^2}{R}$ from eq.$\left(1\right)$ we get,

$P_2=\frac{3E^2}{R}=3\times 30=90\text{W}$

Hence, option $\left(c\right)$ is correct.