Question

A heater coil connected across a given potential difference has power $P$. Now, the coil is cut into two equal halves and joined in parallel. Across the same potential difference, this combination has power.

• A. $P$
• B. $4P$
• C. $\frac{P}{4}$
• D. $2P$

Answer 1

The correct option is B $4P$

Cutting the coil in 2 pieces produces 2 coils of resistance $\frac{R}{2}$ each. Connecting these in parallel,

$\frac{1}{R^{\prime }}=\frac{2}{R}+\frac{2}{R}=\frac{4}{R}⟹R^{\prime }=\frac{R}{4}$ where $R^{\prime }$ is the total resistance

$P=\frac{V^2}{R}$ means power is inversely proportional to $R$ if $V$ is kept constant. Since $R$ is decreased by a factor 4, $P$ increases by a factor 4.