Question

A wire when connected to $220\, V$ mains supply has power dissipation $P_1$. Now the wire is cut into two equal pieces which are connected in parallel to the same supply. Power dissipation in this case is $P_2 \, then \, P_2 : P_1$ is

• A. 1
• B. 4
• C. 2
• D. 3

Answer 1

Answer: (B)

4

Answer 2

When wire of resistance say R is cut into two pieces, its resistance becomes half i.e. R /2. Here equivalent resistance
$R_{eq} = \frac{1}{2} \frac{R}{2} = \frac{R}{4}$
$\therefore$ $P_2 = \frac{V^2}{R/4} = 4 \frac{V^2}{R} = 4P_1$
or $P_2 : P_1 = 4$