Question

A uniform heating wire of resistance $36\Omega$ is connected across a potential difference of $240V$. The wire is then cut into half and potential difference of $240V$ is applied across each half separately. The ratio of power dissipation in first case to the total power dissipation in the second case would be $1:x$, where $x$ is............

Answer 1

Answer: 4

First case $P_1=\frac{V^2}{R}=\frac{(240{)}^2}{36}$
Second case Resistance of each half $=18\Omega$
$P_2=\frac{(240{)}^2}{18}+\frac{(240{)}^2}{18}=\frac{(240{)}^2}{9}$
$\frac{P_1}{P_2}=\frac{1}{4}$
$x=4.00$