Question

A uniform heating wire of resistance $36\, \Omega$ is connected across a potential difference of $240 \,V$. The wire is then cut into half and potential difference of $240\, V$ 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

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