Q 12-03-143JEE MainJEE Main 2023 (13 Apr, Shift 1)Easy
A potential $V_0$ is applied across a uniform wire of resistance $R$. The power dissipation is $P_1$. The wire is then cut into two equal halves and a potential of $V_0$ is applied across the length of each half. The total power dissipation across two wires is $P_2$. The ratio of $P_2:P_1$ is $\sqrt x:1$. The value of $x$ is ______.
Numerical value type. Enter your answer.
Answer: 16
$P_1=\dfrac{V_0^2}{R}$. Each half has $\dfrac R2$ and dissipates $\dfrac{2V_0^2}{R}$; together $P_2=\dfrac{4V_0^2}{R}$.
$P_2:P_1=4:1=\sqrt{16}:1$, so $x=16$.
Solution by Sreeraj P, M.Sc Physics