A potential V_o 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…

A potential $\displaystyle \mathrm{V}_{\mathrm{o}}$ is applied across a uniform wire of resistance R . The power dissipation is $\displaystyle \mathrm{P}_1$. The wire is then cut into two equal halves and a potential of $\displaystyle \mathrm{V}_{\mathrm{o}}$ is applied across the length of each half. The total power dissipation across two wires is $\displaystyle \mathrm{P}_2$. The ratio $\displaystyle \mathrm{P}_2: \mathrm{P}_1$ is $\displaystyle \sqrt{x}: 1$. The value of $\displaystyle x$ is $\displaystyle \_\_\_\_$