Current Electricity

A potential \(\mathrm{V}_{0}\) 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 \(P_{2}: \mathrm{P}_{1}\) is \(\sqrt{x}: 1\). The value of \(x\) is ___________.