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 ___________.

The current flowing through a conductor connected across a source is $$2 \mathrm{~A}$$ and 1.2 $$\mathrm{A}$$ at $$0^{\circ} \mathrm{C}$$ and $$100^{\circ} \mathrm{C}$$ respectively. The current flowing through the conductor at $$50^{\circ} \mathrm{C}$$ will be ___________ $$\times 10^{2} \mathrm{~mA}$$.

Two identical cells each of emf $$1.5 \mathrm{~V}$$ are connected in series across a $$10 ~\Omega$$ resistance. An ideal voltmeter connected across $$10 ~\Omega$$ resistance reads $$1.5 \mathrm{~V}$$. The internal resistance of each cell is __________ $$\Omega$$.

In the circuit diagram shown in figure given below, the current flowing through resistance $$3 ~\Omega$$ is $$\frac{x}{3} A$$.

The value of $$x$$ is ___________