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 $P_2: P_1$ is $\sqrt{x}: 1$. The value of $x$ is $.............$.

In a building there are $15$ bulbs of $45\; \mathrm{W}, 15$ bulbs of $100\; \mathrm{W}, 15$ small fans of $10 \;\mathrm{W}$ and $2$ heaters of $1 \;\mathrm{kW}$. The voltage of electric main is $220\; \mathrm{V}$. The minimum fuse capacity (rated value) of the building will be: .......... $A$

Two bulbs, one of $50\, watt$ and another of $25\, watt$ are connected in series to the mains. The ratio of the currents through them is

The figure shows a network of five resistances and two batteries The total electrical power consumed by the circuit is ............... $W$

The resistor of resistance '$R$' is connected to $25\, V$ supply and heat produced in it is $25\, J/sec$. The value of $R$ is .......... $\Omega $

Four equal resistance dissipated $5 \,W$ of power together when connected in series to a battery of negligible internal resistance. The total power dissipated in these resistance when connected in parallel across the same battery would be ........... $W$