When a resistance of $2\,\Omega$ is connected across the terminals of a cell,the current is $0.5\,A$. When the resistance is increased to $5\,\Omega$,the current is $0.25\,A$. The $e.m.f.$ of the cell is ................. $V$.

What is the current $i$ in the circuit as shown in the figure (in $A$)?

In the adjoining circuit shown,the potential difference between points $A$ and $B$ will be:

The total current supplied to the circuit by the battery is ............. $A$.

The galvanometer deflection,when key $K_1$ is closed but $K_2$ is open,equals $\theta_0$ (see figure). On closing $K_2$ also and adjusting $R_2$ to $5\,\Omega$,the deflection in the galvanometer becomes $\frac{\theta_0}{5}$. The resistance of the galvanometer is,then,given by [Neglect the internal resistance of battery]: .................. $\Omega$

$A$ heater is designed to operate with a power of $1000 \ W$ in a $100 \ V$ line. It is connected in combination with a resistance of $10 \ \Omega$ and a resistance $R$,to a $100 \ V$ mains as shown in the figure. For the heater to operate at $62.5 \ W$,the value of $R$ should be .................. $\Omega$.