The e.m.f. of a cell is $E \text{ volts}$ and its internal resistance is $r \text{ ohm}$. The resistance in the external circuit is also $r \text{ ohm}$. The potential difference across the cell will be

$A$ current source drives a current in a coil of resistance $R_1$ for a time $t$. The same source drives current in another coil of resistance $R_2$ for the same time. If the heat generated is the same,find the internal resistance of the source.

The equivalent resistance of the arrangement of resistances shown in the figure between the points $A$ and $B$ is ............... $\Omega$.

In the given circuit,the power generated in the $1 \, \Omega$ resistance will be maximum for $x$ equal to ................ $\Omega$.

$A$ $8 \Omega$ resistor is connected to a battery that has an internal resistance of $0.2 \Omega$. If the voltage across the battery (the terminal voltage) is $10 \ V$,then the emf of the battery is (in $V$)

$A$ $50\, W$ bulb is in series with a room heater and the combination is connected across the mains. To get maximum heater output,the $50\, W$ bulb should be replaced by a bulb of: (in $, W$)