Two wires of the same material have lengths in the ratio $1 : 2$ and radii in the ratio $2 : 1$. If they are connected in parallel to a battery,what is the ratio of heat produced in them?

In the adjacent circuit,a voltmeter of internal resistance $R$,when connected across $B$ and $C$,reads $\frac{100}{3} \ V$. Neglecting the internal resistance of the battery,the value of $R$ is ................. $k \Omega$.

An external resistance $R$ is connected to a battery of $e.m.f.$ $V$ and internal resistance $r$. The joule heat produced in resistor $R$ is maximum when $R$ is equal to

The current $i$ in the adjoining circuit will be:

In the circuit shown in the figure,the reading of the voltmeter is $V_1$ when only $S_1$ is closed,and the reading of the voltmeter is $V_2$ when only $S_2$ is closed. The reading of the voltmeter is $V_3$ when both $S_1$ and $S_2$ are closed. Then:

The potential difference between the points $P$ and $Q$ is nearly: (in $\,V$)