Three identical batteries are connected in series with a wire of length $L$. The temperature of the wire increases by $T$ in time $t$. If $N$ such batteries are connected in series with a wire of the same material but length $2L$,the temperature increases by the same amount $T$ in the same time $t$. Find the value of $N$.

In the circuit shown in the figure,the resistance of the voltmeter is $6 \, k\Omega$. The voltmeter reading will be ................. $V$.

The reading of the voltmeter in the circuit shown is ............. $V$. (in $.25$)

In how much time will one litre of ${H_2}$ be collected by a $5\, A$ current? (Given: $Z = 1 \times {10^{ - 8}}\,kg/C$ and density of ${H_2} = 0.09\,kg/{m^3}$)

$A$ current of $1.5\, A$ flows through a copper voltameter. The thickness of copper deposited on the electrode surface of area $50\, cm^2$ in $20\, min$ will be (Density of copper $= 9000\, kg/m^3$ and $E.C.E.$ of copper $= 0.00033\, g/C$).

An infinite line charge of uniform electric charge density $\lambda$ lies along the axis of an electrically conducting infinite cylindrical shell of radius $R$. At time $t=0$,the space inside the cylinder is filled with a material of permittivity $\varepsilon$ and electrical conductivity $\sigma$. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density $j(t)$ at any point in the material?