$A$ wire of length $L$ and $3$ identical cells of negligible internal resistances are connected in series. Due to current,the temperature of the wire is raised by $\Delta T$ in a time $t$. $A$ number $N$ of similar cells is now connected in series with a wire of the same material and cross-section but of length $2L$. The temperature of the wire is raised by the same amount $\Delta T$ in the same time $t$. The value of $N$ is

For a thermocouple,the temperature of inversion is that temperature at which the thermo $e.m.f.$ is:

Ten $60 \, W, 220 \, V$ bulbs are connected in series to a $220 \, V$ supply. The power consumed in the circuit is ......... $W$.

$A$ silver and zinc voltameter are connected in series and a current $i$ is passed through them for a time $t$ liberating $W \, g$ of zinc. The weight of silver deposited is nearly ..............$W$.

In the circuit shown below,the resistance and the emf source are both variable. The graph of seven readings of the voltmeter and the ammeter ($V$ and $I$,respectively) for different settings of resistance and the emf,taken at equal intervals of time $\Delta t$,are shown below by the dots connected by the curve $EFGH$. Consider the internal resistance of the battery to be negligible and the voltmeter and ammeter to be ideal devices. (Take $R_0 = \frac{V_0}{I_0}$). Then,the plot of the resistance as a function of time corresponding to the curve $EFGH$ is given by:

The potential difference across $8\,\Omega$ resistance is $48\,V$ as shown in the figure. The value of potential difference across $X$ and $Y$ points will be ............. $V$.