In the circuit diagram shown in the figure below, the current flowing through the resistance $3\, \Omega$ is $\frac{x}{3}\, A$. The value of $x$ is $...........$

Consider the circuit given here. The potential difference $V_{BC}$ between the points $B$ and $C$ is (in $V$)

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:

$A$ coil takes $15\,min$ to boil a certain amount of water,and another coil takes $20\,min$ for the same process. What is the time taken to boil the same amount of water when both coils are connected in series?

For the circuit shown in the figure:
$(A)$ The current $I$ through the battery is $7.5 \text{ mA}$.
$(B)$ The potential difference across $R_L$ is $18 \text{ V}$.
$(C)$ The ratio of powers dissipated in $R_1$ and $R_2$ is $3$.
$(D)$ If $R_1$ and $R_2$ are interchanged,the magnitude of the power dissipated in $R_L$ will decrease by a factor of $9$.

Column $- I$ gives certain physical terms associated with the flow of current through a metallic conductor. Column $- II$ gives some mathematical relations involving electrical quantities. Match Column $- I$ and Column $- II$ with appropriate relations.

Column $- I$	Column $- II$
$(A)$ Drift Velocity	$(P)$ $\frac{m}{n e^{2} \rho}$
$(B)$ Electrical Resistivity	$(Q)$ $n e v_{d}$
$(C)$ Relaxation Period	$(R)$ $\frac{e E}{m} \tau$
$(D)$ Current Density	$(S)$ $\frac{E}{J}$