Two cables of copper are of equal lengths. One of them has a single wire of area of cross-section $A$, while the other has $10$ wires of cross-sectional area $A / 10$ each. Determine their suitability for transporting $A.C.$ and $D.C.$

$A$ battery of $e.m.f.$ $E$ is connected in series with a resistor $R$ and a voltmeter $V$. An ammeter $A$ is connected in parallel with the battery. Then:

Due to cold weather,a $1\, m$ water pipe of cross-sectional area $1\, cm^2$ is filled with ice at $-10^{\circ}C$. Resistive heating is used to melt the ice. $A$ current of $0.5\, A$ is passed through a $4\, k\Omega$ resistance. Assuming that all the heat produced is used for melting,what is the minimum time required? (In $s$)
(Given: latent heat of fusion for water/ice $= 3.33 \times 10^5\, J/kg$,specific heat of ice $= 2 \times 10^3\, J/(kg\cdot K)$ and density of ice $= 10^3\, kg/m^3$)

Two resistances $R_1$ and $R_2$ when connected in series and parallel with a $120\, V$ line,the power consumed is $25\, W$ and $100\, W$ respectively. The ratio of the power consumed by $R_1$ to that consumed by $R_2$ is:

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 $9$.

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: