In a copper voltameter,the mass of copper deposited in $6 \, \text{min}$ is $m \, \text{g}$. If the current-time graph is as shown in the figure,the electrochemical equivalent of copper will be:

The potential difference across the $100\,\Omega$ resistance in the following circuit is measured by a voltmeter of $900\,\Omega$ resistance. The percentage error made in reading the potential difference is

The variation of current $(I)$ and voltage $(V)$ is as shown in figure $A$. The variation of power $P$ with current $I$ is best shown by which of the following graphs?

At time $t = 0$,terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and alternating current $I(t) = I_0 \cos(\omega t)$,with $I_0 = 1 \text{ A}$ and $\omega = 500 \text{ rad s}^{-1}$ starts flowing in it with the initial direction shown in the figure.
At $t = \frac{7\pi}{6\omega}$,the key is switched from $B$ to $D$. Now onwards only $A$ and $D$ are connected. $A$ total charge $Q$ flows from the battery to charge the capacitor fully. If $C = 20 \mu\text{F}$,$R = 10 \Omega$ and the battery is ideal with emf of $50 \text{ V}$,identify the correct statement$(s)$.
$(A)$ Magnitude of the maximum charge on the capacitor before $t = \frac{7\pi}{6\omega}$ is $1 \times 10^{-3} \text{ C}$.
$(B)$ The current in the left part of the circuit just before $t = \frac{7\pi}{6\omega}$ is clockwise.
$(C)$ Immediately after $A$ is connected to $D$,the current in $R$ is $10 \text{ A}$.
$(D)$ $Q = 2 \times 10^{-3} \text{ C}$.

$A$ $25\, W$, $220\, V$ bulb and a $100\, W$, $220\, V$ bulb are connected in parallel across a $440\, V$ line. Which of the following will happen?

$A$ cable consists of a copper wire of radius $9 \, mm$ having a resistance of $5 \, \Omega$. If this cable is replaced by $6$ copper wires each of radius $3 \, mm$,what will be the new resistance of the cable in $\Omega$?