$A$ brass disc and a carbon disc of same radius are assembled alternatively to make a cylindrical conductor. The resistance of the cylinder is independent of the temperature. The ratio of thickness of the brass disc to that of the carbon disc is [$\alpha$ is temperature coefficient of resistance and neglect linear expansion].

In an electroplating experiment,a current of $4 \ A$ is passed for $2 \ min$ to deposit a mass $m$ of silver. If a current of $6 \ A$ is passed for $40 \ s$,the mass of silver deposited is:

There are two electric bulbs of $40\, W$ and $100\, W$. Which one will be brighter when first connected in series and then in parallel?

In the given circuit,with steady current,the potential drop across the capacitor must be

In the circuit shown in the figure,the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition,a current of $1 \,A$ flows through the $1 \,\Omega$ resistor. The key is closed at time $t=t_0$. Which of the following statement(s) is(are) correct?

[Given: $e^{-1}=0.36$]
$(A)$ The value of the resistance $R$ is $3 \,\Omega$.
$(B)$ The current through the $3 \,\Omega$ resistor (connected in parallel to the $1 \,\Omega$ and $R$ branches) is $2 \,A$ when $K$ is open.
$(C)$ At $t=t_0+7.2 \,\mu s$,the current in the capacitor branch is $0.6 \,A$.
$(D)$ For $t < \infty$,the charge on the capacitor is $12 \,\mu C$.

$A$ coil of wire of resistance $50\,\Omega$ is embedded in a block of ice. If a potential difference of $210\,V$ is applied across the coil,the amount of ice melted per second will be