In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is:

An inductor of $2 \, H$ and a resistance of $10 \, \Omega$ are connected in series with a battery of $5 \, V$. The initial rate of change of current is ...... $A/s$.

For $L-R$ circuit,the time constant is equal to

An inductor of inductance $10 \text{ mH}$ having resistance of $100 \ \Omega$ is connected to a battery of $E$.$M$.$F$. $1.0 \text{ V}$ through a switch as shown in the figure below. After the switch is closed,the ratio of instantaneous voltages across the inductor when the current passing through it is $2 \text{ mA}$ and $4 \text{ mA}$ is . . . . . . .

$A$ coil of inductance $40 \, H$ is connected in series with a resistance of $8 \, \Omega$ and the combination is joined to the terminals of a $2 \, V$ battery. The time constant of the circuit is ...... $s$.

$A$ $50 \, V$ potential difference is suddenly applied to a coil with $L = 5 \times 10^{-3} \, H$ and $R = 180 \, \Omega$. The rate of increase of current after $0.001 \, s$ is ....... $A/s$.