Switch $S$ is closed at $t = 0$ in the circuit shown. The change in magnetic flux in the inductor $(L = 500 \, mH)$ from $t = 0$ to an instant when it reaches steady state is ...... $Wb$.

An inductance $L$ and a resistance $R$ are first connected to a battery. After some time,the battery is disconnected,but $L$ and $R$ remain connected in a closed circuit. Then the current reduces to $37\%$ of its initial value in

An inductance coil has a time constant of $4 \, sec$. If it is cut into two equal parts and connected in parallel,then the new time constant of the circuit is.....$sec$.

Inductance of a coil with $10^4$ turns is $10 \text{ mH}$ and it is connected to a $DC$ source of $10 \text{ V}$ with internal resistance of $10 \ \Omega$. The energy density in the inductor when the current reaches $(1/e)$ of its maximum value is $\alpha \pi \times (1/e^2) \text{ J/m}^3$. The value of $\alpha$ is . . . . . . . $(\mu_0 = 4 \pi \times 10^{-7} \text{ Tm/A})$.

An inductor coil stores $U$ energy when $I$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance,is

The total heat produced in resistor $R$ in an $RL$ circuit when the current in the inductor decreases from $I_0$ to $0$ is