$A$ coil has an inductance of $2.5\,H$ and a resistance of $0.5\,\Omega$. If the coil is suddenly connected across a $6.0\,V$ battery,then the time required for the current to rise to $0.63$ of its final value is.....$s$.

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 . . . . . . . $(\mu_0 = 4 \pi \times 10^{-7} \text{ Tm/A})$.

$A$ resistor of $20 \, \Omega$ and an inductor of $5 \, H$ are connected in series with a $5 \, V$ battery. What is the rate of change of current at $t = 0.25 \, s$?

An inductor $(L = 0.03 \; H)$ and a resistor $(R = 0.15 \; k\Omega)$ are connected in series to a battery of $15 \; V$ $EMF$ in the circuit shown below. The key $K_1$ has been kept closed for a long time. Then at $t = 0$,$K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1 \; ms$,the current in the circuit will be ........... $mA$. $(e^5 \cong 150)$

If $L$ is the inductance and $R$ is the resistance,then the $SI$ unit of $\frac{L}{R}$ is

$Henry/ohm$ can be expressed in