A coil having resistance $20 \mathrm{\Omega }$ and inductance $2 \mathrm{H}$ is connected to a battery of emf $4.0 \mathrm{V}.$ Find

$\left(\mathrm{a}\right)$ the current at $0.20 \mathrm{s}$ after the connection is made and

$\left(\mathrm{b}\right)$ the magnetic field energy in the coil at this instant.

An inductor-coil of inductance $20 \mathrm{mH}$ having resistance $10 \mathrm{\Omega }$ is joined to an ideal battery of emf $5.0 \mathrm{V}.$Find the rate of change of the magnitude of induced emf at

$\left(\mathrm{a}\right) \mathrm{t} = 0,$

$\left(\mathrm{b}\right) \mathrm{t} = 10 \mathrm{ms}.$

Consider the circuit shown in figure.

$\left(\mathrm{a}\right)$ Find the current through the battery a long time after the switch $\mathrm{S}$ is closed.

$\left(\mathrm{b}\right)$ Suppose the switch is opened at $\mathrm{t} = 0.$ What is the time constant of the decay circuit?

$\left(\mathrm{c}\right)$ Find the current through the inductor after one time constant.

A superconducting loop of radius $\mathrm{R}$ has self inductance $\mathrm{L}$. A uniform & constant magnetic field $\mathrm{B}$ is applied perpendicular to the plane of the loop. Initially current in this loop is zero. The loop is rotated about its diameter by $180º.$ Find the current in the loop after rotation.