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.

In figure, $\mathrm{\xi }=100 \mathrm{V}, R_1=10 \mathrm{\Omega }, R_2=20 \mathrm{\Omega },\mathit{ }{R}_3=30 \mathrm{\Omega } \mathrm{and} L=2 \mathrm{H}. \mathrm{Find} i_1 \& i_2.$

$\left(\mathrm{a}\right)$ Immediately after switch ${\mathrm{S}}_{\mathrm{w}}$ is closed

$\left(\mathrm{b}\right)$ A long time after

$\left(\mathrm{c}\right)$ Immediately after ${\mathrm{S}}_{\mathrm{w}}$ is opened again

$\left(\mathrm{d}\right)$ A long time later.

In the circuit shown ${\mathrm{S}}_1 \& {\mathrm{S}}_2$ are switches. ${\mathrm{S}}_2$ remains closed for a long time and ${\mathrm{S}}_1$open. Now ${\mathrm{S}}_1$ is also closed. Just after ${\mathrm{S}}_1$is closed, The potential difference$\left(\mathrm{V}\right)$across $\mathrm{R}$  and $\frac{\mathrm{di}}{\mathrm{dt}}$(with sign) in $\mathrm{L}$.

Two inductances $L_{1 }\& L_2$ are connected in series & are separated by a large distance.

$\left(\mathrm{a}\right)$ Show that their equivalent inductance is$L_1+L_2.$

$\left(\mathrm{b}\right)$ Why must their separation be large?