The figure shows an inductor of $2 \mathrm{H}$ through which a current increasing at the rate of $5\mathrm{A}/\sec ,$ is flowing. Find the potential difference ${\mathrm{V}}_{\mathrm{X} }– {\mathrm{V}}_{\mathrm{Y}}.$

Figure shows a part of a circuit. Find the rate of change of the current, as shown.

Suppose the $\mathrm{EMF}$ of the battery in the circuit shown varies with time $\mathrm{t}$ so the current is given by $\mathrm{i}\left(\mathrm{t}\right)=3+5\mathrm{t},$ where $i$ is in amperes &$\mathrm{t}$ is in seconds. Take $\mathrm{R}=4 \mathrm{\Omega }, \mathrm{L}=6 \mathrm{H}$& find an expression for the battery $\mathrm{EMF}$ as a function of time.

The network shown in figure is a part of a complete circuit. What is the potential difference ${\mathrm{V}}_{\mathrm{B}} – {\mathrm{V}}_{\mathrm{A}},$ when the current in the circuit is $5\mathrm{A}$ and is decreasing at a rate of ${10}^3 (\mathrm{A}/\mathrm{s})$?

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.