The magnetic flux through a coil of resistance 'R' changes by an amount ' $\Delta \phi$ 'in time ' $\Delta…
The magnetic flux through a coil of resistance 'R' changes by an amount ' $\Delta \phi$ 'in time ' $\Delta t$ '. The amount of induced current and induced charge in the coil are respectively
$\left(\frac{\Delta \phi}{\Delta t}\right) \mathrm{R}$ and $\frac{\mathrm{R}}{\Delta \phi}$
$\frac{\Delta \phi}{\mathrm{R}}$ and $\mathrm{R}\left(\frac{\Delta \mathrm{t}}{\Delta \phi}\right)$
$\frac{\Delta \phi}{\mathrm{R}}+\mathrm{R}$ and $\frac{\Delta \phi}{\Delta \mathrm{t}}$
$\left(\frac{\Delta \phi}{\Delta \mathrm{t}}\right) \times \frac{1}{\mathrm{R}}$ and $\frac{\Delta \phi}{\mathrm{R}}$
Solution
According to Faraday's law of electromagnetic induction,
$\begin{aligned}
& |e|=\frac{\Delta \phi}{\Delta t} \\
& I R=\frac{\Delta \phi}{\Delta t} \\
& I=\left(\frac{\Delta \phi}{\Delta t}\right) \frac{1}{R}
\end{aligned}$
$\therefore \quad$ The total quantity of electric charge passing through the circuit is
$\begin{aligned}
\mathrm{Q} & =\mathrm{I} \times \Delta \mathrm{t} \\
& =\frac{\Delta \phi}{\mathrm{R}}
\end{aligned}$