Question

A coil having $n$ turns and resistance $R\Omega$ is connected with a galvanometer of resistance $4R\Omega$. This combination is moved in time $t$ second from a magnetic field $w_1$ weber to $w_2$ weber. The induced current in the circuit is

• A. $\frac{-\left(w_2-w_1\right)}{5Rt}$
• B. $\frac{-n\left(w_2-w_1\right)}{5Rt}$
• C. $\frac{-\left(w_2-w_1\right)}{Rnt}$
• D. $\frac{-n\left(w_2-w_1\right)}{Rt}$

Answer 1

Answer: (B)

Current is given by
$I=\frac{E}{R^{\prime }}$
Substituting, $E=-\frac{nd\varphi }{dt}$, we get
$I=-\frac{n}{R^{\prime }}\cdot \frac{d\varphi }{dt}...(i)$
Given that $w_1$ and $w_2$ are the values of the flux associated with one tum of the coil.
Therefore, Eq. (i) becomes,
$I=-\frac{n}{R^{\prime }}\left[\frac{w_2-w_1}{t_2-t_1}\right]...(2)$
Total resistance of the combination is $R^{\prime }=R+4R=5R$,
substituting the values of $R^{\prime }$ and $\left(t_2-t_1\right)=t$ in
Eq. (ii), we get
$I=-\frac{n}{5R}\left(\frac{w_2-w_1}{t}\right)$
$\Rightarrow I=\frac{-n\left(w_2-w_1\right)}{5Rt}$