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 $w_2$. The induced current in the circuit is

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

Answer 1

The correct option is B $\frac{-n(w_2-w_1)}{5Rt}$

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 turn of the coil.
Therefore, equation (i) becomes,
$I=-\frac{n}{R^{{}^{\prime }}}\left[\frac{w_2-w_1}{t_2-t_1}\right]$ ....(ii)
Total resistance of the combination is $R^{{}^{\prime }}=R+4R=5R$, substituting the values of $R^{{}^{\prime }}$ and $(t_2-t_1)=t$ in equation (ii), we get
$I=-\frac{n}{5R}\left(\frac{w_2-w_1}{t}\right)$
$\Rightarrow I=\frac{-n(w_2-w_1)}{5Rt}$