Q. A coil having $n$ turns and resistance $R\ \Omega\ $is connected with a galvanometer of resistance $4R\ \Omega$. This combination is moved in time $t$ sec from a magnetic field $W_{1}\ wb\ to\ W_{2}\ wb$. The induced current in the circuit is
A) $\frac{W_{2} - W_{1}}{5\ Rnt}$
B) $\frac{n(W_{2} - W_{1})}{5\ Rt}$
C) $- \frac{(W_{2} - W_{1})}{Rnt}$
D) $- \frac{n(W_{2} - W_{1})}{Rt}$
Explanation
(b) The rate of change of flux or emf induced in the coil is
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e = - n\frac{d\phi}{dt}$
$\therefore$ induced current $i = \frac{e}{R'} = - \frac{n}{R'}\frac{d\phi}{dt}$
Given, $R^{'} = R + 4R = 5R,\ d\phi = W_{2} - W_{1},\ dt = t.$
(Here, $W_{1}$and $W_{2}$are flux associated with one turn).
Putting the given values is Eq.(i), we get
$\therefore\ \ \ \ \ \ \ i = - \frac{n}{5R}\ \frac{(W_{2} - W_{1})}{t}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.