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 $t$ seconds from a magnetic flux $\phi_1$ Weber to $\phi_2$ Weber. The induced current in the circuit is

• A. $\frac{\phi_{2} - \phi_{1}}{5Rnt} $
• B. $ - \frac{n (\phi_{2} - \phi_{1})}{5Rnt} $
• C. $ - \frac{ (\phi_{2} - \phi_{1})}{Rnt} $
• D. $ - \frac{ n (\phi_{2} - \phi_{1})}{Rt} $

Answer 1

Answer: (B)

Given,
Number of tums in coil $=n$
We know that,
Gument $(i)=\frac{e}{R;}=\frac{-\Delta \phi}{R'\Delta t}$ $\left[\therefore e=-\Delta\right]$
$R'=R+4 R $
$i =-\frac{\left(\phi_{2}-\phi_{1}\right)}{(R+4 R) \Delta t}$
$ i =\frac{\left(\phi_{2}-\phi_{1}\right)}{5 R(\Delta t)}$
Here, coil have $n$ number of turns.
Hence, $i=-\frac{n\left(\phi_{2}-\phi_{1}\right)}{5 R(\Delta t)}$
Induced current, $i=-\frac{n\left(\phi_{2}-\phi_{1}\right)}{5 R t}$