Question

A coil having $n$ turns and resistance $R \Omega$ is connected with a galvanometer of resistance $4 R \Omega$. 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. $\frac{-\left(w_{2}-w_{1}\right)}{5 R t}$
• B. $\frac{-n\left(w_{2}-w_{1}\right)}{5 R t}$
• C. $\frac{-\left(w_{2}-w_{1}\right)}{R n t}$
• D. $\frac{-n\left(w_{2}-w_{1}\right)}{R t}$

Answer 1

Answer: (B)

Current is given by
$I=\frac{E}{R'}$
Substituting, $E=-\frac{n d \phi}{d t}$, we get
$I=-\frac{n}{R'} \cdot \frac{d \phi}{d t}\,\,\, ...(i)$
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 $R^{\prime}=R+4 R=5 R$,
substituting the values of $R'$ and $\left(t_{2}-t_{1}\right)=t$ in
Eq. (ii), we get
$I =-\frac{n}{5 R}\left(\frac{w_{2}-w_{1}}{t}\right) $
$\Rightarrow I =\frac{-n\left(w_{2}-w_{1}\right)}{5 R t}$