A coil having n turns and resistance R ohm is connected with a galvanometer of resistance 4R ohm. This combination is moved in a region where magnetic flux changes from $W_{1} w e b e r t o W_{2}$ weber in t second. The induced current in the circuit is

$- \frac{(W_{2} - W_{1})}{5 R n t}$

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$- \frac{n (W_{2} - W_{1})}{5 R t}$

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$- \frac{(W_{2} - W_{1})}{R n t}$

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$- \frac{n (W_{2} - W_{1})}{R t}$

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Solution

The correct option is B
$- \frac{n (W_{2} - W_{1})}{5 R t}$

The rate of change in flux in a single loop is $\frac{W_{2} - W_{1}}{t}$ .
Hence, the voltage generated across all the loops is $- \frac{n (W_{2} - W_{1})}{t}$
The resistance of the coil is $R + 4 R = 5 R$
Therefore, the current is equal to $\frac{- n (W_{2} - W_{1})}{5 R t}$

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