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 field $W_1$ weber to $W_2$ weber. The induced current in the circuit is

JEE Main · 2004 · 24 Apr 2004 · Offline · Electromagnetic Induction

A coil having

n

turns and resistance

R Ω

is connected with a galvanometer of resistance

4 R Ω

. This combination is moved in time

t

seconds from a magnetic field

W_{1}

weber to

W_{2}

weber. The induced current in the circuit is

(A) $- \frac{W _{2} - W _{1}}{5 R n t}$
(B) $- \frac{n ( W _{2} - W _{1} )}{5 R t}$ ✓ Correct
(C) $- \frac{W _{2} - W _{1}}{R n t}$
(D) $- \frac{n ( W _{2} - W _{1} )}{R t}$

Answer: (B)

Solution

With

n

turns the induced emf is

ε = - n \frac{d ϕ}{d t} = - n \frac{W _{2} - W _{1}}{t}

, where

W_{1}

and

W_{2}

are the flux values through a single turn. The total resistance in the circuit is

R + 4 R = 5 R

, so the induced current is

I = \frac{ε}{5 R} = - \frac{n ( W _{2} - W _{1} )}{5 R t}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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