Question

coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4RΩ. This combination is moved in time t seconds from a magnetic field W₁ weber to W₂ weber. The induced current in the circuit is
(a) $-\frac{W_2-W_1}{5Rnt}$
(b) $-\frac{n(W_2-W_1)}{5Rnt}$
(c) $-\frac{(W_2-W_1)}{Rnt}$
(d) $-\frac{n(W_2-W_1)}{Rt}$

Answer 1

answer : option (b) $-\frac{n(W_2-W_1)}{5Rt}$

number of turns of coil = n

resistance of the coil = R

resistance of galvanometer = 4R

change in magnetic flux in one turns of coil = $W_2-W_1$

so, total change in flux through coil = $n(W_2-W_1)$

we know, galvanometer is connected with coil in series combination so, Req = R +4R = 5R

now, induced emf = - change in flux/time

= - $\frac{n(W_2-W_1)}{t}$

now, induced current = $\frac{\xi_{in}}{R_{eq}}$

= $-\frac{n(W_2-W_1)}{5Rt}$

[ note : here, little mistake is done in typing option (b), $-\frac{n(W_2-W_1)}{5Rt}$ should be write in place of $-\frac{n(W_2-W_1)}{5Rnt}$]