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 field $${W_1}$$ weber to $${W_2}$$ weber. The induced current in the circuit is
A.
$$ - \frac{{\left( {{W_2} - {W_1}} \right)}}{{Rnt}}$$
B.
$$ - \frac{{n\left( {{W_2} - {W_1}} \right)}}{{5Rt}}$$
C.
$$ - \frac{{\left( {{W_2} - {W_1}} \right)}}{{5Rnt}}$$
D.
$$ - \frac{{n\left( {{W_2} - {W_1}} \right)}}{{Rt}}$$
Answer :
$$ - \frac{{n\left( {{W_2} - {W_1}} \right)}}{{5Rt}}$$
Solution :
$$\eqalign{
& \frac{{\Delta \phi }}{{\Delta t}} = \frac{{\left( {{W_2} - {W_1}} \right)}}{t} \cr
& {R_{tot}} = \left( {R + 4R} \right)\Omega = 5R\Omega \cr
& i = \frac{{nd\phi }}{{{R_{tot}}dt}} = \frac{{ - n\left( {{W_2} - {W_1}} \right)}}{{5Rt}} \cr
& \left( {\because {W_2}\,\& \,{W_1}{\text{ are magnetic flux}}} \right) \cr} $$