JEE MAIN - Physics (2004 - No. 33)
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
$${{\left( {{W_2} - {W_1}} \right)} \over {Rnt}}$$
$$ - {{n\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rt}}$$
$$ - {{\left( {{W_2} - {W_1}} \right)} \over {5\,\,Rnt}}$$
$$ - {{n\left( {{W_2} - {W_1}} \right)} \over {Rt}}$$
Explanation
$${{\Delta \phi } \over {\Delta t}} = {{\left( {{W_2} - {W_1}} \right)} \over t}$$
$${R_{tot}} = \left( {R + 4R} \right)\Omega = 5R\Omega $$
$$i = {{nd\phi } \over {{R_{tot}}dt}} = {{ - n\left( {{W_2} - {W_1}} \right)} \over {5Rt}}$$
( as $${W_2}\,\,\& \,\,{W_1}$$ are magnetic flux )
$${R_{tot}} = \left( {R + 4R} \right)\Omega = 5R\Omega $$
$$i = {{nd\phi } \over {{R_{tot}}dt}} = {{ - n\left( {{W_2} - {W_1}} \right)} \over {5Rt}}$$
( as $${W_2}\,\,\& \,\,{W_1}$$ are magnetic flux )
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