A coil of resistance $$400\,\Omega $$ is placed in a magnetic field. If the magnetic flux $$\phi \left( {Wb} \right)$$ linked with the coil varies with time $$t$$ (second) as $$\phi = 50\,{t^2} + 4.$$
The current in the coil at $$t = 2\,s$$ is
A.
$$0.5\,A$$
B.
$$0.1\,A$$
C.
$$2\,A$$
D.
$$1\,A$$
Answer :
$$0.5\,A$$
Solution :
Induced emf in a coil is given by
$$E = \left| { - \frac{{d\phi }}{{dt}}} \right|$$
Given, $$\phi = 50\,{t^2} + 4\,$$
and resistance, $$R = 400\,\Omega $$
So, $$E = {\left| { - \frac{{d\phi }}{{dt}}} \right|_{t = 2}} = {\left| {100\,t} \right|_{t = 2}} = 200\,V$$
So, current in the coil will be
$$I = \frac{E}{R} = \frac{{200}}{{400}} = \frac{1}{2} = 0.5\,A$$
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