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A coil of resistance 400 $\Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (Wb) linked with the coil varies with time t (sec) as $\phi = 50t^2 + 4$, the current in the coil at t = 2 sec is
A
1 A
B
0.5 A
C
0.1 A
D
2 A
Detailed Solution
$|\text{emf}| = \frac{d\phi}{dt} = \frac{d}{dt}(50t^2 + 4) = 100t$
At t = 2 s, emf = 100 × 2 = 200 V
$i = \frac{\text{emf}}{R} = \frac{200}{400} = 0.5$ A
At t = 2 s, emf = 100 × 2 = 200 V
$i = \frac{\text{emf}}{R} = \frac{200}{400} = 0.5$ A