The magnetic flux (in Wb) linked with a coil of resistance \( 400\ \Omega \) varies with time \( t \)(s) as \( \varphi = 50t^{2} + 4 \). The induced current at time \( t = 2 \) s is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 0.5\ \mathrm{A} \)
By Faraday’s law, the induced emf equals the rate of change of flux; the constant term in φ does not contribute.
\( \displaystyle |e| = \frac{d\varphi}{dt} = \frac{d}{dt}(50t^{2} + 4) = 100t \)
\( \text{at } t = 2\ \mathrm{s}: \ |e| = 100 \times 2 = 200\ \mathrm{V} \)
\( \displaystyle I = \frac{|e|}{R} = \frac{200\ \mathrm{V}}{400\ \Omega} = 0.5\ \mathrm{A} \)