MHTCET 15 May 2024 Shift 1 Paper

Concept:The e.m.f. induced in the secondary coil is given by Faraday's law of mutual induction.The magnitude of the induced e.m.f. is $E = M \frac{dI}{dt}$, where $M$ is the mutual inductance.Explanation:The primary current is alternating, so it can be written as $I = I_0 \sin(\omega t)$.Given peak current $I_0 = \frac{2}{\pi}$ A and frequency $f = 50$ Hz.The angular frequency is $\omega = 2\pi f = 2\pi \times 50 = 100\pi$ rad/s.Differentiating the current with respect to time gives:$$\frac{dI}{dt} = I_0 \omega \cos(\omega t) = \frac{2}{\pi} \times 100\pi \cos(\omega t) = 200 \cos(\omega t)$$The peak value of $\cos(\omega t)$ is $1$, so the maximum rate of change of current is $200$ A/s.Now, $E_{\text{peak}} = M \times \left(\frac{dI}{dt}\right)_{\text{peak}} = 1 \times 200 = 200$ V.Answer:The peak e.m.f. induced in the secondary coil is $200$ V.Therefore, the correct option is D. $200$ V.