An alternating current with an angular freque | vedclass

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(B) The induced electromotive force $(e)$ in the secondary coil is given by Faraday's law of induction: $e = -M \frac{di}{dt}$.From the given triangul

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$191$

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(B) The induced electromotive force $(e)$ in the secondary coil is given by Faraday's law of induction: $e = -M \frac{di}{dt}$.From the given triangular waveform,the current changes from $0$ to $I_0 = 1\,A$ in a time interval of $\Delta t = T/4$,where $T$ is the time period.The angular frequency is $\omega = 200\,rad/s$. The time period $T$ is given by $T = \frac{2\pi}{\omega} = \frac{2\pi}{200} = \frac{\pi}{100}\,s$.Therefore,the time interval $\Delta t = \frac{T}{4} = \frac{\pi}{400}\,s$.The rate of change of current is $\frac{di}{dt} = \frac{1 - 0}{\pi/400} = \frac{400}{\pi}\,A/s$.The magnitude of the induced voltage is $|e| = M \left| \frac{di}{dt} ight| = 1.5 	imes \frac{400}{\pi} = \frac{600}{\pi}$.Calculating the value: $|e| \approx \frac{600}{3.14159} \approx 190.98\,V$,which rounds to $191\,V$.

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