Flux phi (in weber) in a closed circuit of re | vedclass

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(D) According to Faraday's law of electromagnetic induction,the induced electromotive force $(EMF)$ is given by $e = -\frac{d\phi}{dt}$.Given the flux

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$0.2$

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(D) According to Faraday's law of electromagnetic induction,the induced electromotive force $(EMF)$ is given by $e = -\frac{d\phi}{dt}$.Given the flux $\phi = 6t^2 - 5t + 1$,we differentiate with respect to time $t$:$\frac{d\phi}{dt} = \frac{d}{dt}(6t^2 - 5t + 1) = 12t - 5$.The induced current $i$ is given by $i = \frac{|e|}{R} = \frac{1}{R} \left| \frac{d\phi}{dt} \right|$.Given resistance $R = 10\,\Omega$,at $t = 0.25\,s$:$|e| = |12(0.25) - 5| = |3 - 5| = |-2| = 2\,V$.Therefore,the magnitude of the induced current is $i = \frac{2\,V}{10\,\Omega} = 0.2\,A$.

Flux $\phi$ (in weber) in a closed circuit of resistance $10\,\Omega$ varies with time $t$ (in sec) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25\,s$ (in $,A$)?

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