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(C) Given: Resistance $R = 10 \ \Omega$,magnetic flux $\phi = 6t^2 + 7t + 1 \ mWb$,and time $t = 1 \ s$.According to Faraday's law of electromagnetic

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$19 \ mV$

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(C) Given: Resistance $R = 10 \ \Omega$,magnetic flux $\phi = 6t^2 + 7t + 1 \ mWb$,and time $t = 1 \ s$.According to Faraday's law of electromagnetic induction,the induced e.m.f. $(e)$ is given by the rate of change of magnetic flux:$e = \left| \frac{d\phi}{dt} \right|$Differentiating $\phi$ with respect to $t$:$\frac{d\phi}{dt} = \frac{d}{dt}(6t^2 + 7t + 1) = 12t + 7$Substituting $t = 1 \ s$ into the expression:$e = 12(1) + 7 = 19 \ mV$Therefore,the induced e.m.f. at $t = 1 \ s$ is $19 \ mV$.

The magnetic flux through a loop of resistance $10 \Omega$ varies according to the relation $\phi = 6t^2 + 7t + 1$,where $\phi$ is in milliweber and time is in seconds. At time $t = 1 \ s$,the induced e.m.f. is:

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