The magnetic flux through a loop of resistanc | vedclass

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(B) Given: Magnetic flux $\phi = 5t^2 - 4t + 1 	ext{ Wb}$ and resistance $R = 10 \Omega$.According to Faraday's law of induction, the induced electro

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$0.2$

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(B) Given: Magnetic flux $\phi = 5t^2 - 4t + 1 	ext{ Wb}$ and resistance $R = 10 \Omega$.According to Faraday's law of induction, the induced electromotive force $(EMF)$ is $e = -\frac{d\phi}{dt}$.Differentiating $\phi$ with respect to $t$: $\frac{d\phi}{dt} = \frac{d}{dt}(5t^2 - 4t + 1) = 10t - 4$.The induced current $I$ is given by $I = \frac{|e|}{R} = \frac{|-d\phi/dt|}{R} = \frac{|-(10t - 4)|}{10} = \frac{|4 - 10t|}{10}$.At $t = 0.2 	ext{ s}$, the current is $I = \frac{|4 - 10(0.2)|}{10} = \frac{|4 - 2|}{10} = \frac{2}{10} = 0.2 	ext{ A}$.

The magnetic flux through a loop of resistance $10 \Omega$ is given by $\phi = 5t^2 - 4t + 1 \text{ Wb}$. How much current is induced in the loop after $0.2 \text{ s}$ (in $\text{ A}$)?

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