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(C) The induced emf $E$ in a coil is given by Faraday's law: $E = -L \frac{di}{dt}$.$1$. During interval $a$: The current $i$ is constant,so $\frac{di

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(C) The induced emf $E$ in a coil is given by Faraday's law: $E = -L \frac{di}{dt}$.$1$. During interval $a$: The current $i$ is constant,so $\frac{di}{dt} = 0$. Thus,$E = 0$.$2$. During interval $b$: The current $i$ decreases linearly with time,so $\frac{di}{dt}$ is a negative constant. Since $E = -L \frac{di}{dt}$,$E$ will be a positive constant.$3$. During interval $c$: The current $i$ increases linearly with time,so $\frac{di}{dt}$ is a positive constant. Thus,$E = -L \frac{di}{dt}$ will be a negative constant.Comparing these results with the given options,the graph that shows zero emf,then a constant positive emf,and then a constant negative emf is the correct representation.

The current $i$ in an induction coil varies with time $t$ according to the graph shown in the figure. Which of the following graphs shows the induced emf $(E)$ in the coil with time?

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