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(D) The induced $emf$ $(e)$ in a coil is given by the formula: $e = -L \frac{di}{dt}$, where $L$ is the self-inductance of the coil and $\frac{di}{dt}

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(D) The induced $emf$ $(e)$ in a coil is given by the formula: $e = -L \frac{di}{dt}$, where $L$ is the self-inductance of the coil and $\frac{di}{dt}$ is the rate of change of current.$1$. In the first part of the graph, the current $i$ decreases linearly with time $t$. Therefore, the slope $\frac{di}{dt}$ is constant and negative. Since $e = -L 	imes (	ext{negative slope})$, the induced $emf$ $e$ will be a positive constant value.$2$. In the second part of the graph, the current $i$ increases linearly with time $t$. Therefore, the slope $\frac{di}{dt}$ is constant and positive. Since $e = -L 	imes (	ext{positive slope})$, the induced $emf$ $e$ will be a negative constant value.$3$. Combining these, the graph of $e$ versus $t$ will show a positive constant value for the first interval and a negative constant value for the second interval. This corresponds to the graph shown in option $D$.

The current through a coil varies according to the following graph. Plot the graph for induced $emf$ versus time for the coil.

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