The current (I) in the inductance is varying | vedclass

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(D) The induced voltage $(V)$ across an inductor is given by the formula $V = -L \frac{dI}{dt}$.From the given $I-t$ graph, the current increases line

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(D) The induced voltage $(V)$ across an inductor is given by the formula $V = -L \frac{dI}{dt}$.From the given $I-t$ graph, the current increases linearly from $t = 0$ to $t = T/2$. During this interval, the slope $\frac{dI}{dt}$ is positive and constant. Therefore, $V = -L 	imes (	ext{positive constant}) = 	ext{negative constant}$.From $t = T/2$ to $t = T$, the current decreases linearly. During this interval, the slope $\frac{dI}{dt}$ is negative and constant. Therefore, $V = -L 	imes (	ext{negative constant}) = 	ext{positive constant}$.Thus, the voltage $V$ is a negative constant for the first half and a positive constant for the second half. Comparing this with the given options, the correct representation is a square wave where the voltage is negative for $0 < t < T/2$ and positive for $T/2 < t < T$, which corresponds to the shape shown in option $D$.

The current $(I)$ in the inductance is varying with time according to the plot shown in the figure. Which one of the following is the correct variation of voltage $(V)$ with time in the coil?

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