The current (I) in an inductor is varying with time (t) as shown in the figure. Which of the following…
The current (I) in an inductor is varying with time (t) as shown in the figure. Which of the following graphs shows the correct variation of voltage $(\mathrm{V})$ with time $(\mathrm{t})$ in the inductor?
Solution
To determine the variation of voltage (\(V\)) with time (\(t\)) across an inductor, you must find the rate of change (slope) of the current (\(I\)) with respect to time (\(t\)).
The relationship is given by the formula:\(V=L\frac{dI}{dt}\)where: \(V\) is the instantaneous voltage across the inductor.\(L\) is the inductance.\(\frac{dI}{dt}\) is the instantaneous rate of change of current, which corresponds to the slope of the current vs. time graph.
Analysis of the current vs. time graph From \(t=0\) to \(t=T/2\):The current increases linearly with a constant, positive slope.Since \(\frac{dI}{dt}\) is a positive constant, the voltage \(V\) will also be a constant positive value.From \(t=T/2\) to \(t=T\):The current decreases linearly with a constant, negative slope.
Since \(\frac{dI}{dt}\) is a negative constant, the voltage \(V\) will be a constant negative value.
Corresponding voltage vs. time graph Based on this analysis, the voltage graph must show a constant positive value for the first half of the cycle and a constant negative value for the second half. This is represented by a square or rectangular wave.
