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The current (I) in the inductance is varying with time according to the plot shown in figure. Which one of the following is the correct variation of voltage with time in the coil?
A
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B
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C
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D
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Detailed Solution
Voltage across an inductor: $V = L\frac{dI}{dt}$ (the induced emf is $-L\frac{dI}{dt}$)
From 0 to $\frac{T}{2}$ the current rises linearly, so $\frac{dI}{dt}$ is a positive constant and V is constant and positive.
From $\frac{T}{2}$ to T the current falls linearly at the same rate, so V is constant and negative with the same magnitude.
So the V–t graph is a rectangular (square) wave: a positive step up to $\frac{T}{2}$, then an equal negative step up to T.
From 0 to $\frac{T}{2}$ the current rises linearly, so $\frac{dI}{dt}$ is a positive constant and V is constant and positive.
From $\frac{T}{2}$ to T the current falls linearly at the same rate, so V is constant and negative with the same magnitude.
So the V–t graph is a rectangular (square) wave: a positive step up to $\frac{T}{2}$, then an equal negative step up to T.