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The current i in a coil varies with time as shown in the figure. The variation of induced emf with time would be
A
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B
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C
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D
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Detailed Solution
Induced emf in the coil: $e = -L\frac{di}{dt}$, so the emf is proportional to the negative of the slope of the i–t graph.
From 0 to T/4 the current increases linearly (constant positive slope), so the emf is constant and negative.
From T/4 to T/2 the current is constant (zero slope), so the emf is zero.
From T/2 to 3T/4 the current decreases linearly (constant negative slope), so the emf is constant and positive.
From 3T/4 to T the current is again constant, so the emf is zero.
The correct graph is the one showing a constant negative emf from 0 to T/4, zero from T/4 to T/2, a constant positive emf from T/2 to 3T/4 and zero afterwards.
From 0 to T/4 the current increases linearly (constant positive slope), so the emf is constant and negative.
From T/4 to T/2 the current is constant (zero slope), so the emf is zero.
From T/2 to 3T/4 the current decreases linearly (constant negative slope), so the emf is constant and positive.
From 3T/4 to T the current is again constant, so the emf is zero.
The correct graph is the one showing a constant negative emf from 0 to T/4, zero from T/4 to T/2, a constant positive emf from T/2 to 3T/4 and zero afterwards.