The current I in an inductance coil varies with time according to the graph shown. Which one of the following plots shows the variation of voltage in the coil with time?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3)
The self-induced emf of the coil is \( e = -L\,dI/dt \), so the voltage graph follows the slope of the current graph.
From 0 to \( t_0 \) the current rises along a straight line of constant slope \( +k \), so the emf has a constant negative value:
\( e = -Lk \)
From \( t_0 \) to \( 2t_0 \) the current falls along a straight line of slope \( -k \), so the emf has the equal and opposite constant value:
\( e = +Lk \)
The plot is therefore a constant negative level that jumps at \( t_0 \) to an equal positive level, as in Option (3).
Why the other options are incorrect
Option (1) — Incorrect. This repeats the shape of the current itself; the emf depends on the slope of the current, not on its value.
Option (2) — Incorrect. A voltage that varies linearly would need a current that varies as \( t^{2} \), but the current here is linear.
Option (4) — Incorrect. A smooth sinusoidal voltage needs a sinusoidal current; the slope of a straight line is constant, so there is no smooth variation.
Note: A similar question was also asked in CUET (UG) 2023 on 14-06-2023 (Slot 3).