A (current versus time) graph of the current passing through a solenoid is shown in figure. For which time is the back electromotive force (u) a maximum. If the back emf at s is e, find the back emf at . OA, AB and BC are straight line segments.
Thus, negative sign indicates that induced emf (e) opposes any change (increase or decrease) of current in the coil.
When the rate of change of current is maximum, then back emf in solenoid is (u) a maximum. This occurs in AB part of the graph. So maximum back emf will be obtained between
Since, the back emf at is e.
Also, the rate of change of current at ,
and slope (s) of OA (from to )
So , we have
If .
where, L is a constant (coefficient of self -induction).
and emf is
Similarly, we have for others values.
For
Thus,