A (current vs time) graph of the current passing through a solenoid is shown in Fig 6.9. For which time is the back electromotive force (u) a maximum. If the back emf at t = 3s is e, find the back emf at t = 7 s, 15s and 40s. OA, AB and BC are straight line segments.
A (current vs time) graph of the current passing through a solenoid is shown in Fig 6.9. For which time is the back electromotive force (u) a maximum. If the back emf at t = 3s is e, find the back emf at t = 7 s, 15s and 40s. OA, AB and BC are straight line segments.

We may deduce from the graph that when the rate of change of magnetic flux reaches its highest, the electromagnetic force, which is proportional to the rate of change of current, reaches its maximum. When the time axis reaches its maximum angle at AB, the present rate will be at its highest.

As a result, when t = 3 seconds, s = OA slope

As a result, the current rate of change at t = 3 = 14 A/s.

As a result, the electromotive force is equal to L/5.

It is -3e when the emf is between 5 and 10 seconds.

It is +1/2e when the emf is between 10 and 30 seconds.