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 know that induced EMF is given by



thus negative sign indicates that induced EMF (∈) oppose any change increases or decreases of current in the coil


when maximum rate of change of current then back EMF in solenoid is (u) is maximum


this AB occur on the graph


so maximum back EMF will be obtained between 5s < t < 10s



for 0 < t < 5s ,


since back EMF at t = 3s


hence rate of change of current t=3s


if where L = constant


EMF is


similarly, we have for other value


for 5s < t < 10s




thus at t = 7s u1 = -3e


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