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.

Question

Philoid · Accepted Answer

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