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Q. Consider a pair of coupled coils as shown in Figure of the text, with currents, voltages, and polarity dots as indicated. Show that the mutualinductance is L12 = L21 = M by following these steps:
(a) Starting at time t0 with i1(t0) = i2(t0) = 0, maintain i2 = 0 and increase i1 until, at time t1,i1(t1) = I1 and i2(t1) = 0. Determine the energy accumulated during this time.Now maintaining i1 = I1, increase i2 until at time t2,i2(t2) = I2. Find the corresponding energy accumulated and the total energy stored at time t2.
(b) Repeat the process in the reverse order, allowing the currents to reach their final values. Compare the expressions obtained for the total energy stored and obtain the desired result.
Solenoids find application in a variety of electrically controlled valves. The magnetic structure shown in Figure is a simplified representation of a solenoid in which the flux in
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