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 mutual
inductance 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.