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Two coils, labelled 1 and 2, have mutual inductance M and each has resistance R. The current in coil 1 varies with time as I1 = k*t², where k is constant. Find the total charge that flows through coil 2 between t = 0 and t = T.

1. M*k*T²/R
2. 2*M*k*T/R
3. M*k*T/R
4. M*k*T²/(2*R)

Correct answer: M*k*T²/R

Solution

Induced EMF in coil 2: e = M*dI1/dt. Current i2 = e/R = (M/R)*dI1/dt. Charge q = integral[0..T] i2 dt = (M/R)*integral dI1 = (M/R)*[I1(T) - I1(0)] = (M/R)*(k*T² - 0) = M*k*T²/R.

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