= Solution
Use north-minus-south terminal voltages for both oppositely wound coils, with coil A measured at high input impedance so its AC current is zero. Then $v_B=L_B\dot I_B$ and $v_A=M\dot I_B$, with $M<0$. Hence
$$
\boxed{v_A(t)=\frac{M}{L_B}v_B(t)=-\frac{n_1}{n_2}V_0\sin\omega t.}
$$
The magnitude is the turns ratio times the drive, and these terminal references give a phase reversal. Reversing one voltmeter lead reverses the displayed sign. A fixed DC bias in A does not change this incremental result, while short-circuiting A would require solving both coupled current equations.
Back to article page
