Mutual Induction — Question 3

Question 3

Dot conventions determine the signs of coupled terminal voltages

Two fixed linear coils have L1=.200 H, L2=.500 H, and M=.100 H. Positive currents enter the dotted terminals; each passive voltage is dotted potential minus undotted potential. At an instant, $\dot i_1=3.00$ A/s and $\dot i_2=-4.00$ A/s.

1. Find both terminal voltages.

2. Find the mutual contribution to each induced emf, distinguishing it from terminal voltage.

Question 3 - Solution

Dot conventions determine the signs of coupled terminal voltages

(a) Method and calculation

$$v_1=L_1\dot i_1+M\dot i_2,\quad v_2=M\dot i_1+L_2\dot i_2.$$$$\boxed{v_1=.200\,V,\quad v_2=-1.70\,V}.$$

(b) Interpretation and further calculation

$$\mathcal E_{1,\mathrm{mut}}=-M\dot i_2,\quad\mathcal E_{2,\mathrm{mut}}=-M\dot i_1.$$$$\boxed{\mathcal E_{1,\mathrm{mut}}=+.400\,V,\quad\mathcal E_{2,\mathrm{mut}}=-.300\,V}.$$

Physical check

The induced emf opposes linkage change; the passive terminal voltage is the applied voltage balancing it in a lossless coil.