Chapter 13, Problem 1RQ

Refer to the two magnetically coupled coils of Fig. 13.69(a). The polarity of the mutual voltage is:

1. (a) Positive
2. (b) Negative

Figure 13.69

To determine

Choose the correct option, which is the polarity of the mutual voltage.

Answer to Problem 1RQ

The correct option from the given choices is $\underset{\_}{\left(\text{b}\right)\text{Negative}}$.

Explanation of Solution

Given data:

Refer to Figure 13.69(a) in the textbook for the two magnetically coupled coils.

Calculation:

Modify the Figure 13.69(a) by indicating positive and negative terminals and mentioning coils 1 and 2. The modified figure as shown in Figure 1.

Consider that the currents are denoted as $i_1$ and $i_2$. The mutual inductance between two coils is denoted as M.

In Figure 13.69(a), the current $i_1$ enters at the dotted terminal of coil 1 and the voltage is negative in the dotted terminal of coil 2. Therefore, the mutual voltage $M\frac{d{i}_1}{dt}$ is negative.

Similarly, the current leaves at the dotted terminal of coil 2 and the voltage is positive in the dotted terminal of coil 1. Hence, the mutual voltage $M\frac{d{i}_2}{dt}$ is negative.

Therefore, the polarity of mutual voltage is negative. Hence, the option (b) is correct and option (a) is incorrect.

Conclusion:

Thus, the correct option from the given choices is $\underset{\_}{\left(\text{b}\right)\text{Negative}}$.