Inductors and Inductance — Question 6

Question 6

Series inductances add when their magnetic coupling is negligible

Two ideal linear inductors L1 and L2 are in series, sufficiently separated that mutual induction is negligible. The same current i enters their positive voltage terminals (the passive convention).

1. Derive the equivalent inductance from terminal voltages.

2. For L1=3.00 mH and L2=7.00 mH, find the total voltage when current increases at 200 A/s.

Question 6 - Solution

Series inductances add when their magnetic coupling is negligible

(a) Method and calculation

$$v_1=L_1\dot i,\quad v_2=L_2\dot i,\quad v=v_1+v_2.$$$$\boxed{L_{\mathrm{eq}}=L_1+L_2}.$$

(b) Interpretation and further calculation

$$L_{\mathrm{eq}}=.00300+.00700=.0100\,H.$$$$\boxed{v=(.0100)(200)=2.00\,V}.$$

Physical check

Nearby coupled coils require mutual-inductance terms; simple addition is conditional on negligible coupling.