Self-Induction — Question 5

Question 5

A voltage limit sets a minimum time for interrupting inductor current

A .200-H ideal inductor initially carries 3.00 A. A controlled circuit brings the current monotonically to zero while limiting the magnitude of the inductor passive voltage to 120 V.

1. Find the minimum possible interruption time.

2. Find the average inductor voltage if the interruption instead takes .0100 s, and identify the optimal waveform for attaining the minimum time.

Question 5 - Solution

A voltage limit sets a minimum time for interrupting inductor current

(a) Method and calculation

$$L\Delta i=\int_0^T vdt=-LI_0,\quad\left|\int_0^T vdt\right|\le V_{\max}T.$$$$\boxed{T\ge LI_0/V_{\max}=.00500\,s}.$$

(b) Interpretation and further calculation

$$\overline v=L(0-3.00)/.0100=\boxed{-60.0\,V}.$$$$\boxed{v=-120\,V\text{ throughout the shortest interval}}.$$

Physical check

The bound follows from current continuity and finite available voltage, without assuming a particular switch or clamp implementation.