Self-Induction — Question 3

Question 3

A prescribed sinusoidal current requires both resistive and inductive terminal voltage

A real coil has constant inductance L and winding resistance r. A current source imposes $i=I_0\sin\omega t$. Use passive terminal voltage across the complete coil.

1. Find v(t).

2. Find v at a positive current maximum and at an upward current zero crossing.

Question 3 - Solution

A prescribed sinusoidal current requires both resistive and inductive terminal voltage

(a) Method and calculation

$$v=ri+L\dot i.$$$$\boxed{v=rI_0\sin\omega t+\omega LI_0\cos\omega t}.$$

(b) Interpretation and further calculation

$$\omega t=\pi/2:\quad\boxed{v=rI_0}.$$$$\omega t=0:\quad\boxed{v=\omega LI_0}.$$

Physical check

Zero current does not imply zero inductor voltage; the derivative may be greatest at that instant.