LC Oscillations, Qualitatively — Question 1

Question 1

A discharged capacitor can coexist with the largest circuit current

An ideal LC loop starts with capacitor charge Q and zero current. Use $U=q^2/(2C)+Li^2/2$ and define $i=\dot q$ on the initially positive plate.

1. Find the current magnitude when the capacitor first reaches zero charge.

2. Determine whether the motion stops there and give the sign of the next capacitor charge.

Question 1 - Solution

A discharged capacitor can coexist with the largest circuit current

(a) Method and calculation

$$U=Q^2/(2C)=LI_{\max}^2/2.$$$$\boxed{I_{\max}=Q/\sqrt{LC}}.$$

(b) Interpretation and further calculation

$$q=0,\quad i=-I_{\max}\ne0\Rightarrow q(t+dt)\simeq-I_{\max}dt.$$$$\boxed{q(t+dt)<0;\quad U_C=0,\ U_L=U}.$$

Physical check

Zero capacitor voltage is not zero total energy; the inductor continues transferring charge.