LC Oscillations, Qualitatively — Question 6

Question 6

Doubling the initial voltage changes amplitudes but preserves the ideal clock

Two identical ideal LC loops are released from rest with capacitor voltages V and 2V. Use $Q=CV$, $I_{\max}=Q/\sqrt{LC}$, and $T=2\pi\sqrt{LC}$.

1. Compare their stored energies and peak currents.

2. Compare their periods and explain why a larger energy does not make the ideal oscillation faster.

Question 6 - Solution

Doubling the initial voltage changes amplitudes but preserves the ideal clock

(a) Method and calculation

$$U_1=CV^2/2,\quad U_2=C(2V)^2/2.$$$$\boxed{U_2/U_1=4,\quad I_{\max,2}/I_{\max,1}=2}.$$

(b) Interpretation and further calculation

$$T_1=2\pi\sqrt{LC}=T_2.$$$$\boxed{T_2/T_1=1}.$$

Physical check

Amplitude independence relies on constant linear L and C.