LC Oscillations, Quantitatively — Question 4

Question 4

Peak measurements and period identify both circuit elements

An ideal LC oscillator has measured peak capacitor voltage 12.0 V, peak current .0300 A, and angular frequency 2500 radians per second.

1. Infer C and L without knowing the initial phase.

2. Find maximum charge and total energy.

Question 4 - Solution

Peak measurements and period identify both circuit elements

(a) Method and calculation

$$I_{\max}=\omega CV_{\max}\Rightarrow\boxed{C=I_{\max}/(\omega V_{\max})=1.00\,\mu F}.$$$$\boxed{L=V_{\max}/(\omega I_{\max})=.160\,H}.$$

(b) Interpretation and further calculation

$$Q=CV_{\max}=12.0\,\mu C.$$$$\boxed{U=\tfrac12CV_{\max}^2=72.0\,\mu J}.$$

Physical check

The ratio of voltage to current gives the impedance scale, while frequency determines the LC product.