Question

Design an oscillating LC circuit - provide the values of L and C - having a frequency of 4, 32 × 104 ra /s and stored energy of 0.30 mJ. The maximum voltage drop across the capacitor should be 200 V.

Answer 1

Begin with the energy stored in the circuit. When the circuit oscillates, all of the energy transfers between the capacitor and the inductor, so we can write the expression for energy in the capacitor (remember to convert millijoules to joules used in SI):

$$E=\frac{1}{2}CV^2,$$

$$C=\frac{2E}{V^2}=15\cdot10^{-9}\text{ F}.$$

The resonant frequency is

$$\omega=\frac{1}{\sqrt{LC}},$$

$$L=\frac{1}{\omega^2C}=0.0357\text{ H}.$$