LC Circuits

• Inductors oppose change in current!

Kirchhoff’s Law! (Now, we are going to tailor it to our specific system!)

$$\frac{1}{c}Q+(L)\frac{d^{2}Q}{d{t}^2}=0$$

• This is a differential equation!

• The first term represents the capacitor, and the second represents the inductor!

Looking at the oscilloscope, we end up with this function!

$$Q(t)=Q_{max}cos(\omega t)$$

• Knowing this now, we can plug that back in to receive another equation

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

ω = Angular Frequency (rads/sec) L = Self Inductance (H, Henrys) C = Coulombs (C) T = Period (Seconds)

$$T=\frac{2\pi }{\omega }$$ $$T=2\pi \sqrt{LC}$$