Lecture 34

Lecture 34Energy in a Capacitor and Inductor:

In Capacitors: For Inductors:

Mechanical Analogy: Mass Spring System

Corresponds to:

LC circuits oscillate much in the same way a mass spring system oscillates

LC Circuit

Basic Equations:

Loop Equation:

Power Equation:

Conservation of Energy:

Solving the Loop Equation – Analogy to Mass-Spring System

Solution:

Comment:General Solution:

(δ is the initial phase angle of the oscillation)

Often set δ = 0, where at t = 0, the initial condition is chosen to be x = xmax

LC Circuit Analogy

Check:

where

RLC Circuit – Loop Equation

Always positive

Each term can be positive or negative.

PL + PC stays negative

Graph of Q and I of Dampened Oscillation: