Lecture 34
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Lecture 34. Energy 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:.

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Lecture 34

Energy 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



Check:

where


RLC Circuit – Loop Equation

Graph of Q and I of Dampened Oscillation:

Each term can be positive or negative.

PL + PC stays negative

Always positive


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