lecture 34 energy in a capacitor and inductor: in capacitors:for inductors:
TRANSCRIPT
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Lecture 34Energy in a Capacitor and Inductor:
In Capacitors: For Inductors:
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Mechanical Analogy: Mass Spring System
Corresponds to:
LC circuits oscillate much in the same way a mass spring system oscillates
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LC Circuit
Basic Equations:
Loop Equation:
Power Equation:
Conservation of Energy:
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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
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LC Circuit Analogy
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Check:
where
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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: