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Lecture 12

# Lecture 12 - Messier RC circuit 29 29 29 29 2 1 2 1 20 2 10...

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Lecture 12 RL circuits: natural response More complex RC circuits,

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Parallel RC circuit ( 29 ( 29 0 , exp 0 0 I I R L t I t I L IR dt dI dt dI L V IR = = - = - = - = = τ τ + V - L R By KCL, governing Eq, get 1 st order Differential equation: Solution is decaying exponential set by “L/R time constant” and initial condition Solve as before I 0 I t 0 τ I 0 exp(-t/ τ )
Parallel RC circuit: time shift ( 29 ( 29 ( 29 0 , exp exp 0 1 0 1 0 1 0 1 V V RC t t V t t V t V t t V t V t t = = - = - - = = < τ τ τ + V - C R Now assume have a switch that closes when t=t 1 Just get a time shift in the response: time constant doesn’t change. V 0 V t 0 t 1 V 0 exp(-t/ τ )

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Messier RC circuit ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 R V V Io C C C RC C RC C C t I RC t I RC t I dt t dI C t I dt dV C t I dt dV R t V t V t I V t V V t V t 0 0 , , 0 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 1 20 2 10 1 - = + = + - = - - = = - = - = = = < τ + V 1 - Two capacitors, implies two initial conditions: C1 R C2 + V 2 - Only one current, so set up its diff. eq Tau from series capacitor combo, R I 0 I t
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Unformatted text preview: ) Messier RC circuit ( 29 ( 29 ( 29 ( 29 2 1 2 1 20 2 10 1 exp exp C C C RC t V V V t V t V V V t V + = --+ = --+ = ∞ ∞ ∞ ∞ τ ( 29 ( 29 ( 29 ∞ = ∞ → ∞ ∴ → ∞ ∞ → V V V I t 2 1 + V 1-What happens to capacitor voltages? C1 R C2 + V 2-Voltages settle to same voltage: find with charge conservation So V 10 , V 20 settle to V ∞ exponentially V 10 I t 0 V 20 V ∞ ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 ( 29 2 1 2 2 1 1 2 2 1 1 2 1 2 1 2 1 2 2 1 1 2 1 C C V C V C V V C V C C C V V C V C Q Q Q V C V C Q Q Q tot tot + + = + = + + = + = + = + = ∞ ∞ ∞ ∞...
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