Lecture 11 - Tau from series capacitor combo, R I I t 0 I...

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Spring 2011 ECE 2100, Cornell Univ. A. Molnar 1 Lecture 11 RL circuits: natural response More complex RC circuits,
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Spring 2011 ECE 2100, Cornell Univ. A. Molnar 2 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 + 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 )
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Spring 2011 ECE 2100, Cornell Univ. A. Molnar 3 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 + 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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Spring 2011 ECE 2100, Cornell Univ. A. Molnar 4 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
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Unformatted text preview: Tau from series capacitor combo, R I I t 0 I exp(-t/ ) Spring 2011 ECE 2100, Cornell Univ. A. Molnar 5 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 + = --+ = --+ = ( 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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Lecture 11 - Tau from series capacitor combo, R I I t 0 I...

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