Laplace transforms: R series with RC parallel circuit: Difference between revisions
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===Problem Statement=== |
===Problem Statement=== |
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Find the Voltage across the capacitor for t>=0: |
Find the Voltage across the capacitor for t>=0: |
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Voltage across capacitor at t(0-)=0 |
Voltage across capacitor at t(0-)=0 |
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v(t0)=0 Volts |
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v( |
: <math>v(t0)=0 Volts</math> |
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: <math>v(t)=10 Volts</math> |
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R1=20 Ohm |
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: <math>R_1=20 \boldsymbol{\Omega}</math> |
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: <math>R_2=30 \boldsymbol{\Omega}</math> |
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R2=30 Ohm |
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C=.1 Farad |
: <math>C=.1 Farad</math> |
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Loop 1 |
Loop 1 |
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<math>v(t)=R1( |
:<math>v(t)=R1(i_1+i_2)+R2(i_1)</math> |
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<math>10=20( |
:<math>10=20(i_1+i_2)+30(i_1)</math>_______________________________________equation (1) |
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Loop 2 |
Loop 2 |
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<math>v(t)=R1( |
:<math>v(t)=R1(i_1+i_2)+\dfrac{1}{C}\int{i_2 dt}</math> |
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<math>10=20( |
:<math>10=20(i_1+i_2)+\dfrac{1}{0.1}\int{i_2 dt}</math>_______________________equation (2) |
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Revision as of 23:26, 20 October 2009
Problem Statement
Find the Voltage across the capacitor for t>=0:
Voltage across capacitor at t(0-)=0
Loop 1
- _______________________________________equation (1)
Loop 2
- _______________________equation (2)
Solving equations (1) and (2) simultaneously
Laplace Transform S-domain
Inverse Laplace transform T-domain
Voltage on Capacitor