Laplace transforms: R series with RC parallel circuit: Difference between revisions
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Voltage on Capacitor |
Voltage on Capacitor |
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:<math>v_{capacitor}=10/20(i_1+i_2)</math> |
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:<math>v_{capacitor}=10-20((1/5)(1-e^{-(5/6)t})+(1/2)(e^{-(5/6)t}))</math> |
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:<math>v_{capacitor}=10-4+4e^{-(5/6)t}-10e{-(5/6)t}</math> |
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:<math>v_{capacitor}=6-6e^{-(5/6)t}</math> Volts |
Revision as of 00:33, 22 October 2009
Problem Statement
Find the Voltage across the capacitor for t>=0:
Voltage across capacitor at t(0-)=0
Use Loop Equations to solve for the currents in and
- Loop 1
- _______________________________________equation (1)
- Loop 2
- _______________________equation (2)
Solving equations (1) and (2) simultaneously
- Substituting equation (1) into equation (2) gives...
- simplifies to...
Laplace Transform S-domain
Inverse Laplace transform T-domain
- substitute this equation back into equation (1)
Voltage on Capacitor
- Volts