Laplace transforms: R series with RC parallel circuit: Difference between revisions
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Use Loop Equations to solve for the currents in <math>i_1</math> and <math>i_2</math> |
Use Loop Equations to solve for the currents in <math>i_1</math> and <math>i_2</math> |
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:Loop 1 |
:Loop 1 |
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:<math>10=20(i_1+i_2)+\dfrac{1}{.1}\int{i_2 dt}</math>_______________________equation (2) |
:<math>10=20(i_1+i_2)+\dfrac{1}{.1}\int{i_2 dt}</math>_______________________equation (2) |
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Solving equations (1) and (2) simultaneously |
Solving equations (1) and (2) simultaneously |
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:<math>20((10-20i_2)/50+i_2)+\dfrac{1}{.1}\int{i_2 dt}=10</math> |
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:simplifies to... |
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:<math>12i_2+10\int{i_2 dt}=6</math> |
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Revision as of 23:57, 21 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
Voltage on Capacitor