Laplace transforms: R series with RC parallel circuit: Difference between revisions
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Line 46: | Line 46: | ||
:Loop 1 |
:Loop 1 (left Box) |
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:<math>v(t)=R1(i_1+i_2)+R2(i_1)\,</math> |
:<math>v(t)=R1(i_1+i_2)+R2(i_1)\,</math> |
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:Loop 2 |
:Loop 2 (Right Box) |
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:<math>v(t)=R1(i_1+i_2)+\dfrac{1}{C}\int{i_2 dt}\,</math> |
:<math>v(t)=R1(i_1+i_2)+\dfrac{1}{C}\int{i_2 dt}\,</math> |
Revision as of 15:56, 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 (left Box)
- _______________________________________equation (1)
- Loop 2 (Right Box)
- _______________________equation (2)
Solve equations (1) and (2) simultaneously
- Substituting equation (1) into equation (2) gives...
- simplifies to...
Take the Laplace Transform to move to the S-domain
Take the inverse Laplace transform to move back into the t-domain
- substitute this equation back into equation (1)
Voltage on Capacitor
Answer
- Volts
Apply the Initial and Final Value Theorems to find the initial and final values
- Initial Value Theorem
- Final Value Theorem
- Initial Value:
- Initial Value = 0 Volts
- Final Value:
- Final Value = 6 Volts
- Volts
- Volts
Bode Plot
simplified to...
Written by: Andrew Hellie
Checked by: