Laplace transforms: R series with RC parallel circuit: Difference between revisions
Jump to navigation
Jump to search
Line 7: | Line 7: | ||
: <math>v(t0)=0 Volts</math> |
: <math>v(t0-)=0 Volts</math> |
||
: <math>v(t)=10 Volts</math> |
: <math>v(t)=10 Volts</math> |
||
Line 18: | Line 18: | ||
Use Loop Equations to solve for the currents in <math>i_1</math> and <math>i_2</math> |
|||
⚫ | |||
⚫ | |||
:<math>v(t)=R1(i_1+i_2)+R2(i_1)</math> |
:<math>v(t)=R1(i_1+i_2)+R2(i_1)</math> |
||
:<math>10=20(i_1+i_2)+30(i_1)</math> |
:<math>10=20(i_1+i_2)+30(i_1)</math> |
||
:<math>i_1=(10-20i_2)/50</math>_______________________________________equation (1) |
|||
Loop 2 |
:Loop 2 |
||
:<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> |
||
:<math>10=20(i_1+i_2)+\dfrac{1}{ |
:<math>10=20(i_1+i_2)+\dfrac{1}{.1}\int{i_2 dt}</math>_______________________equation (2) |
||
Line 35: | Line 39: | ||
Solving equations (1) and (2) simultaneously |
Solving equations (1) and (2) simultaneously |
||
:Equation 1 into equation 2 gives... |
|||
: |
|||
Revision as of 23:50, 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
- Equation 1 into equation 2 gives...
Laplace Transform S-domain
Inverse Laplace transform T-domain
Voltage on Capacitor