• Support PF! Buy your school textbooks, materials and every day products Here!

Coupled RC circuit

  • Engineering
  • Thread starter no_alone
  • Start date
  • #1
32
0

Homework Statement


Hello I want to solve the following circuit, I want to know how the voltage on R1 and R2 develop with time,
It start at t=0 when there is no voltage in the circuit ( all V=0). Its a symbolic question, I need to show the equation.
V1(t) = ? ,
V2(t) = ?
The current is a DC

Homework Equations



jr8ev9.png


The Attempt at a Solution



Well, noting much.. I just wrote it in a better way:
http://i62.tinypic.com/5w9gxz.png


VR1 = VC1
VR1 + VRc + VC2 = 0
VR2 = VC2
IR1 + IC1 + VRC = Iinj
IRc = IR2 + VC2
[tex] V_1 = V_{C1} = V_{R1} \\ V_2 = V_{R2} = V_{C2} [/tex]

[tex] \frac{V_1}{R_1} + \frac{dV_1}{dt}*C_1 + \frac{V_{Rc}}{R_c} = I_{inj} \\
\frac{V_{Rc}}{R_c} = \frac{V_2}{R_2} + C_2*\frac{dV_2}{dt}[/tex]


-->

[tex] \frac{dV_1}{dt}*C_1 = I_{inj} -\frac{V_{Rc}}{R_c} - \frac{V_1}{R_1} \\
\frac{dV_2}{dt}*C_2 = \frac{V_2}{R_2} -\frac{V_{Rc}}{R_c} [/tex]
 
Last edited:

Answers and Replies

  • #2
donpacino
Gold Member
1,439
282
Do you know how to do nodal analysis?

evaluate the circuit in the frequency domain using nodal analysis.

In case you don't know nodal analysis, simply write a KCL at node V1 and V2 and solve.
 
  • #3
gneill
Mentor
20,792
2,770
You haven't defined the question sufficiently. Do you have component values or is this strictly a symbolic problem? What are the properties of the current source? Is it a DC source or an AC source? Any initial conditions?
 
  • #4
32
0
Hi @gneill and @donpacino thank you for the replay, I added some info about the question.
I also tried to make some progress.
 
  • #5
donpacino
Gold Member
1,439
282
I would start by defining the node in the upper left as V1, the node in the upper right as V2, and the bottom node as ground. so VRc=V1-V2, V1=VR1=VC1, etc
Do a laplace transform (will allow you to solve the system with algebra) to get to the frequency domain.

write two kcls at the upper left and right nodes using V1,V2,Iinj,R1,R2,Rc,C1,C2
then do some algebra and do an inverse laplace transform to get to your time domain solution.

alternatively you can solve the second order differential equation.

just a note: I am operating under the assumption that at t=0 the current source changes values. If it does not then you can disregard the capacitors.
 
  • #6
32
0
thank you donpacino but I do not know how to do laplace transform...
 
  • #7
donpacino
Gold Member
1,439
282
ok, then do what i told you, but solve the differential equation in the time domain. you will still do a KCL, but in the time domain similar to what you did above
 

Related Threads on Coupled RC circuit

Replies
2
Views
703
  • Last Post
Replies
3
Views
821
  • Last Post
Replies
1
Views
1K
Replies
1
Views
5K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
6K
  • Last Post
Replies
2
Views
542
Top