# Simplifying circuit

Discussion in 'Homework Help' started by jobu180, Nov 1, 2008.

1. ### jobu180 Thread Starter New Member

Nov 1, 2008
7
0
I'm trying simplify the following circuit:

( R1 in series with C1) || C2

I'm looking for Z .

Thanks.

2. ### hgmjr Moderator

Jan 28, 2005
9,030
214
HINT:

Assign the series RC leg the reference Z1 and assign the C2 leg the reference Z2.

Then write the expression for Z1||Z2.

With the expression Z1||Z2 figured out, you can then plug in the impedances for each of the elements and solve.

hgmjr

3. ### jobu180 Thread Starter New Member

Nov 1, 2008
7
0
Z1||Z2

Z1 = R1+C1
Z2 = C2

Z = Z1*Z2/(Z1+Z2)

Z = (R1*C2+C1*C2)/(R1+C1+C2)

Correct?

4. ### hgmjr Moderator

Jan 28, 2005
9,030
214
Sorry, No.

Remember:

$\Large Z_{\small 1}=R_{\small 1}+X_{c\small 1}$

$\Large X_{c} = \frac{1}{sC}$

hgmjr

Last edited: Nov 1, 2008
5. ### jobu180 Thread Starter New Member

Nov 1, 2008
7
0
That's right, so ...

Z1 = R1 +1/sC1
Z2 = 1/sC2

Z = (R1/sC2 + 1/s^2C1C2) / (R1 +1/sC1+1/sC2)

Hope that's right.

Thanks.

6. ### hgmjr Moderator

Jan 28, 2005
9,030
214
You have the the equation correct. You probably need to simplify the expression to be totally complete.

hgmjr