# RC circuits

Does anyone know of any instance where the the time constants of two RC circuits in series is additive. It seems that when R1=R2 and tao1~tao2 this holds?

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berkeman
Mentor
Does anyone know of any instance where the the time constants of two RC circuits in series is additive. It seems that when R1=R2 and tao1~tao2 this holds?
Welcome to the PF.

What is the context of the question? In general, you need to solve the whole circuit together, to figure out what the composite time constant is. This is because the circuits load each other (when there is no buffer amp between them), which changes their individual behaviors.

I am trying to determine capacitance using impedance spectroscopy with two RC circuits in series with the same resistance (1Mohm) and it seems that the circuit is behaving essentially as two capacitors in parallel so that the reference capacitance (50pF) can be subtracted from the total capacitance to get the sample capacitance.
Thanks jjk or PVDF.

berkeman
Mentor
Thanks jjk or PVDF.
Thank you to yourself? :uhh:

CNC
I am trying to determine capacitance using impedance spectroscopy with two RC circuits in series with the same resistance (1Mohm) and it seems that the circuit is behaving essentially as two capacitors in parallel so that the reference capacitance (50pF) can be subtracted from the total capacitance to get the sample capacitance.

CNC
That last post (#3) should have been the same as #5 "not thanks to myself" and I don't know what the probelm is, I am also having problems logging back in hence the multiple usernames.

berkeman
Mentor
That last post (#3) should have been the same as #5 "not thanks to myself" and I don't know what the probelm is, I am also having problems logging back in hence the multiple usernames.
Yes, the PF software is having some issues at the moment. We'll clean up the multiple user names later (it's against the PF rules, but understandable at the moment).

On your question, write out the equations and solve them to see what the effect of the two series RC circuits is...

CNC
Using a Voigt model to model the circuit indicates that I should only see one time constant the greater of the two, any reason why experimentally I am seeing the sum of the two time constants?

berkeman
Mentor
Using a Voigt model to model the circuit indicates that I should only see one time constant the greater of the two, any reason why experimentally I am seeing the sum of the two time constants?
Can you please post some of this work that you've been doing? Thanks.

CNC
The circuitry I have been using is --RC--RC-- where the two RC circuits are in parallel, and the Z'=∑R_k/((1+(ωCR)^2 )) and Z" = -ω∑(CR^2)/((1+(ωCR)^2 )), however upon using this to model the data ie C1=50pF and C2=100pF, R1=R2=1Mohm and sweeping frequency 0.1-100 kHz it is an RC semicircle but the max. gives a tao = 0.1 ms (R2*C2), the experimental data on the other hand, upon subtracting the reference tao C1*R1 from the total tao I get 0.11 ms. I am only trying to determine C2 and I get the right C when subtracting C(total) from C1 but circuit analysis wise I don't see why this works?

Last edited:
berkeman
Mentor
The circuitry I have been using is --RC--RC-- where the two RC circuits are in parallel, and the Z'=∑R_k/((1+(ωCR)^2 )) and Z" = -ω∑(CR^2)/((1+(ωCR)^2 )), however upon using this to model the data ie C1=50pF and C2=100pF, R1=R2=1Mohm and sweeping frequency 0.1-100 kHz it is an RC semicircle but the max. gives a tao = 0.1 ms (R2*C2), the experimental data on the other hand, upon subtracting the reference tao C1*R1 from the total tao I get 0.11 ms. I am only trying to determine C2 and I get the right C when subtracting C(total) from C1 but circuit analysis wise I don't see why this works?
I'm sorry to be dense, but what do you mean by "the two RC circuits are in parallel"? Where are you injecting your signal, and where are you measuring the output signal. And what is the source impedance of your signal generator?

CNC
I meant to say that the two parallel RC circuits are in series and I'm injecting the signal into one side and measuring the output signal using counter eletrodes all hook together in a coaxial harness, and the source impedance of the generator is ~50 ohms.