# RC circuit question

1. May 7, 2005

### dk702

The circuit is (10K ohm resistor in parallel with unknown Capacitor) which are in series with a 4.7k ohm resistor and a 0.1microF capacitor. V_in is applied over the entire circuit and V_out is taken over the 4.7k ohms and 0.1microF.

So here is the question.

In the circuit, H(s)=V_out(s)/V_in(s)(transfer function I imagine). It is a known that this ratio H(s) is independent of frequency. In other words, H(s) is simply a constant. Find The value of the unknown Capacitor in microfarads if all components are ideal.

My current thinking is that since H(s) is just a constant and not a function of frequency, there is no phase difference between V_in and V_0. I then assumed DC must be applied. If this is true then the Caps are charged and no current is flowing. Therefore, the circuit simplifies to the unknown Cap in series with the 0.1microF. Then by using Q=CV, I found unknown C=(V_out/(V_in-V_out))*0.1microF.

If you find any flaw in my thinking please point it out to me. Also if you want a picture of the circuit please email me at cq2120-forums@yahoo.com.

2. May 8, 2005

### SGT

Where did you got the idea that H(s) is independent from frequency? It is clearly a function of the complex frequency s = σ + jω

3. May 8, 2005

### dk702

It was part of the problem that was given to me.

The entire question was

"In the circuit, H(s)=V_out(s)/V_in(s). It is known that this ratio H(s) is independent of frequency. In other words. H(s) is simply a constant. Find the value of the uknown capacitor in microfarads if all components are ideal"

4. May 8, 2005

### SGT

Well, that is quite different! Anyway, if it is said that the TF is independent of frequency, this means that it is a constant for any frequency and not only for DC. This would be trivial.
What happens is that the reactances of the series and the parallel capacitor cancel each other.
Let R1 and C1 be the parallel resistor and capacitor and R2 and C2 be the series elements.
The impedance of the series branch is Z2(s) = R2 + 1/(sC2).
The impedance of the parallel branch is Z1(s) =1/(1/ R1 + sC1).
The TF is H(s) = Z2(s)/(Z1(s) + Z2(s)).
For H(s) to be independent of frequency, the sum of all terms containing s in the numerator and in the denominator must be zero.
I don't think you will be able to equate those terms to zero with only one unknown.

Last edited by a moderator: May 9, 2005