# Solve RC Circuit: Find Unknown Capacitor Value

• dk702
In summary, the unknown capacitor in microfarads is equal to the voltage output over the 4.7k ohm resistor and the 0.1microF capacitor when DC is applied.
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.

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

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"

dk702 said:
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"

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.

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## What is an RC circuit?

An RC circuit is an electrical circuit that consists of a resistor (R) and a capacitor (C) connected in series or parallel. It is commonly used in electronic devices to control the flow of current and to store electrical energy.

## What is the purpose of solving an RC circuit to find an unknown capacitor value?

The purpose of solving an RC circuit to find an unknown capacitor value is to determine the value of the capacitor in the circuit. This information is important for designing and troubleshooting electronic devices, as the performance of the circuit depends on the proper selection and use of the capacitor.

## What information is needed to solve an RC circuit and find an unknown capacitor value?

To solve an RC circuit and find an unknown capacitor value, you will need to know the value of the resistor (R), the voltage across the circuit, and the time constant of the circuit. The time constant is the product of the resistance and capacitance (RC).

## How do you solve an RC circuit to find an unknown capacitor value?

To solve an RC circuit and find an unknown capacitor value, you can use the equation C = t/RC, where C is the capacitance, t is the time constant, and R is the resistance. Rearrange the equation to solve for C, and substitute the known values to find the unknown capacitor value.

## Are there any other methods for solving an RC circuit and finding an unknown capacitor value?

Yes, there are other methods for solving an RC circuit and finding an unknown capacitor value, such as using a multimeter to measure the capacitance directly or using a circuit simulator software. However, the most common and accurate method is using the time constant equation mentioned above.

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