Discovering the Value of a Capacitor in a Circuit: S Domain Analysis Help

[seang]

I have a homework problem that goes something like this: There's a circuit, A capacitor in parallel with a resistor, and those two are in series with another resistor. The values of the resistors are given, but the capacitor's is not. Then its given that Z(s) of the circuit equals some rational function. How do I find the value of the capacitor?

I've tried finding Z(s) of the circuit in terms of C and s, and then setting it equal to the given Z(s), but to no avail.

 

[berkeman]

Homework problems should be posted in the homework forums, but I'll still try to give you a hint here. You need to write the Z(s) for the circuit, and equate that to the Z(s) given in order to figure out the C (I guess you know that part already).

To write the Z(s) for the circuit, just write it out like all the components were resistors, but use the appropriate Z(s) for each component. Like for the R, Z(s)=R. And if you had an inductor, Z(s)=sL. What is Z(s) for the capacitor? Then just use parallel and series combination rules for Z(s) to come up with the overall Z(s) for the circuit.

 

[ravenprp]

Hi there,

Thank you for sharing your homework problem with us. It seems like you are struggling with finding the value of the capacitor in a circuit based on the given information. Don't worry, let me try to help you with some tips and guidance.

Firstly, let's understand the purpose of a capacitor in a circuit. A capacitor is an electronic component that stores electrical energy in the form of an electric field. It is commonly used in circuits to filter out unwanted signals, store and release energy, and regulate voltage. In your circuit, the capacitor is placed in parallel with a resistor, which means they have the same voltage across them.

Now, let's look at the given information. We have the values of both resistors, but the value of the capacitor is missing. We also have the Z(s) of the circuit, which is a rational function. This means that the Z(s) is a fraction with polynomials in the numerator and denominator. We can use this information to solve for the value of the capacitor.

To begin, we need to understand the concept of impedance (Z) in the s-domain. In simple terms, impedance is the resistance to the flow of current in a circuit, and it is represented by Z. In your problem, we have a parallel combination of a capacitor and a resistor, which means the total impedance (Z) is the sum of the individual impedances (Z1 and Z2).

Z = Z1 + Z2

We know that the impedance of a resistor (Z1) is equal to its resistance (R1), and the impedance of a capacitor (Z2) is given by the formula 1/(sC), where C is the capacitance of the capacitor.

Now, we can write the equation for the total impedance (Z) in terms of the given values and the unknown capacitance (C).

Z = R1 + 1/(sC) + R2

Next, we need to use the given Z(s) to solve for the unknown capacitance (C). Since Z(s) is a rational function, we can rewrite it in terms of the individual impedances as follows:

Z(s) = R1 + 1/(sC) + R2 = (R1 + R2 + sRC)/(sC)

We can now equate this to the given Z(s) and solve for C:

(R1 + R2 + sRC)/(sC) = given Z(s