RC parallel circuit, find the value of R and C

In summary, the parallel circuit has an admittance of 1/z. The resistor analogy is two conductances in parallel, and Z= R/(1+jwCR).
  • #1
Agent47
7
0

Homework Statement



The circuit is a Parallel RC

Z= 105KΩ∠-27 and Frequency is 50 Hz.

I was given the following information and hints.

1/z = 1/R + jwc

I need to find the common denominator of 1/R + jwc, Invert it to find z and simplify Z into one real and one imaginary part.


Homework Equations



Need to find the value of R and C

The Attempt at a Solution



I started with finding the common denominator,

= 1/R +(jwc*R)/R

1/z = (1+jwRC)/R

To find z i simplified the equation above,

R = z(1+jwCR)

z = R/(1+jwCR)

Im not sure if i did this right as i can't find R and C. Any help will be much appreciated.
 
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  • #2
Why not start by calculating 1/Z, since you're given a numerical (complex) value for Z?
 
  • #3
If i do 1/z i would get 8.485x10-6 +j 4.323x10-4. I am not sure on how i would get and RC from 1/z = (1+jwRC)/R.
 
  • #4
Agent47 said:
If i do 1/z i would get 8.485x10-6 +j 4.323x10-4. I am not sure on how i would get and RC from 1/z = (1+jwRC)/R.

You don't need RC. You can pick out the admittances of the two components directly from the complex value of 1/z.

1/z is the admittance of the parallel circuit. How do admittances in parallel add?

(The resistor analogy is two conductances in parallel).
 
  • #5
I worked out R= 118K ohm and C = 1.37x10-8. I checked by putting the values back into the equation and got the correct z. I guess i don't understand what my lecturer is going on about finding the common denominator etc.
 
  • #6
Agent47 said:
I worked out R= 118K ohm and C = 1.37x10-8. I checked by putting the values back into the equation and got the correct z. I guess i don't understand what my lecturer is going on about finding the common denominator etc.

I suppose your lecturer had envisioned a different path to solution. But this one is pretty straightforward, no?
 
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  • #7
I agree that the way you have explained is much simpler, ill ask my lecturer on what his method is. Thanks for your help.
 

FAQ: RC parallel circuit, find the value of R and C

1. How do I find the value of R in an RC parallel circuit?

The value of R in an RC parallel circuit can be found by using the formula R = V/I, where V is the voltage across the resistor and I is the current flowing through the resistor. You can measure these values using a voltmeter and an ammeter, respectively. Alternatively, you can use Ohm's Law (V = IR) to calculate the resistance if you know the voltage and current.

2. How can I determine the value of C in an RC parallel circuit?

The value of C in an RC parallel circuit can be calculated using the formula C = Q/V, where Q is the charge stored on the capacitor and V is the voltage across the capacitor. You can measure the charge using a multimeter or calculate it using the formula Q = CV. The voltage can be measured using a voltmeter.

3. What is the relationship between R and C in an RC parallel circuit?

In an RC parallel circuit, R and C are inversely related. This means that as the value of one component increases, the value of the other decreases. This relationship can be described by the equation RC = constant, where the constant value depends on the specific circuit.

4. How does the value of R and C affect the behavior of an RC parallel circuit?

The value of R and C in an RC parallel circuit determines the time constant, which is the time it takes for the capacitor to charge to 63.2% of its maximum charge when a voltage is applied. A larger value of R or C will result in a longer time constant and a slower charging or discharging rate. Additionally, a smaller value of R will result in a larger current flowing through the circuit.

5. Can I use a different value for R or C in an RC parallel circuit?

Yes, you can use different values for R and C in an RC parallel circuit. However, the values must be chosen carefully to ensure that the circuit behaves as intended. Using a larger value of R will result in a slower charging or discharging rate, while using a smaller value of C will result in a larger current flowing through the circuit. It is important to consider the time constant and the desired behavior of the circuit when selecting values for R and C.

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