# Calculating Impedance Using Capacitive Reactance

1. Oct 3, 2012

### PeachBanana

1. The problem statement, all variables and given/known data

A 29kΩ resistor is in series with a 62mH inductor and an ac source. Calculate the impedance of the circuit if the source frequency is 80Hz .

2. Relevant equations

XL = ωL
Z = [(R^2 + (XL - XC)^2)] ^ 1/2

3. The attempt at a solution

R = 29,000 Ω

XL = 0.062 H (2∏ * 80 Hz)
XL = 31.16 Ω

I'm having difficulty figuring out how to find XC. XC = 1 / ωC but what is "C?"

2. Oct 3, 2012

### vela

Staff Emeritus
Your formula for Z applies to RLC circuits. You have an RL circuit. Do you know how that formula for Z was derived? It was probably using a phasor diagram. If you understand the derivation, it's pretty easy to see what you need to do.

3. Oct 3, 2012

### PeachBanana

Was the formula for "Z" derived using the Pythagorean theorem? If so, I still do not see the connection to capacitance.

4. Oct 3, 2012

### vela

Staff Emeritus
Describe how the formula was derived.

5. Oct 3, 2012

### PeachBanana

It looks as if it uses the following relations:

Vrms = Irms * Z
Vnaught = InaughtZ

The book also shows a phasor diagram where Vnaught is the sum vector and acts as the hypotenuse of the triangle.

6. Oct 4, 2012

### vela

Staff Emeritus
And where does the triangle come from?

7. Oct 4, 2012

### PeachBanana

The triangle comes from a phasor diagram. I'm attaching an image made in paint of the one I see in the textbook. It's a tad messy, but it is readable.

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8. Oct 4, 2012

### vela

Staff Emeritus
In your picture, I should actually point in the same direction as VR=IR.

Do you understand why the one leg is VL-VC and why you add all the voltages?

9. Oct 4, 2012

### PeachBanana

Are the voltages being added together to find the peak voltage source, Vnaught?
Is Vc subtracted from Vl because Vc lags the current by 90°?

10. Oct 4, 2012

### vela

Staff Emeritus
Yes, it's Kirchoff's voltage law applied to the elements in series.

And because VL leads the current by 90°. The two phasors point in opposite directions, so when you add them vector-wise, you subtract their magnitudes.

So back to your original problem, if you follow the same analysis, what do you get for the impedance?

11. Oct 5, 2012

### PeachBanana

Since this is an RL circuit then

Z = [(R^2 + XL^2)]^1/2

12. Oct 6, 2012

### vela

Staff Emeritus
Yup, you have it.