Finding Impedance of RC Series Circuit - Value of R & C

[freshbox]

Given that:
It=3<110°A
Vt=120<40°V and ω=314.2rad/sec

Find the impedance of the series ciruit elements in rectangular form and state the type and value of the respective elements.

I have found the impedance and know that it is a RC circuit as current 110° is leading voltage 40°.
How do I find the value of R and C with the help of ω=314.2rad/sec?



Thanks!

 

[gneill]

Identify the resistive and reactive parts of your impedance. If the reactive portion is due to a single component, how would you calculate it given the component's value?

 

[freshbox]

I would use Xc=1/ωC to solve for the reactance of the Capacitor. But I have 2 unknown:Xc and C. How do I solve?

 

[gneill]

I would use Xc=1/ωC to solve for the reactance of the Capacitor. But I have 2 unknown:Xc and C. How do I solve?

Identify the resistive and reactive parts of your impedance.

 

[freshbox]

I'm sorry gneill. I have identified a resistor and a capacitor in the circuit. Because Resistance+Reactance(C)=Impedance. Does that answer your question? And I am trying to find the reactance of Xc, but I have 2 unknown and unable to solve it. I think my understanding is wrong somewhere :(

 

[gneill]

Okay, what did you obtain for the impedance?

 

[freshbox]

40<-70°Ω
or
13.68-j37.59Ω

 

[gneill]

40<-70°Ω
or
13.68-j37.59Ω

Alright, that looks good. Now, the real part of the impedance corresponds to the resistance of the series circuit, while the imaginary part of the impedance corresponds to the reactive part.

So can you identify Xc in your impedance?

 

[freshbox]

Ok I got the answer. But i don't understand, how do you know that the real part = resistance whereas the imaginary part = Xc.

Thanks.

 

[gneill]

Ok I got the answer. But i don't understand, how do you know that the real part = resistance whereas the imaginary part = Xc.

Thanks.

When you cover complex impedance you'll learn the theory. You've probably noted already when dealing with reactances that they introduce phase angles in currents and voltages, something you never had to worry about with pure (real valued) resistances. When you add resistance and reactances to find a total "resistance magnitude" you sum their squares and take the square root. That's just like vector components. So in that sense, reactances are a component of impedance that lies at 90° to resistance.

The real portion is the resistance and the imaginary portion is the reactance. Together they are called "impedance". Complex numbers let you represent these two "components" of impedance as a real portion and an imaginary portion.

 

[freshbox]

Cool, thanks for the explanation :)