Parallel Impedance

  • #26
So whole impedance meaning the answer is a complex number?
And from that you can work out the modulus and phase.

So just say R = 2 and Xc = 10

Zr = 2 + j0
Zc = 0 + j10?

so then you can use dlgodds formula?


You lost me a bit with
V = Itotal/(1/R + jωC)I)

SO the final formula, is the bottom squared and then rooted just to get rid of the -j?
 
  • #27
tiny-tim
Science Advisor
Homework Helper
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So whole impedance meaning the answer is a complex number?
And from that you can work out the modulus and phase.

So just say R = 2 and Xc = 10

Zr = 2 + j0
Zc = 0 + j10?

so then you can use dlgodds formula?
yes (though dlgoff's formula is a far more general one, dealing with series resistors also, and an inductor) :smile:
You lost me a bit with
V = Itotal/(1/R + jωC)I)

SO the final formula, is the bottom squared and then rooted just to get rid of the -j?
No, we're not "getting rid of" the j part,

we're finding the magnitude (modulus) of the whole thing. :wink:
 
  • #28
ahhhhhhhhhhhhhhh. It worked!!!!! Doing it the very long way using complex numbers for both R and Xc and putting it into my second formula.

Then with the complex number answer, use it to get the modulus and the phase.

So even though bits are choped off, they are still there, like the 1cos(x) = cos(x) example.

for example, everything has an impedance but if a certain part is 0 its just written as the part with the number. So R = just the real part.

..So even though its not like that, I like to understand it that way just so I can see what is going on, and then from there I can see how and where bits go away etc

So now im going to see if I can work it the same to get to the first formula

p.s, So impedance, as a complex number, what does the real and imaginary part represent? So a resistor as 0 imaginary part...it has 0 what?...My guess 0 reactance? So real is resistance due to power loss? and imaginary "resistance" based on frequency (based on phase shifts?)?
 
Last edited:
  • #29
tiny-tim
Science Advisor
Homework Helper
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251
So impedance, as a complex number, what does the real and imaginary part represent? So a resistor as 0 imaginary part...it has 0 what?...My guess 0 reactance? So real is resistance due to power loss? and imaginary "resistance" based on frequency (based on phase shifts?)?
If the impedance is Z = R + jX,

then the average power is Irms2R,

and the instantaneous power is the average power ± Irms2|Z| = ± Irms2√(R2 + X2). :smile:

(and instantaneous V = RI + XdI/dt)
 

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