Calculate capacitive impedance

Discussion in 'Homework Help' started by rts, Feb 14, 2014.

  1. rts

    Thread Starter New Member

    Jan 31, 2014
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    Hi, I'm a very mature student and doing an course in Electrical engineering with no previous knowledge. I have a question which asks me to calculate the capacitive impedance in an a-c series circuit. The capacitor value is 200 microfarads, the frequency is 50 Hz and the resistor value is 2 Mohms. I have used the formula for Xc and found the Capacitive reactance to be 15.92 ohms. I then used the following to find the Impedance; Z = Sqr(R2 + Xc2) The answer that I got was 2 Mohms. Is this the correct method? The course is a home study course so I don't have easy access to a tutor. Any help would be very much appreciated.
     
  2. #12

    Expert

    Nov 30, 2010
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    A resistor does not have capacitive impedance. I think you got the answer and kept going off the end of the page.

    and, yes, the difference is so small that a lot of calculators will not display it.
     
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  3. shteii01

    AAC Fanatic!

    Feb 19, 2010
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    There is some ambiguity in the way you presented the problem.

    You used words like capacitive and impedance. This lead me to believe that you are trying to find impedance of the capacitor. If that is the case, then I believe the correct answer is -15.91j Ohm in complex notation. If you want angle notation, then you have 15.91 Ohm at -90°.

    For reference: http://en.wikipedia.org/wiki/Capacitor#AC_circuits
     
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  4. rts

    Thread Starter New Member

    Jan 31, 2014
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    Hi. Thanks for the prompt response. I quoted the question exactly as it was asked. Should I contact the tutor and ask for some clarification? I'm finding the course quite difficult but would like to keep going. I could well become a nuisance on this forum, asking what may seem like simple questions. Thank you in anticipation.
     
  5. shteii01

    AAC Fanatic!

    Feb 19, 2010
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    From what you wrote earlier, am I correct to understand that you have an AC source with one resistor and one capacitor in series?

    Is this problem with multiple parts?
     
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  6. #12

    Expert

    Nov 30, 2010
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    Simple questions are our specialty. :p

    They make us look smart.;)
     
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  7. vk6zgo

    Active Member

    Jul 21, 2012
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    There is a growing & (to me) annoying,trend of referring to Capacitive Reactance & Inductive Reactance as "Capacitive Impedance" & "Inductive Impedance" respectively.

    It is true,& has been pointed out on another thread,that "Reactance is a subset of Impedance",but our predecessors found it necessary to coin the term"Reactance" to properly distinguish between that characteristic of an Inductor or Capacitor & that of a complex circuit which may contain L,C,& R.

    I think "the Ancients" got it right,but apparently some folks don't!

    Perhaps the question is misusing the term "Capacitive Impedance" in this case to refer to the Impedance of an RC network,which is certainly more "capacitive" than a plain R or an RL circuit.

    My suggestion is to give answers for both the value of Z for the complete circuit,and of Xc for the capacitor.
     
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  8. WBahn

    Moderator

    Mar 31, 2012
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    The reactance is the imaginary part of impedance and, as such, is a real number.

    Z = R + jX

    Z is impedance
    R is resistance
    X is reactance

    So the impedance of a capacitor is 1/(jωC) while the reactance is -1/(ωC).
     
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  9. WBahn

    Moderator

    Mar 31, 2012
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    What resistor? As others have guessed, it appears that you are talking about a series RC circuit.

    The capacitive reactance is -15.92Ω and it's impedance is -j15.92Ω or 15.92Ω@-90°.

    Your book may treat both capacitive and inductive reactance as positive quantities. That is pretty common and it is quite unfortunate (in my opinion). If it is an option, I would recommend looking for one that treats reactance as a signed quantity.

    When you say Z = Sqr(R2 + Xc2), do you mean the '2' to mean squaring? If so, then the conventional way to write this in text is:

    Z = sqrt(R^2 + Xc^2)

    Note also the use of sqrt instead of sqr. Some people use sqr to mean "square" and not "square root".

    That the answer for the magnitude of the impedance (which is what that equation finds) makes sense. The resistance and the reactance are at right angles to each other (90° out of phase) and the magnitude of the impedance is the length of the hypotenuse of the triangle having the resistance and the reactance as the two sides. So imagine a triangle that has one side that is 2 million millimeters (2 km) long and the other side is just 16 mm long. Are you going to be able to tell the difference between the length of the long side and the length of the hypotenuse?

    (For the record, it's 2000000.0000633Ω).
     
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  10. rts

    Thread Starter New Member

    Jan 31, 2014
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    Thanks for all the advice, which I will take on board. I'll work on the information that has been given. Hopefully I'll get the correct answer, and be able to express it in the correct way. I have gained a lot more knowledge thanks to this site. Very much appreciated.
     
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