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AC Circuits

  1. Jul 29, 2015 #1
    1. The problem statement, all variables and given/known data
    A series RLC circuit is connected to a 60 Hz AC source which produces an amplitude of εmax=20 V. The circuit element values are R= 20 Ω, L= 20 mH, C= 150 μF.

    Calculate the total impedance of the circuit.

    2. Relevant equations
    Xc=1/ωC
    XL=ωL
    Z=√(R^2 +(XL-Xc)^2)
    tan φ = (XL-Xc)/R
    ω=1/√LC
    εmax=Imax*Z

    3. The attempt at a solution
    I started out with Z=√(R^2 +(XL-Xc)^2) , and to get XL and Xc I used ω=2*pi*f .
    I got my XL and Xc marked wrong. It wasn't a calculation mistake, so am I approaching the answer incorrectly?
     
  2. jcsd
  3. Jul 29, 2015 #2

    Hesch

    User Avatar
    Gold Member

    It seems that your approach is correct, though I don't like your sign conventions. Example:

    tan φ = (XL-Xc)/R.

    I'd rather write:

    tan φ = (XL+Xc)/R , but the value of Xc is negative.

    I don't know if you are familiar with complex calculations where Z could be calculated as

    Z = R + jωL + 1/( jωC ) = R + jωL + ( -j / ( ωC ) ).
     
  4. Jul 29, 2015 #3
    Inductive reactance

    Xl = 2pi f L

    Capacitive reactance

    Xc = 1 / (2pi f c)




    If you can use complex numbers (makes this much simpler)

    z = R + j(Xl - Xc)



    So, for example if
    Xl = 12 ohms
    Xc = 17 ohms
    R = 25 ohms

    you would have

    z = 25 - j5 ohms

    (because 12-17 = -5)


    and you can happily use ohms law to get the current

    i = v / z
     
    Last edited: Jul 29, 2015
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