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Homework Help: Calculate the total impedance of the circuit

  1. Jul 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Consider a circuit, composed of a resistance R and an inductance L in series with an AC generator providing a voltage V(t)=V(subscript 0) cos (omega*t)

    calculate the total impedance of the circuit, and the phase difference between its resistive and inductive components

    3. The attempt at a solution

    I am totally confused about what it is asking for when it asks for the 'total impedance'. does it have anything to do with the complex impedance?
  2. jcsd
  3. Jul 21, 2011 #2


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    Staff: Mentor

    Yup. Every passive component (resistor, capacitor, inductor) has an impedance represented by a complex number. Resistors happen to have a zero value for the imaginary term. You're being asked to find the net impedance represented by the resistor in series with the inductor.
  4. Sep 3, 2011 #3
    I really don't know how to do this. I only have a day and a half before I get tested on this. Please help
  5. Sep 3, 2011 #4
    Z=sqrt(R^2+(X(subscript L)-X(subscript C))^2))

    but how am I supposed to use that equation and is it the right equation?
  6. Sep 3, 2011 #5
    Use for impedances the fact that

    Z(subL) = jwL


    i is same

    Vo* (e**0)=[Io](e**j phi t)( R+jwl)

    and the fact that



    I(t)=I(sub0) (e**phi j t )
    Last edited: Sep 3, 2011
  7. Sep 3, 2011 #6
    Z=V/I=(V0cos(omega*t))/(I0exp(phi t))?

    how do I calculate the phase difference?
  8. Sep 3, 2011 #7
    Sorry I forgot the j's . Please re-read my previous post.
  9. Sep 3, 2011 #8
    forgot j's where?
  10. Sep 3, 2011 #9

    But for the solution if you want a clear explanation, I will try my best


    there are phasors I,V,Z ( phasors )

    i,v,R ( normal i'll call them ) currents, etc

    I(big I ) is in the form= Io * cos(wt+phi)

    Phasor - wise it is interpreted as Io * e**(jphit)

    There are impedances where denoted by Z

    Z=R for resistor and ZL=jwL for an inductor, 1/(jwC) for a capacitor.

    You also have the relation v(small)=L*di/dt for the inductor.

    All you need is some calculus to relate knowns to unknowns.

    That's all I remember from my Electrics classes, so I can only offer this much help.

    Good Luck !
  11. Sep 3, 2011 #10


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    Science Advisor
    Homework Helper

    Last edited by a moderator: Apr 26, 2017
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