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Homework Help: Phasor algebra in AC circuit analysis

  1. Jan 5, 2016 #1


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    1. The problem statement, all variables and given/known data
    Find the peak value of current through the AC source of the following L-C-R circuit, if peak voltage is ##V_0## and angular frequency is ##\omega_0##.

    2. Relevant equations
    I have learnt Vector algebra and calculus (single variable). I was taught how to use phasor diagrams for AC circuits. (only the basics).
    From my book:

    3. The attempt at a solution
    $$i_R=\frac{V_0}{R}\sin\omega t$$
    $$i_C=V_0\omega C\cos\omega t$$
    $$i_L=-\frac{V_0}{\omega L}\cos \omega t$$
    $$i=\frac{V_0}{R}\sin\omega t+V_0\big(\omega C-\frac{1}{\omega L}\big)\omega C\cos\omega t$$

    If current is taken along positive ##X##-axis, then $$i=\frac{V_0}{Z}=\frac{V_0}{R}+V_0\big(\omega C-\frac{1}{\omega L}\big)j$$

    $$\vert Z\vert=\frac{1}{\sqrt{\frac{1}{R^2}+\big(\omega C-\frac{1}{\omega L}\big)^2}}$$

    $$i_0=\frac{V_0}{Z}=V_0\sqrt{\frac{1}{R^2}+\big(\omega C-\frac{1}{\omega L}\big)^2}$$

    These are the problems I face:
    1. The answer given is: $$V_0\big({\frac{1}{R^2}+\big(\omega C-\frac{1}{\omega L}\big)^2}\big)^2$$
    (probably a printing error)

    2. I applied phasor algebra blindly. Hence, I am not sure if I solved it properly.

    3. So should I learn phasor algebra? Can you suggest a book for learning it (or a webpage)?
  2. jcsd
  3. Jan 5, 2016 #2


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    Homework Helper
    Gold Member

    I believe you have solved it correctly! There's definitely a printing mistake in the answer given in the book. If you've done this problem by yourself, then I think you have a proper understanding of phasor algebra.
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