1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Phasor algebra in AC circuit analysis

Tags:
  1. Jan 5, 2016 #1

    Titan97

    User Avatar
    Gold Member

    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##.
    Untitled.png

    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

    cnh1995

    User Avatar
    Homework Helper

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Phasor algebra in AC circuit analysis
Loading...