1. Not finding help here? Sign up for a free 30min 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!

Find power of resistor and source in AC circuit

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data
    If an average power of 500W is dissipated in the 20Ω resistor, find Vrms, I S RMS, the power factor seen by the source, and the magnitude of VS
    (Based on circuit in attached diagram)

    2. Relevant equations

    Pave= Irms*Vrms*pf*[itex]\frac{1}{2}[/itex]
    Imaginary number referred to as "j", not "i".

    3. The attempt at a solution
    VA=V
    By a node equation at node A, we see that [itex]\frac{V}{20}[/itex]= [itex]\frac{VS}{-j*20}[/itex], so V = VS [itex]\angle[/itex]-90

    Loop 1: (j*20-j*20)IS -j*20I= VS
    By observation, I=V/20, so V=VS[itex]\angle[/itex]90.
    Loop 2: (20+j*20)I-j*20IS=0, so IS= 1.41[itex]\angle[/itex]135 *I
    = 1.41[itex]\angle[/itex]135 *[itex]\frac{V}{20}[/itex]= 0.0705 V [itex]\angle[/itex]135

    Since I and V are in phase, the power across the resistor is 1
    Solve for V:
    500=V*[itex]\frac{V}{20}[/itex][itex]\frac{1}{2}[/itex], so V=[itex]\sqrt{20,000}[/itex]=
    100[itex]\sqrt{2}[/itex]=141.4.

    Vrms=[itex]\frac{V}{\sqrt{2}}[/itex] =100,

    Since V = 100[itex]\sqrt{2}[/itex] IS =7.05 *[itex]\sqrt{2}[/itex] [itex]\angle[/itex]135, so I S RMS = 7.05

    V=VS[itex]\angle[/itex]90, so VS=V[itex]\angle[/itex]-90
    And IS= 0.0705 V [itex]\angle[/itex]135,
    So power factor pf = cos(135-90)= 0.707

    VS=V[itex]\angle[/itex]-90 = -141.4*j, so magnitude given by 141.4.

    I think I got this right, but I just want to make sure.
     

    Attached Files:

  2. jcsd
  3. Apr 6, 2013 #2
    Just realized the diagram I attached was small, hopefully this one's easier to read.
     

    Attached Files:

  4. Apr 6, 2013 #3

    rude man

    User Avatar
    Homework Helper
    Gold Member

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

Have something to add?
Draft saved Draft deleted