Maximum Power Transferred

  1. 1. [​IMG]

    3.
    Pmax = Vth^2/4Rth

    so im guessing i treat R as the Rth and find Rth.

    to find Rth i must turn off all independent sources. Since the dependent source exists i added a one voltage source at the Rth terminals and put a current i which i will find. then i can use v=i*Rth to solve for Rth.

    my mesh analysis equations:
    Vx + 1 =0
    -1 + i2 + 2Vx=0

    therefore i2 = 3

    2i3 + 1 =0
    i3 =-1/2



    i3 + i1 = i2

    therefore

    i1 = 1/2 + 3

    i1 = 7/2


    Rth = (1)/(7/2) = 2/7


    now to find Vth

    I used nodal analysis and mesh analysis both

    1) (12-Vth)/2 = (Vth-2Vx)/1
    2) -12 + Vx + Vth=0

    Solving I found Vth = 15 V


    Pmax = Vth^2/4Rth = (15)^2 / (4(2/7)) = 196.874 W



    CAN SOMEONE PLEASE CHECK THAT!!!!!


    thank you!!!!!!!!!!!!!!!!!!!!!!





     
  2. jcsd
  3. Defennder

    Defennder 2,616
    Homework Helper

    I didn't get Vth to be 15V. I got [tex]8\frac{4}{7}[/tex]. But I got the same value for Rth.
     
  4. are my equations right?

    for solving Vth?

    1) (12-Vth)/2 = (Vth-2Vx)/1
    2) -12 + Vx + Vth=0
     
  5. 1) (12-Vth)/2 = (Vth-2Vx)/1
    2) -12 + Vx + Vth=0

    vx= 12 - vth

    (12-Vth)/2 = (Vth-2( 12 - vth))/1

    12-Vth = 2Vth-48+4vth

    12+48=vth+2vth+4vth
    60=7vth

    okk ur right its 8.5ish


    ok kool
     
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