Maximum Power Transferred

salman213

1.

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!!!!!!!!!!!!!!!!!!!!!!

Defennder

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

salman213

are my equations right?

for solving Vth?

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

salman213

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