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

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# Maximum Power Transferred

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