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