Find the value of R where RL equals 50 Ω, for maximum power transfer
I= 2A, R_L=50 ohms
The Attempt at a Solution
First, I created an open circuit including everything except R_L. Then i tried to solve for the Open Circuit Voltage,V_oc. Since current is only flowing through the left loop, it is safe to assume that I_x = the given current which is 2A. Therefore the voltage source =10V. The voltage on the bottom of the circuit will be 0, since it is grounded. I think the top voltage should be v1+10V. V1 would be i_x*40 which is 80. It is going in the opposite direction, so -80. That gives me V_oc=-70.
Next I closed the circuit, still excluding R_L, and solved for the short circuit current with mesh analysis. I called the left loop i1 and the right loop i_sc. So it follows that
solving for i_sc gives
My teacher told us that the power transferred is at a max when R_thevenin=R_Load, so
Solving for R I get R=-51.4 ohms, which is wrong...what am i doing wrong? Thank you!