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## Homework Statement

Find the value of R where RL equals 50 Ω, for maximum power transfer

I= 2A, R_L=50 ohms

## Homework Equations

R_th=V_oc/I_sc

KCL,KVL,V=IR

## 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

i1=2

i_sc-i1=i_x

i_sc*(40+R)-i1*40=5*i_x

solving for i_sc gives

i_sc=90/(45+r)

My teacher told us that the power transferred is at a max when R_thevenin=R_Load, so

R_thevenin=-70/[90/(45+R)]=50

Solving for R I get R=-51.4 ohms, which is wrong...what am i doing wrong? Thank you!