1. The problem statement, all variables and given/known data In the circuit shown, what must be the size of the resistor R such that the power delivered to the 8 Ω resistoris 160 Watts? Circuit is in the first image 2. Relevant equations ∑I at Junction= 0 ∑ΔV though loop=0 P=I2R ΔV=ε-Ir 3. The attempt at a solution The circuit I have drawn is in the second image. The first thing I did was found the current that is going through R1 is 4.47 A. Since R1 and R2 are in series, I thought that they had the same resistance as well. Next, I used the first part of Kirchoff's law to find the junction equations: Junction B: I1= I2+ I3 Junction E=I4 +I6=I5 Next, I created some loops using the second part of Kirchoff's law: Loop AFEBA: -ε1+ R1I5+R2I5+R3I6-ε2+rI6+R4I2=0 Note, that for the ε2, there is a internal resistance within the battery, such that the ΔV=ε-Ir. I think that the I would be equal to the one in the unknown resistor, I6. Loop EDCBE: -ε3+R5I3-R4I2+ε2-I6r -R3I6=0 Loop ACDFA: -R5I3 +ε3-R2I5-R1I5+ε1=0 From the last loop, I was able to find the I3 is 4.83 A. I used this in the other loops and simplified. The problem is that I don't understand how to continue to solve this problem. Also, I am not completely sure with the circuit I have drawn the currents are all correct the way I have drawn them. Any help will be much appreciated.