1. The problem statement, all variables and given/known data In the figure R1 = 2.22 Ω, R2 = 5.08 Ω, and the battery is ideal. What value of R3 maximizes the dissipation rate in resistance 3? R2 and R3 are wired in parallel to each other. R1 is in series with the combination of R2 and R3. Emf is not given. 2. Relevant equations E-I1R1-I2R2=0 (first loop) E-I1R1-I3R3=0 (second loop) 1/R= sum of 1/R for parallel resistors R= R1+... RN for series resistors P=IV=I^2*R=V^2/R 3. The attempt at a solution I began by solving the system of equations for the loops. So, I2R2=I3R3. I know the sum of the currents for resistors 2 and 3 is equal to the current through resistor 1. I know I need to take the derivative of an expression for power and set it equal to zero to maximize the dissipation rate. I am having a lot of trouble formulating the power expression however. I understand voltage is equivalent in parallel resistors and current is equivalent in parallel resistors, but I am not sure which is the proper way to form the power function.