Calculating Resistance and Power Dissipation in a Circuit

AI Thread Summary
The discussion centers on calculating resistance and power dissipation in a circuit with a current of 0.25 A. The user attempts to find the resistance R using Kirchhoff's voltage law but arrives at an incorrect value of 42 ohms. There is confusion about whether to use the energy from both batteries or a more complex equation to determine power dissipation. The user acknowledges various formulas for power, including PR = IV, I^2R, and V^2/R, but is unsure how to apply them correctly. The conversation also includes a humorous aside about a link shared by another user.
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1. There is a current of 0.25 A in the circuit of the figure
What is the value of the resistance R?

Hockay so. I know the change of voltage throughout the loop is 0.
therefore
0 = E1 - I(R1+R2) - E2 - 1R(unknown)
0 = 6V - 0.25A*18ohm - 12V - 0.25A*R
through algebra i get R=42.
And that's wrong. So i dontk now what I am doing wrong.

And it also asks for the power dissipated by R and i don't know whether to use the energy of both batteries or do a long equation with info from the whole circuit or what. I do know how ever that i should use the PR = IV or I^2R or (V^2/R)

thanks a bunch.
 
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