Determine the power absorbed by element 1.
Image from: Irwin, J. David., and R. M. Nelms. Basic Engineering Circuit Analysis, Tenth Edition. N.p.: John Wiley & Sons, 2010. Print.
Solution:
We will find power for each element in terms of I_x and then solve for I_x at the end. Remember that current multiplied by the voltage gives us power.
P_{36v}=-36I_xW
P_1=12I_xW
P_{2I_{x}}=48I_xW
P_2=-16W
P_3=-32W
In the circuit, all power absorbed must equal the power supplied. In our case, three sources supply power (the elements with negative power values), and the power absorbed by the two other elements must equal each other. In other words, if we add all of the power together, the ones that supply power and absorb power, it must all equal to 0. Thus, we can write the following equation:
-36I_x-16-32+12I_x+48I_x=0
48=24I_x
I_x=2A
now, we can solve to find the power absorbed by element 1:
P_1=12(2)
P_1=24W