Calculating a voltage and power dissipated in a circuit after creating a supernode


I am looking at this circuit and I am trying to calculate Vx and power supplied by the 1A source.

I believe my calculations for node V2 are correct but I am not too sure about my V1 and V3 supernode calculations. The answer I get for Vx is 1V which is not correct. The answer should be -12.4V. Also, the power supplied by the 1A source should be 31.76W, but I calculate (1A)(V1)=(1A)(77V)=77W, which is also incorrect. I would assume that I am making a big mistake with my supernode calculation to be getting values that are very different from what they should be?

I tried doing KCL for V1, V2, and V3 separately and I still get incorrect answers.
I get V1= 25V, V2= -15V, and V3=28V. So Vx=V2=-15V and I get Pdisipated=(V1)(1A)=(25V)(1A)=25W. Granted I am closer to the correct answers this time, but then again these are wrong.

Work for KCL at all three nodes

Best Answer

Your equation for \$V_2\$ is correct, however, everything else seems to have errors. You mix up currents and voltages, be careful about that!

As \$V_2=V_x\$, I am only using \$V_x\$ from now on. I will use a coherent unit system of \$[V,A,\Omega]\$, so I won't use any unit notations.

For the middle node: $$8+\frac{V_x-V_1}{8}+\frac{V_x}{5}=0$$ $$1)320-5V_1+13V_x=0$$

For the supernode: $$8-\frac{V_3}{2}+1+\frac{V_x-V_1}{8}=0$$ $$2)\frac{V_x-V_1}{8}=\frac{V_3}{2}-9$$

And the relationship between \$V_1\$ and \$V_3\$: $$3)V_3-2V_x=V_1$$

Using 1), 2) and 3), after some calculations you can determine the values of \$V_x, V_1\$ and \$V_3\$, and with that, the power supplied by the current source. I did the calculations and the given solutions are indeed correct.