Power dissipated between two points

In the follwing, if the power dissipated between a and b is 210 watts, what is the value of Vb?

• I don't get it. The resistors dissipate 180W regardless of whatever the battery voltages are because there's 3A going trough the circuit. So are the batteries supposed to dissipate the missing 30W ? Commented Oct 18, 2020 at 16:48
• ...and is the power in the battery really "dissipated"? Commented Oct 18, 2020 at 17:03
• Hello Ahmed, is indeed an interesting question from the simplicity of the circuit. However, as you could see, is a bit unclear and we struggle to make a reply. Maybe, if you share more information from where or why you ask that would help. Commented Oct 18, 2020 at 17:18
• Ahmed, if you are done with this question now, you should take the 2 minute tour to see how to formally accept my answer. If you have residual questions about my answer then please leave a comment below it. Commented Dec 24, 2020 at 17:19

To have a net voltage of 10 volts requires $$\V_B\$$ to be 20 volts i.e. there is 20 volts in opposition to the 30 volt battery. Or, you could make an argument to say that $$\V_B\$$ is 40 volts because it still produces a net voltage of 10 volts when considered to be in series opposition with the 30 volts battery. What you have to decide is what is meant by power dissipation; is it net power supplied by the batteries or net charge power received by the batteries.