In the follwing, if the power dissipated between a and b is 210 watts, what is the value of Vb?
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\$\begingroup\$ 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 ? \$\endgroup\$– UnimportantCommented Oct 18, 2020 at 16:48
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\$\begingroup\$ ...and is the power in the battery really "dissipated"? \$\endgroup\$– bobfluxCommented Oct 18, 2020 at 17:03
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\$\begingroup\$ 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. \$\endgroup\$– Eloy CalatravaCommented Oct 18, 2020 at 17:18
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1\$\begingroup\$ 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. \$\endgroup\$– Andy akaCommented Dec 24, 2020 at 17:19
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1 Answer
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The voltage sources must dissipate the difference between the total power (210 watts) and the power dissipated by the three resistors (180 watts). The power difference is therefore 30 watts and, given that 3 amps is flowing, that must mean that the net voltage across the two batteries (if they were combined as one) is 30 watts ÷ 3 amps = 10 volts.
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.
I can't answer that based on the details in your question.
answered Oct 18, 2020 at 17:11