Supermesh Analysis of circuit of two loops

Question

I have am having trouble moving forward with the following problem. The problem says that Find the value of Vs in the circuit below such that the power supplied by the current source is 0. The final answer is -92.4V.

Using supermesh analysis, I know that i2-i1=3A for the two loops and that Vs=-24V -i1(19ohm). I am having trouble when it comes to the idea that the power supplied by the current source is zero. If I say the the node above the current source is v1 and the node below is the ground for the entire circuit, shouldnt v1 be 0 for the current source to have zero power supplied. I am not sure where my logic is wrong or I am completely messing up.

Here's a schematic:

Answer 1

Your logic is impeccable! :-)
You just need to trust the answer and see where it leads you..

3 Choices

The less you take from me nd the more you do yourself the more you will learn and the happier you will be afterwards. So, I have given you a progressive answer. Use as little as possible.
Check answer once youv'e got it correct.

• (1) Single clue
  (2) Progressive clues
  (3) Answer

(1) You can take it from me that you are correct and that

• For

  3 amps x 'X' volts to equal zero

  then X must equal zero.
  So V1 must equal zero

And go away and work it out.

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OR

(2) Try these few progressive clues:

Stop after each clue and think.

• If V1 = 0 then what is the current from the 18V supply?

Stop reading. Think about it.

Then clue 2 - stop reading now to avoid clue 2. .
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• Clue 2:
  The current from the 18V supply and the 3A current both flow into Vi.
  Where do they go to?

Stop reading. Think about it.

Then clue 3 - stop reading now to avoid clue 3. .
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• Clue 3
  For the currents in clue 2 to go where they must go, to what is the necessary voltage of Vs?

Stop reading. Think about it.

OR - answer below - Then clue 2 - stop reading now to avoid answer. .
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(3) ANSWER:

• For power in current source to be zero, voltage across source must be zero. Call voltage at top of current source Vi.
  So Vi = 0

• If Vi=0 then 18V supply sees a load of 3+2 = 5 ohms.
  Current from 18V supply is i=V/R = 18/5 = 3.6A.

• Node at Vi has current from current source + current from V18 flowing into it.
  So Current in = 3A + 3.6A = 6.6A.

  • Current into Vi MUST go somewhere.
    Only path is via Vs.
    Voltage across V2 + 8R + 6R = 0

  • For 6.6A to flow in 6+8 = 14 ohms via Vs the voltage must be V = IxR = 6.6 x 14 = 92.4V.

  Required polarity to "suck' current via 14 ohms as shown is -92.4V

  • QED.

Answer 2

I don't know what you mean by "supermesh analysis", but this can be solved with very basic analysis and common sense.

This problem is easily solved by using Thevenin and Norton equivalents. First simplify the left voltage source and its two resistors into one Thevenin source, and the same with the right voltage source and its two resistors:

Now combine the left voltage source and the current source to its Thevenin equivalent:

For a current source to not deliver any power the voltage accross it must be 0. We now have a simple voltage divider problem. What voltage of V2 will cause the node between the two resistors to be 0V? It should be obvious how to determine the answer is -92.4V from this simplified version of the problem. The final answer is therefore: