Electronic – equivalent load resistance

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.

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.

Your value for \$I_S\$ is way too high. Where did it come from? Note that the ideality factor is usually closer to 2 for rectifier diodes.

Here is a typical model:-

.MODEL D1N4001 D IS=29.5E-9 RS=73.5E-3 N=1.96 CJO=34.6P VJ=0.627 +M=0.461 BV=60 IBV=10U

None of the numbers in the datasheet you linked are directly useful in determining \$I_S\$, however you could use this figure from the datasheet:

and play with different values of \$I_S\$ until you get reasonable agreement at lower current values. I say "lower current values" because real rectifier diodes have a resistive component to their \$V_F\$ which is more important at higher currents, and your ideal equation does not take that into account. Although \$I_S\$ is temperature-dependent, the figure specifies that it is measured with brief pulses of current, so we can assume that the \$T_J\$ is 25°C.