Given two (non linear) dc electrical circuits with the same number of nodes. If these two circuits have the same voltage in every node (reference node are selected at the same node)

Can it be concluded that the two circuits are equivalent and why or under what conditions?

Thankyou in advance

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    \$\begingroup\$ I'm voting to close this question as off-topic because it's a homework question with no attempt at a solution. \$\endgroup\$ Apr 27 '16 at 9:32
  • \$\begingroup\$ If two cars are traveling at the same speed down the same road at the same time, are they both Fords? \$\endgroup\$
    – Andy aka
    Apr 27 '16 at 9:48

No, they would not be equivalent.

Suppose you have a circuit in steady state, and somewhere in there it has a diode. It will have a current Id and a voltage drop Vd. You could replace it with a resistor with R=Vd/Id, and nothing would change in terms of the current node voltages and currents.

Is it an equivalent circuit? Of course not, because once the conditions change (e.g. different excitation, or time passes and a comparator changes state, etc.), the diode will behave differently (non-linearly) compared to a simple resistor.

A snapshot in time of the node voltages in a circuit is not enough to characterize it, or even to determine that it is equivalent to another circuit that happens to have the same node voltages.

  • \$\begingroup\$ Thankypu, so if the condition of the circuit remains unchanged, can the diode be viewed as the resistor? \$\endgroup\$
    – Derpson
    Apr 27 '16 at 9:45
  • \$\begingroup\$ @Derpson. A diode has a VI curve. A resistor has another VI curve (a straight line). At some V,I combination(s) they will intersect, meaning they would both have the same current and voltage, so under those conditions, and if nothing changes, they are indistinguishable. \$\endgroup\$ Apr 27 '16 at 9:49

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