I am trying to solve a circuit with two current sources.

I1, I2, V1, V2 are known. R1, R2, R3 are unknown.

I've tried node analysis, but I can only come up with two equations

\$\dfrac{V_2}{R_1} + \dfrac{V_2-V_1}{R_2} = I_1 \tag{1}\$

\$\dfrac{V_1-V_2}{R_2} + \dfrac{V_1}{R_3} = I_2 \tag{2}\$

so I have two equations and three unknowns.. How can I get the third equations?

Diagram is here

  • \$\begingroup\$ Try researching "superposition" in relation to electrical circuits. \$\endgroup\$
    – Skaevola
    Jun 6, 2013 at 20:15
  • 1
    \$\begingroup\$ Apart from V1 and V2, there is a third node of which you didn't write down the equation yet. Take a good look at the circuit. \$\endgroup\$
    – jippie
    Jun 6, 2013 at 20:19
  • \$\begingroup\$ jippie - Yes, the reference node at the bottom. But that doesn't really count, right? \$\endgroup\$
    – TomTichy
    Jun 6, 2013 at 20:25
  • \$\begingroup\$ It matters. It will give you your third equation to solve for your 3 unknowns. Every node matters, just like every mesh matters if you are doing a complete analysis. \$\endgroup\$
    – efox29
    Jun 6, 2013 at 20:33
  • \$\begingroup\$ Hm.. you guys are tantalizing me :) this is actually a thermal circuit problem, I am trying to calculate a very simple thermal model for a motor. So say reference node is V3. Then I have: (V1-V3)/R3 + (V3-V2)/R1=I1+I2 And since V3=0, then I have the 3d equation? \$\endgroup\$
    – TomTichy
    Jun 6, 2013 at 20:40

2 Answers 2


The third equation is

\$ \dfrac{V_2}{R_1} + \dfrac{V_1}{R_3} = I_1 + I_2 \$

  • \$\begingroup\$ @Teomat, to elaborate a little, you had the equations for the two nodes between the resistors (V1 and V2). This is for the bottom rail/node (implicitly GND or 0, or maybe ambient temperature as your comment suggests). \$\endgroup\$
    – Nick T
    Jun 7, 2013 at 23:37

The circuit as given is not solvable. The third equation as given by @Rasoul and others is the result of adding eq1 and eq2. And hence is not independent.

I was able to solve it only by realizing that I knew something else about the system. I knew that 1/R1 + 1/(R2+R3) = 1/R R is known as well. After using MatLab's fsolve function for this non-linear system, I was able to solve for R1, R2 and R3.

without the R constraint, there are infinitely many solutions.


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