# Kirchoff law circuit exercise [closed]

Hi I am starting to study electronic circuits and I found an exercise with this circuit. Now, I don't really care about the numeric results, I care more about understanding how to solve this kind of exercise. So let's just say that given V1,V2, R1,R2,R3,R4 we want to find the power dissipated by R3.

I have tried to look both at nodes, and tried to apply Kirchoff law, but I get confused on how many different currents I should consider. Could you please help me visualize how many different currents I are there? I would say I1, ..., I6 but I think that's wrong.

• Only 2 currents. 2 loops. Feb 7 at 8:07
• aren't there three loops?
– mlp
Feb 7 at 8:10
• @mlp No, that would be over-specifying. Just two are required. That's within the "mesh analysis" concept. You could also use nodal analysis, as well. Either works.
– jonk
Feb 7 at 8:18
• There are three loops but only two meshes. A mesh is a loop that does not contain another loop. You only need to write equations for the meshes. Feb 7 at 17:11
• @Antonio51 I did not mean to offend, and I was replying to the OP's comment rather than yours. This (loops vs. meshes) is the language that is typically used in English textbooks for circuit theory. Feb 7 at 18:38

Could you please help me visualize how many different currents I are there?

Prooving, because you doubt ... by writing and solving the equations needed!

The two written equations are the two independent loops needed.

And if one wants a complete answer, with verification "superposition" theorem ...
The solution is up to you.

• Thanks, I couldn't understand at first what you wrote, but when I did all the calculations I checked with this and it was the same result. What program did you use to solve the equations?
– mlp
Feb 7 at 20:10
• Ok. It was the "goal" when I wrote the equations, as others. The program used is Maple from maplesoft.com. Don' forget that results must be confirmed by another different means of calculus. I use generally a spice simulator as microcap v12, free from spectrum-soft.com/download/download.shtm. Good luck. Feb 7 at 22:03
• Have you noted how the "superposition" theorem can be verified easily? Feb 7 at 22:05

You can use mesh or node analysis.

Node analysis:

$$(V_A-V_1)/R_2 + (V_A-V_B)/R_1 = 0$$

$$V_B/R_3 + (V_B-V2)/ R_4 + (V_B-V_A)/R_1=0$$

You can find power dissipation of R3 with

$$(V_B \times V_B)/R_3$$

Equating two equations to each other, you get the necessary results.

Mesh analysis:

$$V_1= R_1 \times I_1 + R_2 \times I_1+ R_3(I_1-I_2)$$

$$-V_2= R_3(I_2-I_1)+I_2 \times R_4$$

You can find power dissipation of R3 with

$$(I_1-I_2) \times (I_1-I_2) \times R_3$$