# 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. Commented Feb 7, 2022 at 8:07
• aren't there three loops?
– mlp
Commented Feb 7, 2022 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
Commented Feb 7, 2022 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. Commented Feb 7, 2022 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. Commented Feb 7, 2022 at 18:38

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
Commented Feb 7, 2022 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. Commented Feb 7, 2022 at 22:03
• Have you noted how the "superposition" theorem can be verified easily? Commented Feb 7, 2022 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

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