# Finding the currents in this circuit

This is the circuit I'm given:

I'm using the Branch Current Method to determine the currents. Firstly I'm choosing the directions of the currents and the way I'm going to sum the voltages with the KVL: Then I follow the algorithm from my textbook(it's not in English so probably it's worthless to mention it) 1. Let the number of nodes be n, create n-1 equations from KCL. Here are the equations I made: $$I_2 + I_5 = I_1$$ $$I_2 + I_6 = I_3$$ $$I_4 + I_3 = I_1$$ 2. Let m be the number of branches in the circuit. Create m-n+1 equations from KVL, here are the equations I made: $$I_1R_1+I_5R_5+I_4R_4=V_1$$ $$I_6R_6+I_3R_3-I_4R_4=V_2$$ $$I_2R_2-I_5R_5-I_6R_6=V_2$$ 3. Solve the system. The whole system looks like this: $$I_2 + I_5 = I_1$$ $$I_2 + I_6 = I_3$$ $$I_4 + I_3 = I_1$$ $$I_1R_1+I_5R_5+I_4R_4=V_1$$ $$I_6R_6+I_3R_3-I_4R_4=V_2$$ $$I_2R_2-I_5R_5-I_6R_6=V_2$$

When I replace the variables with value, I get following system. NOTE i'm replacing I's with X's because Wolframalpha thinks that I'm working with complex numbers or something. $$x2+x5=x1$$ $$x2+x5=x3$$ $$x4+x3=x1$$ $$60*x1+116*x5+110*x4=82$$ $$94*x6+36*x3-110*x4 =56$$ $$78*x2-94*x6-116*x5=56$$

However when I plug this into Wolframalpha, I get results, which don't match with the ones I get from the simulation in PSpice.
WolframAlpha results:

x1 = 7225/6216, x2 = 821/777, x3 = 7225/6216, x4 = 0, x5 = 219/2072, x6 = 7333/48692

Results from simulation:

I'm failing to find my mistake. Any help is appreciated

• I think you made a mistake when summing voltages. You have to use a consistent sign convention. So the first equation would be I1*R1 + I5*R5 + I4*R4 + V1 = 0. I didn't check the rest. Dec 17 '17 at 18:23
• the electrical current direction through the two batteries is inconsistent Dec 17 '17 at 18:28
• mkeith I tried flipping the signs, but it didn't work. @jsotola, mind if you describe what you mean more precisely, I don't manage to understand what you're saying. Sorry for the inconvenience. Dec 17 '17 at 18:36
• I thought that after I pointed out the problem with the first voltage equation, and said that I didn't check the rest, that you would go through the remaining voltage equations and check them yourself. It looks like the third voltage equation is also wrong. Flip the sign for V2 and try again. Dec 17 '17 at 18:45

## 1 Answer

Your KVL equations seem to be wrong. You should assign proper sign to voltage drop across an element in a loop. For example, in the first KVL equation, you are traversing the loop clockwise and the current $I_1$ is also assumed to be in the same direction, so the voltage change across R1 would be negative (i.e. $-I_1R_1$). The same thing applies to all KVL loops. Thus the equations become.

$$-I_1R_1-I_5R_5-I_4R_4=V_1$$ $$I_6R_6+I_3R_3-I_4R_4=V_2$$ $$-I_2R_2+I_5R_5+I_6R_6=V_2$$

Apart from this, you have also done a mistake while inputting equations properly to the wolfram equation solver. Here is the link which generated right result.