# A Complex Three Loop Circuit with Resistors and two batterys only.

Okay,, Im going to try and give precise instructions on how to draw the circuit so you all can see what Im dealing with here. This is not a homework problem really. We just did a lab and worked on measuring the currents through resistors using the Ammeter. Anyways, we worked with two electrical circuits, one with an easy two loop circuit. And the Third one that was trouble for me and my partner, but easily handled, which is the three loop circuit.

Here is the trouble, constructing the linear equations using Kirchoffs 1st and 2nd rule. Then by solving for the currents algebraically using any possible mathematical tool to solve for currents. Substitution is usually a method we would use for only two unknown currents. But with 5 unknown currents with all 5 known resistors, we could use matrices. Anyways, Forget about the algebra part, I am master in mathematical algebra. I am Majoring in Mathematics, and hopefully in the future to work to attain a Ph.D in Theoretical Mathematics. I'm not going to be an engineer because well, I'm too slow with performing physics experiments and I tend to take my time. If you have me build a bridge it would collapse within a couple days even if I was a qualified engineer, jokingly I claim. I do particularly enjoy the theoretical part of physics and I took the class for the theory only, but I must also perform experiments as required by class. This class is ofcourse Physics with Calculus Applied.

The following three loop circuit has about 5 different currents and a 6V battery and a 12V battery with a total of 5 resistors.

I will draw a coordinate system and you shall plot the points and connect the dots to attain the structure of the three loop circuit. Whereas I will give you coordinates for the structure of the wires and the location of resistors and batteries.

Here we go, plot point (1,1). Then plot point (1,11). Draw a line connecting points (1,1) and (1,11).

Now plot (4,1), and draw a line connecting (4,1) and (1,1).
Plot (4,11) and draw a line connecting (4,11) to (4,1). Then draw a line connecting (4,11) and (1,11).

Now plot (8,1) and (8,11). Draw a line connecting (8,1) and (8,11).
Also draw a line connecting (8,1) to (4,1). Then draw a line connecting (8,11) and (4,11).

Now Plot (12,1) and (12,11). Draw a line connecting (12,1) and (12,11)
Also Draw a line connecting (12,11) to (8,11), draw a line connect (12,1) to (8,1).

We have the structure of the circuit. Now I shall tell you the placement of the resistors and batteries.

There lies a resistor R_1 = 150ohms from (1,2) to (1,4) in between the points of (1,1) and (1,11).

There lies a resistor R_2 = 100ohms from (4,2) to (4,4) in between (4,1) and (4,11). There also lies a Battery V_1 = 6V on the line in between (4,4) and (4,11). The coordinates of Battery V_1 has no significance and is not necessary to establish coordinates for it. As long as the Battery is placed somewhere in between Coordinates (4,4) and (4,11).

There lies a resistor R_3 = 220ohms in between (4,11) and (8,11). (NOTICE!: NOT FROM AND TO, but in between!)

There lies a resistor R_4 = 330ohms from (8,7) to (8,9), in between the line connecting (8,1) to (8,11).

There also lies a Battery V_2 = 12V in between (8,1) and (8,7). The exact coordinates of the Battery is again of no significance only but the Battery is between (8,1) and (8,7) (NOT FROM and TO those coordinates).

There lies a resistor R_5 = 680ohms, from (12,2) to (12,4),in between the line connecting (12,1) and (12,11).

5 Currents are needed to be solved.
I_1 = ?
I_2 = ?
I_3 = ?
I_4 = ?
I_5 = ?

IMPORTANT NOTE: The subfixes of the Currents may not relate to the subfixes of the Resistors.

In the circuit i have on my paper I_1 is running from (4,1) to (1,1) to (1,11) to (4,11). Where at (4,11) I_1 is combined with I_3 to make I_2. Thus, I_2 = I_1 + I_3

I_2 runs from (4,11) to (8,11), where at (8,11) I_2 combines with I_4 to make I_5. Thus, I_5 = I_2 + I_4

I hope you do not have any problems constructing the circuit from the given directions. Please help me in using Kirchoffs 1st and 2nd rule so that I can solve for the 5 currents.

Thank you.

EDIT MESSAGE: The Positive terminals of both batteries are pointing in the +y direction.

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I'm no expert in electricity, and I don't even pretend to know what the solution is but we need to know the direction of the + and - sides of the battery. Are both the negative sides facing torward -y? Are both positive sides facing torwards -y, or is one facing +y and the other -y?

Yikes,, I most definitly forgot that! Thank you for reminding me!

The Positive terminals of Both Batteries are pointing in the +y direction.

Zeronem this is really odd to be asking here, but I'm desperate and I think you would be perfect for the task(with your math knowledge). Could you look at the problem I posted called "KE in Reletivity? Strange Integration". I would really appreciate it.