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## Homework Statement

A circuit is constructed with six resistors and two batteries as shown. The battery voltages are V1 = 18 V and V2 = 12 V. The positive terminals are indicated with a + sign, The values for the resistors are: R1 = R5 = 40 Ω, R2 = R6 = 156 Ω R3 = 69 Ω, and R4 = 113 Ω. The positive directions for the currents I1, I2 and I3 are indicated by the directions of the arrows.

__The First question asks me to find the voltage at R___{4}## Homework Equations

V = IR

## The Attempt at a Solution

I wasn't seeing any other way to find v4 than by making a loop for all three sections of the circuit

For the first loop I chose a clockwise orientation

-i

_{3}R

_{3}- V

_{1}+i

_{1}R

_{1}= 0

For my second loop I chose another clockwise orientation

i

_{2}R

_{2}- V

_{2}- i

_{6}R

_{6}+ V

_{1}+ i

_{3}R

_{3}= 0

and for the final loop I also choose a clockwise orientation

V

_{2}-i

_{5}R

_{5}- i

_{4}R

_{4}= 0

Looking at the junction next to R

_{2}I get one more equation

i

_{2}- i

_{3}= i

_{1}

Looking at junction B I get yet another, fifth, equation

i

_{4}- i

_{5}= i

_{6}

my problem is going to arise every time I have to label currents and come up with equations at junctions or loops. I understand how to create a system of equations using these but I will sometimes get solutions to the matrix with all my currents being zero. Also, i'm sometimes creating systems where I have Nx(N+2) rows and columns and I find that creates problems as well, I usually miss an equation. Any advice on how to fix these problems would be greatly appreciated, thank you.

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