PHY 201: Using Kirchhoff's Rules (and Excel) to Solve for the Currents in a Network of Resistors

Simplifying the equations yields:

(R1+R4) I1 + 0 - R4I3 = V.

R1 I1 - R2 I2 + R3I3 = 0 .

- R4 I1 + R5 I2 + (R3 + R4 + R5) I3 .

The simultaneous equations above can be seen as a matrix equation

M | I > = | V > ,

where M is the following resistance matrix

R1+R4 0       - R4
R1 - R2 R3
- R4 R5 R3 + R4 + R5

where | I > is the following current vector
I1
I2
I3

and where | V > is the following voltage vector
V
0
0

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