A tutorial on how mathematics, matrices in particular, are applied to model electric circuits.
There are two closed loops in the above circuit. loop 1: e1, R1 and R3 and loop 2: e2, R2 and R3. e1 and e2 are sources of voltages. R1, R2 and R3 are resistors. i1 is the current flowing across R1 and i2 is the current flowing across R2. We now apply Kirchhoff's law to each loop.
The above is a matrix equation that may be solved using any known method to solve systems of equations. Let e, R and i be matrices given by The solution to the above matrix equation is given by ^{ -1} is the inverse matrix of R and is given by.
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