Linear Algebra and Electricity

We must often analyze electric circuits such as the one shown to the right that cannot be described using the rules for resistors in series or parallel. The goal is to calculate the current flowing in each branch of the circuit or to calculate the voltage at each node of the circuit. We can use loop analysis or mesh analysis (which is a particular type of loop analysis) or nodal analysis to write down a system of equations describing the circuit. We can then use Gaussian elimination to solve this system of equations.

Loop analysis finds the currents directly and nodal analysis find the voltages directly. Which method is simpler depends on the given circuit. Knowing the branch currents, the nodal voltages can easily be calculated, and knowing the nodal voltages, the branch currents can easily be calculated. Nodal analysis is important because its answers can be directly compared with voltage measurements taken in a circuit, whereas currents are not so easily measured in a circuit (one must cut wires). Click on one of the following topics:
You may also wish to review the following background material:  

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