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The process of discovering voltages and currents in an electric circuit by way of Ohm's Law, Kirchoff's Voltage Law, Kirchoff's Current Law, Node Voltage Analysis, Mesh Current Analysis, Superposition, Thevenin's Equivalent.

I recently took a Circuit Analysis course, and these are what we used. They can be used for both dc and ac analysis.
v = voltage
i = current
r = resistance

Passive Sign Convention:
When finding the voltage across an element, the current must be entering the positive end of the element. If otherwise, switch the sign on the current.

Ohm's Law:
v = i * r
i = v / r
r = v / i

Kirchoff's Voltage Law:
Voltages across elements in a loop add up to zero.
You must make sure that you have Passive Sign Convention.

Kirchoff's Current Law:
Current through a node adds to zero.
Current entering a node = Current exiting a node.

Node Voltage Analysis:
Choose a node, preferably connected parallel to many elements or connected to voltage sources.
This node is going to be considered the negative end.
The voltage from every node to this node is considered the node voltage at that point.
The voltage across any element may be found by subtracting the negative side of the voltage sought from the positive side.

N1----element----N2
(+)---------v---------(-)

v(N1) - v(N2) = voltage across the element
Current through that element may be found by dividing the voltage through the element by the resistance of the element.

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