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Kirchhof's Laws

Kirchoff's laws may be used to solve for the currents and voltages in any multiloop circuit.

Kirchhoff's First Law (point rule):   The algebraic sum of the currents at a junction is zero.

Kirchhoff's Second Law (loop rule): The algebraic sum of the changes in potential around any complete loop is zero.

A Simple Circuit

Consider the circuit shown below.

Applying the point rule gives

(1)

Applying the loop rule to the bottom and outer loop gives:

(2)

(3)

Equations (1) - (3) are independent equations that you can solve simultaneously.  For example, given the resistance and voltage values, you can solve for the three currents.

First note that equation (2) gives:

(4)

while equation (3) gives:

(5)

Combining (4) and (5) with the point rule (1) gives:

(6)

(7)

(8)