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# Kirchhoff's Current Law

Kirchhoff's Current Law states:

*The algebraic sum of the currents entering and leaving any junction of conductors is equal to zero.*

This law can be stated mathematically as:

where: *I*_{1}, *I*_{2}, etc., are the currents entering and leaving the junction.
Currents *entering* the junction are considered to be *negative* and currents *leaving* the junction
are considered to be *positive*. When solving a problem using Kirchhoffâ€™s current law, the currents must be placed into the equation *with the proper polarity signs attached*.

**Example:**

Solve for the value of *I*_{3} in figure below.

Solution: First the currents are given proper signs:

The currents are placed into the equation with the proper signs as follows:

Basic equation:

substitution:

combining like terms:

Thus, *I*_{3} is 2 A and its positive sign shows it to be a current *leaving* the junction.

**Example:**

Using figure below, solve for the magnitude and direction of *I*_{3}.

Solution:

Thus, *I*_{3} has a value of 2 A, and the negative sign shows it to be a current entering the junction.