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DC Circuits

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:

Kirchhoff's current law

where: I1, I2, 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 Kirchhoff’s current law, the currents must be placed into the equation with the proper polarity signs attached.

Example:

Solve for the value of I3 in figure below.

Circuit for example problem
Circuit for example problem.

Solution: First the currents are given proper signs:

Kirchhoff's current law solution

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

Basic equation:

Kirchhoff's current law

substitution:

Kirchhoff's current law substitution

combining like terms:

Kirchhoff's current law combining

Thus, I3 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 I3.

Circuit for example problem
Circuit for example problem.

Solution:

Kirchhoff's current law solution 2

Thus, I3 has a value of 2 A, and the negative sign shows it to be a current entering the junction.



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