Understanding Kirchhoff’s Laws for Electrical Circuits

Kirchhoff’s Laws

Kirchhoff’s Laws are a consequence of the conservation principles for charge and electric energy.

Kirchhoff’s First Law

Also known as the Law of Nodes or Law of Currents, it states that the sum of the electrical currents reaching a node equals the sum of the currents leaving that node.

Example

Kirchhoff’s Second Law

Also known as the Law of Nets or Law of Tensions, it states that the sum of voltages around any closed net equals zero.

Example

In single-net electrical circuits, all elements are connected in series, and the same current flows through all of them.

Example 10.1

Using Kirchhoff’s Second Law, determine the current formula for this single-net circuit:

Applying the law:

Solving for current:

In electric circuits with two or more nets, you can apply Kirchhoff’s Laws to find specific current or voltage values. Various software tools are available to assist in solving these circuit problems.

Example 10.2

Find the values using Kirchhoff’s Laws and verify your answer with Solve Elec software, available at: http://solve-elec.softonic.com/

Using Kirchhoff’s Second Law, the voltage at the source equals the sum of the voltages across resistance 1 and resistance 2:

We obtain the equivalent resistance for the parallel components:

The voltage would be:

Solving for the variables:

Software Verification

• Add Resistances: Click the icon and place on screen. Use to arrange.
• Add Source: Click and place on screen.
• Add Ammeters: Use two ammeters to measure currents.
• Connect: Join elements with lines .

Once arranged, input the problem values into the charts provided in the software interface: