Kirchhoff’s Laws: Laying EE Foundations in Voltage, Current, and Spectroscopy

January 27, 2021 by Kimber Wymore

While most EEs are familiar with Kirchhoff’s Laws of Current and Voltage, Kirchoff's research may have an even deeper impact on modern circuit analysis—and even quantum mechanics—than some may realize.

To appreciate where circuits are heading in the future, it is necessary to understand where the foundation was laid. A major contributor to the foundation of electrical engineering is that of Gustav Kirchhoff and his laws of circuitry and spectroscopy. These laws provided a cornerstone for future scholars and engineers to build off, leading us to the technology we have today. 


Portrait of Gustav Kirchhoff

Portrait of Gustav Kirchhoff. Image used courtesy of the Library of Congress


Kirchhoff was a German physicist who helped develop the fundamentals of circuits, namely principles relating to current, voltage, and resistance. Kirchhoff attended the Albertus University of Königsberg, East Prussia (now Kaliningrad, Russia).

While there, he was taught by Franz Ernst Neumann, a German physicist and mathematician. Inspired by his professor's work on electromagnetic induction, Kirchhoff created his circuit laws while still a student in 1845, which elaborated on Georg Ohm’s work


Current Law or Junction Rule

Below is a basic definition of Kirchhoff’s Current Law (KCL):

The sum of all currents leaving a node in any electrical network is always equal to zero.

Kirchhoff’s Current Law and equation. Screenshot used courtesy of


Kirchhoff’s Current Law states that as the current flows into a junction, it is considered positive (+). Respectively, the current flowing out of a junction is considered negative (-). These polarities are necessary because the current that flows in must equal what flows out.


Voltage Law or Loop Rule

Kirchhoff’s Voltage Law (KVL) is as follows:


The sum of the voltage rises and voltage drops over all elements in a closed loop is equal to zero.

Kirchhoff’s Voltage Law and equation. Screenshot used courtesy of


Kirchhoff’s Voltage Law states that as the voltage travels across a circuit loop, the sum of the voltage at the end should equal the starting voltage, which is 0. This result is necessary because a single point cannot have two different voltages. 


Laws of Spectroscopy: Work with Robert Bunsen

In 1851, Kirchhoff met and befriended Robert Bunsen, which led him to relocate to the University of Heidelberg in Germany, where he became a physics professor. With Bunsen, Kirchhoff not only made advances in electricity but in chemistry. They worked to develop what would be known as Kirchhoff’s Three Laws of Spectroscopy

Kirchhoff’s Three Laws of Spectroscopy are when:

  1. A hot solid, liquid, or gas is placed under high pressure, producing light with a continuous spectrum.
  2. An object on the continuous spectrum is viewed through a cool gas under pressure, creating an absorption line spectrum.
  3. A hot gas placed under low pressure produces light on the emission line spectrum


Visual of Kirchhoff’s Three Laws of Spectroscopy

Visual of Kirchhoff’s Three Laws of Spectroscopy. Image courtesy of Penn State Astronomy & Astrophysics


These three laws helped to explain the sun’s spectrum and led to further research into thermal radiation. Through this experimentation, Kirchhoff and Bunsen discovered two elements: cesium and rubidium.


Innovations From Kirchhoff’s Laws

With Gustav Kirchhoff’s discoveries, many starting points, inspirations, and innovations engineers currently utilize and benefit from were able to come to fruition. Here are a few benefits resulting from Kirchhoff’s laws:

  • Kirchhoff’s Laws of Spectroscopy helped James Clerk Maxwell learn that light was an electromagnetic phenomenon and furthered his study on electricity and magnetism.
  • Kirchhoff's work has become fundamental in the creation of quantum mechanics, which is vital in miniaturizing technology. 
  • Kirchoff’s Laws of Circuits have become an essential building block for all electrical engineers, thus providing engineers with the resources to improve and develop new technology.



Modern research and development teams in the electronics sphere stand on the shoulders of scholars like Gustav Kirchhoff to continue progressing. Are you partial to the work of a historical engineer or physicist you'd like us to cover next? Share your suggestion in the comments below. 

1 Comment
  • K
    KC9LGS January 31, 2021

    You might want to look up about absorbtion spectrum revealing that the universe’s constant critical to life many not be uniform in all galaxies.
    See Anton Petrov’s YouTube video about the fine-structure constant.

    Like. Reply