Numb3rs: Kirchhoff's Laws

Euler’s Formula is one of the most important formula’s in mathematics since it allows the simplification of many different ideas.


  • Gustav Kirchhoff:
    • Born 12 March 1824
      • Koenigsberg, Kingdom of Prussia
      • Today: Koenigsberg, Germany
    • Death 17 October 1887
      • Berlin, Kingdom of Prussia
      • Today: Berlin, Germany
    • German physicist
    • best known for:
      • Kirchoff’s Laws
      • black body radiation
      • Bunsen-Kirchhoff Award
        • named after him and colleague, Robert Bunsen

Kirchhoff’s current law (KCL)

Conversation of electric charge leads to the following:

  • At any node (junction) in an electrical circuit
    • the sum of currents flowing into the node equals the sum of the currents flowing out of that node
    • the sum of all current meeting at that point will be \(0\)

Since current is either positive or negative it can be stated that: \[\sum_{k=1}^n I_k = 0\]

\(n\) is the total number of branches where currents flow either towrds or away from the node. The current may also be complex: \[\sum_{k=1}^n \tilde{I}_k = 0\]

Since current is just charge per second the conversation of charge can be applied to current.

Kirchhoff’s voltage law (KVL)

Conversation of Energy leads to the following:

  • The sum of electrical potential differences (voltage) around any closed circuit is \(0\)

Just like in the KCL it can be stated that: \[\sum_{k=1}^n V_k = 0\]

\(n\) equals the total number of voltages meaured. The voltages may also be complex: \[\sum_{k=1}^n \tilde{V}_k = 0\]

Applications & Examples

Come back soon!



The Numb3rs Series

Numb3rs used to be its own subsection on this site, where I wrote math & science tutorials. Unfortunately this never came to frution so I integrated ths articles with the rest of the blog. If you want to check out the other Numb3rs posts, you can get an overview here.

By Cecil Wöbker

I do science during the day and develop or design at night. If you like my work, hire me.

Feel free to follow me on Twitter or email me with any questions.