# 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.

## Background

• 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
• 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: $\sum_{k=1}^n \tilde{V}_k = 0$

Come back soon!

## Sources

• http://physics.mercer.edu/labs/manuals/manual162lab/Kirchhoff.pdf
• http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Basic/Basic4Ki.html
• http://www.facstaff.bucknell.edu/mastascu/elessonshtml/Basic/Basic5Kv.html

## 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

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