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
- black body radiation
- Bunsen-Kirchhoff Award
- named after him and colleague, Robert Bunsen

- Born 12 March 1824

## 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!*

## 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