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

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