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Gustav Robert Kirchoff was a German physicist born in 1824 in Konigsber, Prussia.
The son of a lawyer that had a strong sense of duty to the Prussion state, Gustav was
brought up to believe that someone with his intellectual abilities should become a
university professor.
Educated at the Albertus University of Konigsberg he was heavily
influenced by his mathematical physics professor Franz Neumann and later his
mathematics professor Friedrich Richelot.
While he was studying with Neumann, Kirchhoff formulated his first research theories
on the conduction of electricity. Building upon the work of Ohm’s, in 1845 Kirchhoff
published his Laws of Closed Circuits that apply to all electric circuits. His observations
and deductions led to the method of calculation of current, voltage and resistance in
electrical circuits with multiple loops. Kirchhoff was the first to formulate the correct
understanding of the theory of how electric currents and electrostatics should be combined.
Although Kirchhoff’s laws have immortalized him in the field of Electrical Engineering,
Kirchhoff also had additional discoveries.-- He was the first person to record and
verify that an electrical impulse travels the speed of light. Kirchhoff also made
significant contributions in the study of the spectrum of light as well as blackbody
radiation
Kirchoff died in Berlin on October 17, 1887.
Kirchoff's 1st Law states:
The algebraic sum of all the currents entering any node must be zero.
 In Figure 1, Kirchoff's
current law is shown. The sum of all the currents entering the the node must be
zero. If we know any two of the three currents shown, the third can be
calculated.
For example, if we know i1 and i2, then:
i3 = i1 + i2
Kirchoff's 2nd Law states:
The algebraic sum of the voltage voltages around a closed path in a circuit
is zero.
In Figure 2, Kirchoff's second law is shown. The sum of the voltages around any of the two
closed loops shown will be zero.
This is a definition of the meaning of Potenial. Every
point within the loop has a unique potential value. No matter what summation path we take around a
closed loop, when we return to the starting point of the path, the potential must be exactly the
same as we began.
There is a third loop not shown in the figure, it is the outer loop which circles the two inner loops
shown.
Applying Kirchoff's Voltage law to the outer loop we find that:
-v1 + R1×i1 + R3×i2 + R4×i2 + R5×i2 + R6×*i1 = 0
Although these Laws may appear to be simple, they are powerful analytical tools,
and form the basis for complex mesh analysis of the most complex circuits.
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