Kirchhoff's Circuit Laws

Gustav Robert Kirchhoff was a German physicist who contributed to the basic understanding of the spectroscopy, electrical circuits and the emission of the thermal radiation which by the heated objects. Kirchhoff formulated his circuit laws through experimentation in 1845, while still a university student.

Kirchhoffs Voltage Law is a form of the Conservation of Energy Law and could be expressed as as:

The algebraic sum of the voltage drops in a closed electrical circuit is equal to the algebraic sum of the voltage sources (i.e.. increases) in the circuit.

Mathematically, Kirchhoffs Voltage Law is written as:

ΣV (closed loop) = ΣIR (closed loop) = 0

where Σ is the summation symbol.

A closed loop could be described as any path wherein the actual point in the loop is also the finishing point for the loop. Despite how the loop is drawn or defined, the sum of the voltages in the loop should be zero.  The Loop 1 and loop 2 both are closed loops within the circuit. The total of all the voltage increases or decreases across loop 1  also equals” 0”, and the total of all voltage decreases and increases in loop 2 should also equals “0”. There is also a third closed loop in this circuit, the one that goes around the outside from A to B to C to D and back to A again. But this loop is not independent of the other two so it does not provide any additional information.

Two important laws are based on the physical properties of electric charges, and these laws form the foundation of circuit analysis. They arc Kirchhoff's current law (KCL) and Kirchhoffs voltage law (KVL). While Kirchhoff's current law is based on the principle of conservation of electric charge, Kirchhoff's voltage law is based on the principle of energy conservation.