Kirchhoff's Voltage Law

Kirchhoff's Voltage Law (aka Kirchhoff's 2nd Law) is one of the fundamental principles in electrical circuit theory. It's named after Gustav Kirchhoff, a German physicist who formulated this law in the mid-19th century. KVL is used to analyze and describe the behavior of voltage in closed electrical circuits.

The statement of Kirchhoff's Voltage Law is as follows:

"In any closed loop or mesh within an electrical circuit, the sum of the voltage rises is equal to the sum of the voltage drops."

In other words, when you traverse a closed loop in a circuit and take into account all the voltage sources (voltage rises) and voltage-consuming elements (voltage drops) encountered along the way, the algebraic sum of these voltage changes is always zero. This is based on the conservation of energy, which states that energy cannot be created or destroyed but only transferred or transformed. In an electrical circuit, the voltage changes account for the energy transfer, and KVL ensures that no energy is lost or gained within a closed loop.

Mathematically, Kirchhoff's Voltage Law can be expressed as:

Σ (voltage rises) = Σ (voltage drops)

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