Kirchhoff's Voltage Law

Kirchhoff's voltage law, abbreviated as KVL, is a fundamental principle in electrical circuit analysis.  It states that the algebraic sum of the voltages in any closed loop or mesh in an electrical circuit is zero.  In other words, the sum of the voltage drops across all elements (such as resistors, capacitors, and inductors) and voltage sources within a closed loop is equal to zero.

The law is based on the principle of conservation of energy, stating that the total energy supplied by the voltage sources in a closed loop must be equal to the total energy consumed by the circuit elements.

Kirchhoff's voltage law allows for the analysis and calculation of unknown voltages in complex circuits by setting up and solving a system of equations based on voltage drops and rises around closed loops.  It provides a tool to understand and predict the behavior of electrical circuits and is commonly used in circuit analysis and design.

 

Kirchhoff's Voltage Law Formula
\( 0  \;=\;  V_1 + V_2 + V_3 \;+ ... + \;V_n  \) \( 0  \;=\;  \sum V_k  \)
Symbol	English	Metric
\( V_n \) = number of voltages	\(dimensionless\)	\(dimensionless\)
\( V_1 \) = voltage source or drop	\(V\)	\(kg-m^2\;/\;s^3-A\)
\( V_2 \) = voltage source or drop	\(V\)	\(kg-m^2\;/\;s^3-A\)
\( V_3 \) = voltage source or drop	\(V\)	\(kg-m^2\;/\;s^3-A\)