Understanding Mesh Analysis

Mesh analysis is a technique used to solve electrical circuits, particularly planar circuits, by applying Kirchhoff's laws. In mesh analysis, we define mesh currents in each loop of the circuit and write equations based on these currents. A mesh is defined as a loop that does not contain any other loops within it.

Kirchhoff's Laws and Network Analysis

There are two fundamental Kirchhoff's laws used in circuit analysis:

• Kirchhoff's Current Law (KCL): This law states that the algebraic sum of currents entering a node (or junction) is equal to the algebraic sum of currents leaving that node. Essentially, it's based on the conservation of charge. The sum of currents at a node is zero ($\sum I = 0$). KCL is primarily used in nodal analysis.
• Kirchhoff's Voltage Law (KVL): This law states that the algebraic sum of all the voltage drops and rises around any closed loop in a circuit is equal to zero. It is based on the conservation of energy. The sum of voltages around a closed loop is zero ($\sum V = 0$).

Kirchhoff's first law and Kirchhoff's junction rule are essentially alternative names for Kirchhoff's Current Law (KCL).

Law Applied in Mesh Analysis

Mesh analysis involves traversing each mesh (loop) in the circuit and summing the voltage drops and rises encountered along the path, setting the sum equal to zero. This process directly applies Kirchhoff's Voltage Law (KVL).

For each mesh, a KVL equation is written in terms of the defined mesh currents and the circuit component values (resistances, voltages, etc.). This results in a system of linear equations, which can then be solved simultaneously to find the unknown mesh currents.

Therefore, the fundamental law applied when performing mesh analysis on a network is Kirchhoff's Voltage Law.