# Formulation of Network Equilibrium Equations

The network equilibrium equations are a set of equations that completely and uniquely determine the state of a network at any instant of time. These equations are written in terms of suitably chosen current variables or voltage variables.

These equations will be unique if the number of independent variables be equal to the number of independent equations.

# Generalized Equations in Matrix Forms for Circuits Having Sources

Node Equations

the node equations become

where, Y = AYb AT is called the nodal admittance matrix of the order of (n â€“ 1) Ã— (n â€“ 1). The above equation represents a set of (n â€“ 1) number of equations, known as node equations.

Mesh Equations

where, Z is the loop-impedance matrix of the order of (b â€“ n + 1) Ã— (b â€“ n + 1). The above equation represents a set of (b â€“ n + 1) number of equations, known as mesh or loop equations.

Cut-set Equations

where, Yc is the cut-set admittance matrix of the order of (n â€“ 1) Ã— (n â€“ 1) and the set of (n â€“ 1) equations represented by the above equation is known as cut-set equations.