# Formulation of Network Equilibrium Equations

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,

**is called the***Y*=*AY*_{b}*A*^{T}*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 EquationsMesh Equations

where,

**is the***Z**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 EquationsCut-set Equations

where,

**is the***Y*_{c}*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.*