Supernode

A supernode is their when the ideal voltage source appears between any 2 nodes of an electric circuit.

The usual method to solve this is to write KCL equations for both nodes and simply add them together into one equation ignoring voltage source in question. But, this would mean one less equation than the number of variables in the circuit. A contsraint equation is specified given by the magnitude of ideal voltage source present among the nodes and the respective node voltages. The following example will assist to clarify this scenario.

Example

Determine voltage across 1 A current source in circuit diagram of Figure by given below using nodal analysis.

A simple inspection of circuit diagram reveals existence of 3 nodes excluding the reference and are labelled as V₁,V₂ and V₃ as their respective node voltages. The presence of the ideal voltage source between nodes 2 and 3 creates a supernode and a constraint equation is necessary.

 
As there are 3 variables and 2 equations, thus another equation is required. This can be written as the constraint equation between nodes 2 and 3 as stated below

Constraint Equation
 
Equations can be solved simultaneously to determine node voltages V₁,V₂ and V₃. Herein, the voltage, V₁, across current source is needed. Thus by using Cramer's rule

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