Kirchoff’s Current Law (KCL): "The algebraic sum of all the currents entering or leaving a node in an electric circuit is equal to zero.” In other words, the sum of currents entering is equal to the sum of currents leaving the node in an electric circuit.
Example: For the circuit diagrams depicted in given figure, write the nodal equations.

Figure(a) contains just one node excluding the reference, hence one equation is required.

If Is,R1,R2 and R3 are know in above Equation, V can be determined.

In Figure(b), two equations are written for the two nodes labelled V1 and V2.

Left node

 

 

 

Right node

 

 

above Equations can be simultaneously solved to determine the node voltages provided the resistors’ values and Is are known.

Figure(c) contains 3 nodes hence three equations are required to solve for node voltages V1, V2 and V3.
Left node

 

 

 

Middle node

 

 

 

Right node