Nodal Analysis

The following steps describe nodal analysis method

1. Transform all voltage sources to the current sources, if it is possible.

2. Identify and assign the arbitrary voltage to each node including reference node in network supposing all currents leaving the node. The reference node is assumed to be at zero potential.

3. Write nodal equations by using KCL and simplify them.

4. Solve simultaneous system of the equations.

5. Number of equations is N - here N is the number of nodes in network including the reference node.

Example

Calculate the current supplied by 30 V source and the current through each resistor in circuit diagram shown in the figure below by using (1) nodal analysis, (2) mesh analysis and (3) circuit reduction techniques, here R1 =R2 =R3 =R4 =10Ω.

 

Solution. Nodal Analysis

Source transformation is not possible for this circuit as it needs a resistor in series with voltage source. Three nodes are identified in above circuit diagram and labelled as 0, 1 and 2 as shown in Figure where 0 is reference node. Specify V₁ and V₂ as voltages of nodes 1 and 2 respectively.

The voltage source, Vs and R2 are in parallel therefore V₁=V_s V is known by the inspection. Applying KCL at node 2 assuming all the currents are leaving the node, thus

 

The required currents can be found by using Ohm's law

 

The current supplied by voltage source, I_s can be given by the sum of currents IR₁ and IR₂  that is

 
Circuit diagram showing three nodes labelled as 0, 1, 2 where 0 is the reference node.

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