# Nodal Voltage Analysis Method

The **Nodal Voltage Analysis** is a method to solve the electrical network. It is used where it is essential to compute all branch currents. A node is a terminal or connection of more than two elements.

In Nodal Voltage Analysis, Kirchhoff’s Current Law (KCL) is used, which states that the algebraic sum of all incoming currents at a node must be equal to the algebraic sum of all outgoing currents at that node.

The Nodal Voltage Analysis is commonly used for networks having many parallel circuits with a common terminal grounded.

In the nodal method, the number of independent node pair equations needed is one less than the number of junctions in the network. That is if n denotes the number of independent node equations and j is the number of junctions.

**n = j – 1**

In writing the current expression, the assumptions are made that the node potentials are always higher than the other voltages appearing in the equations.

Let us understand the Nodal Voltage Analysis Method with the help of an example shown below

## Steps for Solving Network by Nodal Voltage Analysis Method

Considering the above circuit diagram the following steps are explained below

**Step 1 –** Identify various nodes in the given circuit and mark them

In the given circuit, we have marked the nodes as A and B.

**Step 2 –** Select one of the nodes as the reference or zero potential nodes at which a maximum number of elements are connected, is taken as reference.

In the above figure node D is taken as the reference node. Let the voltages at nodes A and B be V_{A} and V_{B }respectively.

**Step 3 –** Now apply KCL at the different nodes.

Applying KCL at node A, we have

Where,

Applying KCL at the node B, we have

Solving equation (1) and the equation (2) we will get the value of V_{A }and V_{B}.

The nodal voltage analysis has the advantage that a minimum number of equations needs to be written to determine the unknown quantities.