Nodal analysis is a technique used in electrical engineering to determine the unknown voltages at different nodes in a circuit. This technique is based on Kirchhoff's Current Law (KCL), which states that the sum of currents entering a node is equal to the sum of currents leaving the node. Nodal analysis is generally used to determine the voltage at a particular node in a circuit.

Advantages of Nodal Analysis:

- It is a systematic and efficient method for solving complex circuits.
- It can be used to solve circuits with any number of nodes and voltage sources.
- It reduces the amount of algebraic calculations required to solve a circuit.

Steps Involved in Nodal Analysis:

1. Identify the nodes in the circuit.
2. Select a reference node and assign a voltage of zero to it.
3. Apply KCL at each node, except the reference node, to obtain a set of simultaneous equations.
4. Solve the equations to obtain the unknown voltages at each node.

Example:

Consider the following circuit:


To apply nodal analysis to this circuit, we follow these steps:

1. Identify the nodes in the circuit. In this circuit, there are three nodes: A, B, and C.
2. Select a reference node and assign a voltage of zero to it. Let's choose node C as the reference node.
3. Apply KCL at each node, except the reference node, to obtain a set of simultaneous equations. At node A, we have:

(V1 - VA)/R1 + (VA - VB)/R2 = 0

At node B, we have:

(VB - VA)/R2 + (VB - VC)/R3 = 0

4. Solve the equations to obtain the unknown voltages at each node. Solving these equations, we obtain:

VA = (V1R2 + VB(R1 + R2))/ (R1 + R2)

VB = (VA(R2 + R3) + VC(R2))/R2 + R3)

VC = 0 (since we chose node C as the reference node)

Therefore, the voltage at node A is:

VA = (10*2 + 0*(10 + 2))/(10 + 2) = 16/3 volts

Similarly, the voltage at node B is:

VB = ((16/3)*(2 + 5) + 0*(2))/2 + 5 = 26/3 volts

Thus, nodal analysis can be used to determine the voltage at any node in a circuit, which is useful in designing and analyzing electrical circuits.