Nodal analysis in Planar and Non-planar Networks

Nodal analysis is a method used to determine the voltage and current characteristics of a circuit. It 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 same node. Nodal analysis can be applied to planar and non-planar networks as explained below:

Planar Networks
A planar network is a circuit that can be drawn on a two-dimensional plane without any crossing lines. Planar circuits are the most common type of circuit used in electronics. Nodal analysis can be applied to planar networks in the following steps:

- Identify the nodes in the circuit.
- Assign a reference node (usually the node with the lowest potential) and label the remaining nodes.
- Write KCL equations at each node using the currents leaving the node as positive and the currents entering the node as negative.
- Solve the resulting system of equations to determine the unknown voltages and currents.

Non-planar Networks
A non-planar network is a circuit that cannot be drawn on a two-dimensional plane without any crossing lines. Non-planar circuits are less common than planar circuits but can still be analyzed using nodal analysis. The process for applying nodal analysis to non-planar networks is slightly different from planar networks:

- Identify the nodes in the circuit.
- Choose a reference node and assign a voltage (usually 0V) to it.
- Write KCL equations at each node using the currents leaving the node as positive and the currents entering the node as negative.
- Add an additional equation for each closed loop in the circuit using Kirchhoff's Voltage Law (KVL), which states that the sum of voltages around a closed loop is equal to zero.
- Solve the resulting system of equations to determine the unknown voltages and currents.

Conclusion
Nodal analysis is a powerful tool for analyzing circuits, and it can be applied to both planar and non-planar networks. The process for applying nodal analysis is slightly different for non-planar networks, but the underlying principles remain the same.