Question

find node analysis for the circuit ​

Answer 1

Answer:

Solving of Circuit Using Nodal Analysis

Select a node as the reference node. Assign voltages V1, V2… Vn-1 to the remaining nodes. The voltages are referenced with respect to the reference node.

Apply KCL to each of the non reference nodes.

Use Ohm's law to express the branch currents in terms of node voltages.

Answer 2

Nodal Voltage Analysis complements the previous mesh analysis in that it is equally powerful and based on the same concepts of matrix analysis. As its name implies, Nodal Voltage Analysis uses the “Nodal” equations of Kirchhoff’s first law to find the voltage potentials around the circuit.

So by adding together all these nodal voltages the net result will be equal to zero. Then, if there are “n” nodes in the circuit there will be “n-1” independent nodal equations and these alone are sufficient to describe and hence solve the circuit.

At each node point write down Kirchhoff’s first law equation, that is: “the currents entering a node are exactly equal in value to the currents leaving the node” then express each current in terms of the voltage across the branch. For “n” nodes, one node will be used as the reference node and all the other voltages will be referenced or measured with respect to this common node.

For example, consider the circuit from the previous section.

Nodal Voltage Analysis Circuit

nodal voltage analysis

In the above circuit, node D is chosen as the reference node and the other three nodes are assumed to have voltages, Va, Vb and Vc with respect to node D. For example;

nodal circuit equation

As Va = 10v and Vc = 20v , Vb can be easily found by:

nodal voltage analysis circuit

again is the same value of 0.286 amps, we found using Kirchhoff’s Circuit Law