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**CIRCUIT ANALYSIS AND TECHNIQUES**

Node Voltage Method

The wise selection of loop currents can
significantly reduce the number of simultaneous equations to be solved in a
given problem. Consider the figure below:

Clearly the circuit has 3 essential nodes (n).

- The first step is to select an essential
node as a reference node. The choice is arbitrary, the node with the most
branches attached is often a good choice. The node 3 is selected as the
reference node.
- Then the node voltages can be defined as
the voltage at a given node with respect to the reference node.
- Finally the Kirchoff's current law is
applied to all the non-reference nodes.

On the above circuit there are 3 essential
nodes, so only 2 equations are needed ** ((n-1)=2)** in order to describe the
circuit.

At node 1:

..................(1)

At node 2:

.........................(2)

From ....(1) =>

..........................(3)

From .....(2) =>

..........................(4)

From ......(3) =>

................................(5)

Substitute (5) into (4) =>

...................................(6)

Substitute (6) into (5)
=>