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).

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) =>