Question

Using nodal analysis, calculate voltage across all the resistors as shown below. This circuit analysis will be used in lab #2 6. 330 470 220 V 100 V

Answer 1

Nodal analysis is completely based on Kirchhoff's circuit laws:

Current law (KCL): For any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node.

Voltage law (KVL) : The sum of the potential differences (voltages) around any closed loop is zero.

As we can see that , there are four nodes in the given circuit : A , B , C , and D in which node A is non - essential node (i.e. not useful ) and all others are essential note. And the corresponding voltages are and  $V_{D}$. The node D is our reference node ( i.e. it is grounded ) . so, .

Now, applying Kirchhoff's current law on each essential node :

at B :

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

at C :

  

or,

or,

or,   

Putting this value in equation (1), we get

  

or,   

or,  .

or,

or,

or,   

or,

1100 3861

or,   

So,

  

Therefore,

  

As there are positive and negative signs across the resistors in the question, i have given the answers according to them. So, don't get confused.

For any doubt please comment and please give an up vote. Thank you.