Circuits numermical

 

Nodal Analysis



We have to find  V1 and V2 it by applying nodel analysis at two nodes  ? 

 Step 1: first nodel analysis 


       ( (V1-20) /5)  +(V1/10) +((V1-V2) /10) =0

           (2V1-40+V1+V1-V2) /10 =0

            4V1-V2=40.....................(I) 


        Now,

               Step 2:  second nodel analysis     

 ((V2-V1) /10) + (V2/20) -4=0

 (2V2-2V1+V2-80)/20=0

 3V2 -2V1=80 ......................... (II) 


             Now equate equation (I) and(II)  to get  the value of V1  and  V2

            ( -2V1+3V2=80) *1

            ( 4V1- V2  =40) *3

             .............................. 

              -2V1 +3V2 =80

               12 V1 -3V2=120

             ....................................... 

               10V1      =200

                V1    =20 V

               and put the value of V1 in equation (I) to get the value of V2

                     So, V2 =40 V 



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