Question

For the circuit diagram given below, find the node voltages using Nodal Analysis.

A01 x VI — +1 20 v - + 01

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Answer #1

HERE IS THE SOLUTION

NOW APPLYING NODAL AT 1 AND 2

NOW IF ONE VOLTAGE SOURCE IS CONNECTED BETWEEN TWO NODE DIRECTLY WITHOUT RESISTANCE OR ANYTHING

THEN THAT TWO NODE CALLED SUPER NODE

SO WE CAN SEE THAT THEIR IS A SUPER NODE IN BETWEEN 1 AND 2

SO WE HAVE TO THINK THIS NODE AS SAME HAVE TO PROCEED LIKE BELOW

SO NOW

\frac{V1}{4}+\frac{V1-V3}{1}-1+\frac{V2}{1}-2(V1-V3)=0

SO, \mathbf{\frac{-3}{4}V1+V3+V2=1........(i)}

NOW AS SUBERNODE SO

V1-V2=-4(V3/4)

SO, \mathbf{V2-V1-V3=0.........(ii)}

NOW AGAIN APPLYING NODAL AT 3 WE GET

\frac{V3}{4}+\frac{V3-10}{2}+\frac{V3-V1}{1}=0

SO \mathbf{\frac{7}{4}V3-V1=5.........(iii)}

NOW SOLVING (i) (ii) (iii) THREE EQUATION WE GET

\mathbf{V1=\frac{-44}{13}=-3.384615 V}

  \mathbf{V2=\frac{-32}{13}=-2.461538 V}

  \mathbf{V3=\frac{12}{13}=0.923076 V}

  

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