Solving Circuits with the Nodal Method: Finding Va

[formulajoe]

nodal voltage??

im not real sure on how solve circuits using the nodal method. I've got an equation for node a but i don't know how to solve it. here's the equation
(90-Va)/20 - (Vb-Va)/3 + Va/20 - Ia = 0

thats at node a. how do i solve this?
Ia = 6 A

 

[himanshu121]

What kind of circuit u are dealing Will u pls provide the pic

 

[HallsofIvy]

Taking Ia= 6, you still have two unknown quantities in your equation: (90-Va)/20 - (Vb-Va)/3 + Va/20 - 6 = 0 so you can't "solve" it for specific values. You could solve for either Va or Vb "in terms of" the other.

(90-Va)/20= 9/2- Va/20 and (Vb- Va)/3= Vb/3- Va/3 so simply multiplying the terms in parentheses gives

9/2- Va/20- Vb/3+ Va/3+ Va/20- 6= 0.

The "-Va/20" and "+ Va/20" terms cancel so

Va/3- Vb/3- 12/2+ 9/2= 0 or Va/3- Vb/3= 3/2.

Then Va= 3(3/2+ Vb/3)= 9/2+ Vb or Vb= -3(3/2- Va/3)= Va/3- 9/2.

You might just need Va- Vb= 9/2.