How Do You Solve the Supernode Equation Involving Node C?

[noname1]

I am trying to resolve this super node but i am having trouble with the equation, more specifically node c, this is where i got so far


5 = Va/20 +(Va - Vd)/10 + (Vb - Vc)/12.5
-10 = (Vd - Va)/10 + Vd/25
-Va + Vb = 100

please explain the c node equation

 

[The Electrician]

Assuming the positive end of the 150 volt battery is connected to node C, then the equation is simply: Vc = 150

 

[noname1]

but don't we have to include the 12.5 resistor from node b to node c?

 

[The Electrician]

That resistor is taken care of by your first equation.

When you have a voltage source connected from ground to some node, you need a (constraint) equation that simply says that the voltage at (in this case) node C is 150 volts.

It's similar to your third equation.

 

[noname1]

i am getting an error on node d can anyone tell me what i am doing wrong, its the 3rd equation on the last process

 

[The Electrician]

I think that equation should be:

-5Va + 7Vd = -500

For final answers, I get:

Va = 11.712
Vb = 111.712
Vc = 150
Vd = -63.063