Finding Vx with Nodal Analysis in a Circuit with Multiple Voltage Sources

[qzhang]

Homework Statement

I have to use Nodal analysis to find Vx

Homework Equations

our prof said that if we want to find the number of unknowns and eqxns necessary then we need to find all the nodes in circuit - the reference node - number of voltage sources, for this circuit that would be 4 nodes - 1 ref - 3 vsrc = 0 this doesn't make sense in this circuit

The Attempt at a Solution

my attempt at this problem I'm pretty sure its not right, here is what i did:

KCL @ node b: -(Vx/20k) + (Vx/30k) + (Vx-20)/10k = 0 solving for Vx

I get that Vx = 24V. I got the eqxn above by subtracting the two voltages on the leftmost node and adding the voltages on the rightmost node and then doing the KCL. I'm pretty sure its not right so please help

 

[gneill]

Homework Statement

I have to use Nodal analysis to find Vx

Homework Equations

our prof said that if we want to find the number of unknowns and eqxns necessary then we need to find all the nodes in circuit - the reference node - number of voltage sources, for this circuit that would be 4 nodes - 1 ref - 3 vsrc = 0 this doesn't make sense in this circuit

The Attempt at a Solution

my attempt at this problem I'm pretty sure its not right, here is what i did:

KCL @ node b: -(Vx/20k) + (Vx/30k) + (Vx-20)/10k = 0 solving for Vx

I get that Vx = 24V. I got the eqxn above by subtracting the two voltages on the leftmost node and adding the voltages on the rightmost node and then doing the KCL. I'm pretty sure its not right so please help

There's a problem with your KCL for node b. You have assumed that the potentials at a and c are both zero, but that cannot be the case given the fixed source separating them.

Nodes that are directly interconnected by voltage sources are not really separate nodes, they comprise a "supernode". This is because the voltage sources define and maintain a fixed potential difference between them regardless of what current flows through those sources. In this circuit the points labelled a, c, and ground are all directly interconnected by fixed voltage sources, so their potentials with respect to the reference node (ground) are all fixed and no equations need to be written for them; their potentials with respect to ground can be written by inspection from the circuit diagram (What are they?).