Use the Node Voltage method to solve

[cavalieregi]

Homework Statement

From the above circuit find V_CB and V_DG

Know Data:
V_E = 0 (ground)

Homework Equations

KCL and Ohm's Law are used in Node Voltage Method.

The Attempt at a Solution

I decided I would determine the node voltages then work out V_CB and V_DG afterwards.
1. KCL and Ohm's law at Node C

$15 + V_F + V_D = 3 V_C$ -(1)​

2. Super Node at EG

2.1 KCL and Ohm's law for all currents entering

$2(V_F - V_G) = 2 V_E - V_D - V_B$
$2(V_F - V_G) + V_D + V_B = 2 V_E$ -(2)​

2.2 Potentials at Nodes E and G

$V_G = -5V$ -(3)​

3. KCL and Ohm's law at Node D

$V_C = 2 V_D$ -(4)
​

This is as far as I got I am unsure what to do next so I can get 5 equations so they can all be solved simultaneously.

 

[ehild]

The problem highly simplifies if you replace the series and parallel resistances with their resultants.

 

[cavalieregi]

The problem highly simplifies if you replace the series and parallel resistances with their resultants.

So if I replaced the two between F and G, and the one between C and F right?

 

[ehild]

So if I replaced the two between F and G, and the one between C and F right?

Yes, and the two resistors between C and E, and also the two resistors in series with the 15 V battery.

In the simplifed circuit, you can find the voltage V_C with the node voltage method . Knowing Vc, you can calculate the currents, and knowing the currents, you can determine all node voltages.

 

[cavalieregi]

Simplified Circuit.

This is what I have done. Not sure if correct?

How would I find V_B? Is V_A really = 15V.
NOTE: V_D = 2V_C so it can be eliminated.

 

[cavalieregi]

Simplified Circuit.
View attachment 75137
This is what I have done. Not sure if correct?
View attachment 75135
How would I find V_B? Is V_A really = 15V.
NOTE: V_D = 2V_C so it can be eliminated.

Actually I think I have it just wait.

 

[cavalieregi]

Simplified Circuit.

This is what I have done.

I think I have made a mistake somewhere.
NOTE: V_B is meant to be negative at end where = 76.67V

 

[ehild]

Your solution is very complicated...

The circuit is equivalent with the one in the picture, except B and D nodes disappearing. You can solve it for Vc.

 

[cavalieregi]

Your solution is very complicated...

The circuit is equivalent with the one in the picture, except B and D nodes disappearing. You can solve it for Vc. View attachment 75156

Thanks I have now managed to solve this!

 

[ehild]

Simplified Circuit.
View attachment 75137
This is what I have done. Not sure if correct?
How would I find V_B? Is V_A really = 15V.

No, V_A is not 15 V, as we count the potential with respect to E. V_A-V_B=15 V

 

[cavalieregi]

No, V_A is not 15 V, as we count the potential with respect to E. V_A-V_B=15 V

I figured Va = Vb + 15 and it worked!

 

[ehild]

Thanks I have now managed to solve this!

Splendid! What did you get for V_C?
Have you tried to solve the problem also with the very simple equivalent circuit?

 

[cavalieregi]

Splendid! What did you get for V_C?
Have you tried to solve the problem also with the very simple equivalent circuit?

I got V_C = 2.5 V

 

[ehild]

Using the equivalent circuit, the node equation for the currents at C is: $\frac{15-Vc}{2}=\frac{Vc}{2}+\frac{Vc-(-5)}{1.5}$ You need only this equation to solve for Vc, which is the same you got.