# Use the Node Voltage method to solve

## Homework Statement

From the above circuit find VCB and VDG

Know Data:
VE = 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 VCB and VDG 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.

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

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
Homework Helper
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 VC with the node voltage method . Knowing Vc, you can calculate the currents, and knowing the currents, you can determine all node voltages.

Simplified Circuit.

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

How would I find VB? Is VA really = 15V.
NOTE: VD = 2VC so it can be eliminated.

Simplified Circuit.
View attachment 75137
This is what I have done. Not sure if correct?
View attachment 75135
How would I find VB? Is VA really = 15V.
NOTE: VD = 2VC so it can be eliminated.
Actually I think I have it just wait.

Simplified Circuit.

This is what I have done.

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

ehild
Homework Helper

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

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
Homework Helper
Simplified Circuit.
View attachment 75137
This is what I have done. Not sure if correct?
How would I find VB? Is VA really = 15V.
No, VA is not 15 V, as we count the potential with respect to E. VA-VB=15 V

No, VA is not 15 V, as we count the potential with respect to E. VA-VB=15 V
I figured Va = Vb + 15 and it worked!

ehild
Homework Helper
Thanks I have now managed to solve this!
Splendid! What did you get for VC?
Have you tried to solve the problem also with the very simple equivalent circuit?

Splendid! What did you get for VC?
Have you tried to solve the problem also with the very simple equivalent circuit?
I got VC = 2.5 V

ehild
Homework Helper
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.