Simple Nodal Analysis: Solving Homework

In summary, the homework statement is that there are four equations that need to be solved to find the value of the variable V0. The equation for node 4 is incorrect and needs to be corrected.
  • #1
ravenprp
2,891
0

Homework Statement



http://img258.imageshack.us/img258/2152/screenshot01kf5.th.jpg [Broken]

Homework Equations



KCL
KVL
V = IR

The Attempt at a Solution



I used 4 nodes at the top, one reference node at the bottom.

I have it labeled V1, V2, V3, V4, starting from the far left -> right.

My nodal equations are:

At v1:

+ 7V

At v2:

0 = (v2-v1) / 2 + v2 / 4 + (v2 - v3) / 4

At v3:

(v3-v2) / 4 + v3 / 8 + (v3 - v4) / 8 = 0

At v4:


0 = (v4-v3)/ 8 - 1mA

so we know V0 is v2-v3 = v0.

I'm not sure if this is correct so far.
 
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  • #2
your image is too small to be legible
 
  • #3
So far it's correct.

mjsd said:
your image is too small to be legible

Try clicking on the (thumbprint) image to view a larger one.
 
  • #4
For v4, is it 8V in my case? I'm stuck with the simult. equations, and I'm just curious. I have a 1mA current going through the 8k resistor, so I'm believing its 8V? Can anyone verify this?
 
  • #5
I have simplified it to this:

V1 = 7V (like before)

for node at V2...

4V_2 - 2V_1 - V_3 = 0

for node at V3...

4V_3 - 2V_2 - V_4 = 0

for node at V4...

V_3 - V_4 = 8

So, all of the eq put together...

4V_2 - 2V_1 - V_3 = 0
4V_3 - 2V_2 - V_4 = 0
V_3 - V_4 = 8
V_0 = V_2 - V_3


I'm not sure what to do after here.
 
  • #6
ravenprp said:
For v4, is it 8V in my case? I'm stuck with the simult. equations, and I'm just curious. I have a 1mA current going through the 8k resistor, so I'm believing its 8V? Can anyone verify this?

No, v4 is not 8V, but either one of (v4-v3) or (v3-v4) is and it is not difficult to figure out which one is.

ravenprp said:
I have simplified it to this:

V1 = 7V (like before)

for node at V2...

4V_2 - 2V_1 - V_3 = 0

for node at V3...

4V_3 - 2V_2 - V_4 = 0

for node at V4...

V_3 - V_4 = 8

<snip>

I'm not sure what to do after here.

The nodal equation for node 4 is incorrect. Please check that against your first post. You have above 3 equations with 3 unknowns (v2, v3, v4). It becomes thus a mathematical problem now to resolve the 3 unknowns. The final step, of course, would be to put these values into finding v0 = v2-v3.
 
  • #7
Oh, woops, it should be v_4 - v_3 = 8, as in my first post.

Its this math part that kills me, I'll be back in a few:)

Thanks so far, doodle.
 
  • #8
Nevermind, it's correct. I just checked.

Thanks for all those that helped :)
 

What is Simple Nodal Analysis?

Simple Nodal Analysis is a method used in circuit analysis to determine the voltage and current values at different nodes in a circuit. It is based on the principle of Kirchhoff's Current Law, which states that the sum of currents entering a node must equal the sum of currents leaving the node.

How do you solve a homework problem using Simple Nodal Analysis?

To solve a homework problem using Simple Nodal Analysis, you need to follow these steps:

  1. Assign a reference node and label all the other nodes in the circuit.
  2. Apply Kirchhoff's Current Law at each node by writing an equation that states the sum of currents entering the node is equal to the sum of currents leaving the node.
  3. Use Ohm's Law to write equations for the voltage drops across each resistor in terms of the currents and resistances.
  4. Substitute the equations into the Kirchhoff's Current Law equations and solve for the unknown currents.
  5. Use the known currents to calculate the voltages at each node using Ohm's Law.

What are the advantages of using Simple Nodal Analysis?

Simple Nodal Analysis is a powerful tool for solving complex circuits because it allows for a systematic and organized approach to solving circuit problems. It also simplifies the process by reducing the number of equations needed to solve the problem, making it more efficient and less prone to error.

What are the limitations of Simple Nodal Analysis?

Simple Nodal Analysis can only be used for circuits that can be modeled as a series of nodes connected by resistors. It cannot be used for circuits with non-linear components such as diodes or transistors. Additionally, it assumes ideal conditions and does not account for factors such as parasitic elements or non-ideal behavior of components.

Can Simple Nodal Analysis be used for circuits with multiple voltage sources?

Yes, Simple Nodal Analysis can be used for circuits with multiple voltage sources. In this case, one of the nodes must be chosen as the reference node and the voltages at the other nodes can be calculated with respect to the reference node. The voltage sources will be included in the equations as known values.

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