Node Voltage (is my answer correct )

In summary: Had you just plugged the numbers into the equations you would have just gotten the wrong answer. You're on the right track! Keep it up!In summary, the node voltage method was used to find the voltages at nodes V1, V2, V3, and V4. Kirchov's Current Law was applied to sum the currents going into each node and setting them equal to zero. After solving the equations, it was determined that V1 was 6V, V2 was 16V, V3 was 5.9V, and V4 was 21V.
  • #1
pokie_panda
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http://www.flickr.com/photos/84781786@N03/7822251544/
Find the node VOLTAGE for V1,V2,V3,V4

Homework Equations


KVL

The Attempt at a Solution



V1 = 6V
V4= 16V
V2= V2/1.5k - 6/1.5k + V2/ 1k + V2/3.3k - V3/3.3k
6/1500 = V2/5.8k - V3/3.3k
V3 = V3/2.2k + V3 / 4.7k + V3/3.3k - V2/3.3k - 16/2200
16/2200 = - V2/3.3k + V3/ 10.2k

But I'm getting 2 negative answers
V2= -34.6 V V3= -32.9
 
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  • #2
pokie_panda said:
http://www.flickr.com/photos/84781786@N03/7822251544/
Find the node VOLTAGE for V1,V2,V3,V4

Homework Equations


KVL


The Attempt at a Solution



V1 = 6V
V4= 16V
V2= V2/1.5k - 6/1.5k + V2/ 1k + V2/3.3k - V3/3.3k
Why is that V2 = ? Surely you're forming a sum of currents at the node, which should yield a (zero) current?
6/1500 = V2/5.8k - V3/3.3k
How did you arrive at the V2/5.8k term?
V3 = V3/2.2k + V3 / 4.7k + V3/3.3k - V2/3.3k - 16/2200
16/2200 = - V2/3.3k + V3/ 10.2k
Again, the "V3 =" doesn't make sense. Perhaps you're just being a tad sloppy with terminology? The "=" sign is reserved for use in equations. Did you mean to indicate that "This is the expression for node V3?"

Also again, can you explain how you arrived at the term V3/10.2k?
 
  • #3
I agree with Gneill - Your equations are a bit off - I think you mean:

V1: V1 = 6V
V2: V2 = 16V
V3: 0 = V2 / 1.5k - V1 / 1.5k + V2 / 1.0k + V2 / 3.3k - V3 / 3.3k
V4: 0 = V3 / 3.3k - V2 / 3.3k + V3 / 4.7k + V3 / 2.2k - V4 / 2.2k

Note that using the node voltage method used Kirchov's Current Law which states that all the currents going into a node must equal zero. Using the node voltage method you are simply summing the currents into each node and setting them equal to zero - not V3 or V4.

If you solve these equations you will come up with the correct answer... it took me a couple tries - my arithmetic is rusty, I guess... but I think I just fat fingered a value into my calculator. I did finally arrive at the correct answer, which I verified with software.

Hope this helps.

Also note that:
V2 / 1.5k + V2 / 1.0k + V2 / 3.3k does NOT equal V2 / 5.8k
http://www.mathsisfun.com/fractions_addition.html
I think there was some confusion there as well which could have been the root of your negative number solution.

On the plus side - good for you for realizing there was no way the answer could be negative without a negative voltage source.
 

FAQ: Node Voltage (is my answer correct )

1. What is Node Voltage?

Node voltage is a method used in circuit analysis to calculate the voltage at a specific node (or point) in an electrical circuit. It is based on Kirchhoff's Current Law, which states that the sum of currents entering a node is equal to the sum of currents leaving the node.

2. How is Node Voltage calculated?

To calculate the node voltage, you first need to label each node in the circuit with a unique name or number. Then, using Kirchhoff's Current Law, you can set up equations for each node by equating the sum of currents entering the node to the sum of currents leaving the node. This will result in a system of equations that can be solved to find the node voltages.

3. Why is Node Voltage important?

Node voltage is important because it allows us to determine the voltage at specific points in a circuit, which is necessary for analyzing and designing electrical circuits. It also helps us understand how current flows through the circuit and how different components affect the overall voltage.

4. Can Node Voltage be negative?

Yes, node voltage can be negative. This means that the voltage at that particular node is lower than the reference voltage (usually the ground). It is important to pay attention to the sign of the node voltage, as it indicates the direction of current flow in that branch of the circuit.

5. Are there any limitations to using Node Voltage?

While node voltage is a useful method for circuit analysis, it does have some limitations. It can only be used for circuits that can be represented using Kirchhoff's Current Law, and it cannot be applied to circuits with dependent sources or non-linear elements. In these cases, other methods, such as Mesh Analysis, may be more suitable.

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