Problem with Node Voltage Method

In summary, the power delivered by the 5V voltage source in the network shown in the figure can be determined by applying Kirchhoff's Current Law (KCL) at both nodes in the circuit. By solving for the currents in each branch using the given information, it is determined that the power delivered by the 5V supply is 15 watts.
  • #1
challarao
22
0

1. Find the power delivered by the 5V Voltage source in the network of Fig.
node.jpg

This is my attept at solution:

At node 1 V1...assuming current leaving V1:
KCL equation: -1A+1A+[(V1-5)/3]+[(V1-(V2-10))/2]=0

At node 2 V2...assuming current leaving V2:
KCL equation: -2A-1A+[V2-(V1+10)]=0

But, I'm not certain about the sign convention when there is a voltage source with a resistor between V1 and V2...
I'm also confused that how to proceed when there is a current source and resistor between two nodes...
Where did I go wrong...?
Please help me...
 
Last edited:
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  • #2
If you look at the node labelled 2, you'll note that three branches come together and two of them have specified currents. What does KCL tell you about the current in the remaining branch? Can you now repeat this feat at node 1?
 
  • #3
gneill said:
If you look at the node labelled 2, you'll note that three branches come together and two of them have specified currents. What does KCL tell you about the current in the remaining branch? Can you now repeat this feat at node 1?
Thank you
Yes, there are four branches coming together at node 1.Currents are specified for two of the branches.

At node 1 KCL: -1+1+[(v1-(-5))/3]+[v1-(v2+10)]/2=0

Did I write it correctly?
Thanks...
 
  • #4
challarao said:
Thank you
Yes, there are four branches coming together at node 1.Currents are specified for two of the branches.

At node 1 KCL: -1+1+[(v1-(-5))/3]+[v1-(v2+10)]/2=0

Did I write it correctly?
Thanks...

You won't even need the node voltage... If you know all but one current
flowing through the node, the last one is thus determined y the others.
So what must i2 be?
 
  • #5
I think i2=(v1+5)/2, am I correct?
 
  • #6
Look again at node 1. You've determined what i1 must be, coming from node 2, right? So all branches leading to node 1 have known currents except for the branch with i2. So what's i2?
 
  • #7
As 2A and 1A are reaching node 2...3A must leave it..

So, i1=3A, am I correct..?
and wow i2=3A...I got it now ...I think I'm correct...amn't I?
Thank you very very much...
 
Last edited:
  • #8
challarao said:
As 2A and 1A are reaching node 2...3A must leave it..

So, i1=3A, am I correct..?
and wow i2=3A...I got it now ...I think I'm correct...amn't I?
Thank you very very much...

Yup. :smile:

Now you can figure out the power delivered by the 5V supply.
 

1. What is the Node Voltage Method?

The Node Voltage Method is a technique used in circuit analysis to determine the voltage at each node (connection point) in a circuit. It involves applying Kirchhoff's Current Law (KCL) and Ohm's Law to create a system of equations that can be solved to find the unknown node voltages.

2. When is the Node Voltage Method used?

The Node Voltage Method is typically used when analyzing circuits with multiple voltage sources and resistors connected in series and parallel. It is also useful when there are dependent voltage sources, as it allows for easier incorporation of these sources into the analysis.

3. What are the advantages of using the Node Voltage Method?

One advantage of using the Node Voltage Method is that it can be used to solve for multiple unknown node voltages simultaneously. This can save time and effort compared to other methods such as the Branch Current Method. Additionally, the Node Voltage Method is versatile and can be used for both DC and AC circuits.

4. What are some common challenges when using the Node Voltage Method?

One challenge when using the Node Voltage Method is that it can become more complex and time-consuming for circuits with a large number of nodes. Another challenge is that it requires careful labeling of nodes and keeping track of sign conventions, which can be confusing for some users.

5. Are there any limitations to the Node Voltage Method?

One limitation of the Node Voltage Method is that it is only applicable to circuits with a single reference node (ground). This means that circuits with multiple voltage sources connected to different reference points cannot be solved using this method. Additionally, the Node Voltage Method may not be the best option for circuits with non-linear elements such as diodes or transistors.

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