Calculating Node Voltages with KCl"

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In summary: I'll try to solve it again.In summary, there was a conversation about a homework problem involving two nodes and equations with potential and current values. The equations were incorrect due to a sign error in the I2 term. After discussing and clarifying the correct direction of the voltage source, the equations were corrected to be 80 = Va/0.143 + (Va-(Vb-10))/0.2 and 20 = Vb/0.125 - (Va-(Vb+10))/0.2. It was noted that the given solutions were not appropriate for the circuit as drawn and the equations were corrected to reflect the correct voltage at one end of the 0.2 ohm resistor
  • #1
TheRedDevil18
408
1

Homework Statement



2dw183.jpg


Homework Equations

The Attempt at a Solution



I'm not getting the correct answers, here are my equations

Node A:
80 = ix + i2
80 = Va/0.143 + (Va-(Vb+10))/0.2......1

Node B:
20 = iy-i2
20 = Vb/0.125 - (Va-(Vb+10))/0.2......2

Are these equations correct ?
 
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  • #2
equation 1... i see a sign error
equation 2...same problem
 
  • #3
donpacino said:
equation 1... i see a sign error
equation 2...same problem

I don't see where the sign error is
 
  • #4
There is an error with your I2 term. Look at the relationship between VB and the voltage source
 
  • #5
donpacino said:
There is an error with your I2 term. Look at the relationship between VB and the voltage source

I don't know, Is it -10V ?, I'm confused with the signs :frown:
 
  • #6
TheRedDevil18 said:
80 = Va/0.143 + (Va-(Vb+10))/0.2......1
You drop down from Vb by 10v to get to the 0.2 ohm resistor. Should be ...(Vb-10)...

If you draw an arrow from (-) to (+) on the battery, which you should do and label it +10V, you can see the drop in potential in going from Vb towards the 0.2 ohm. The bottom of the battery is 10v less than the top.
 
  • #7
NascentOxygen said:
You drop down from Vb by 10v to get to the 0.2 ohm resistor. Should be ...(Vb-10)...

If you draw an arrow from (-) to (+) on the battery, which you should do and label it +10V, you can see the drop in potential in going from Vb towards the 0.2 ohm. The bottom of the battery is 10v less than the top.

I still don't get the correct answers. I get Va = 5.65V and Vb = 7.56V
These are my equations
80 = Va/0.143 + (Va-(Vb-10))/0.2

20 = Vb/0.125 - (Va-(Vb+10))/0.2
 
  • #8
TheRedDevil18 said:
I still don't get the correct answers. I get Va = 5.65V and Vb = 7.56V
These are my equations
80 = Va/0.143 + (Va-(Vb-10))/0.2

20 = Vb/0.125 - (Va-(Vb+10))/0.2

that is what I got too. either we both made the same mistake, or the 'solution' is incorrect.
 
  • #9
The answers accompanying the question in post #1 are consistent with the 20A source being directed downwards, so are not appropriate for the circuit as drawn.
 
  • #10
Ok, maybe the solutions are incorrect. I'm a bit confused with the second equation though, why is it Vb+10, because the 0.2 ohm resistor is still connected to the negative end of the battery. Shouldn't it be Vb-10 ?
 
  • #11
It should be Vb - 10 for the reason I gave.
 
  • #12
NascentOxygen said:
It should be Vb - 10 for the reason I gave.

For both the equations ?
 
  • #13
TheRedDevil18 said:
For both the equations ?
Yes, it defines the voltage at one end of that 0.2 Ω resistor.
 
  • #14
Ok thanks guys
 

Related to Calculating Node Voltages with KCl"

1. What is KCl and how is it used in calculating node voltages?

KCl, or potassium chloride, is an ionic compound commonly used in electrochemistry and other scientific experiments. In the context of calculating node voltages, KCl is used as a conductive solution to create a closed circuit and allow for the flow of electrical current.

2. How does KCl affect the accuracy of node voltage calculations?

KCl is used in node voltage calculations to create a known reference point (or ground) for the circuit. This allows for more accurate measurements and calculations of the voltage at each node in the circuit.

3. What equipment is needed to perform node voltage calculations with KCl?

To perform node voltage calculations with KCl, you will need a power source (such as a battery), resistors, a voltmeter, and a conductive solution of KCl. You may also need wires and a breadboard to set up the circuit.

4. What are the steps for calculating node voltages using KCl?

The steps for calculating node voltages using KCl are as follows: 1) Set up the circuit with the power source, resistors, and KCl solution; 2) Measure the voltage at each node using the voltmeter; 3) Use Kirchhoff's Current Law (KCL) to write equations for the currents at each node; 4) Solve the equations simultaneously to find the voltage at each node.

5. Are there any common mistakes to avoid when using KCl for node voltage calculations?

One common mistake to avoid when using KCl for node voltage calculations is not ensuring that the circuit is properly set up and the connections are secure. This can lead to inaccurate voltage measurements and calculations. Additionally, it is important to use the correct concentration of KCl solution and to keep the solution clean to prevent any interference with the electrical current.

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