Nodal analysis exercise,are my equations correct?

In summary: Remember to use consistent units and directions for currents and voltages when summing them. Good luck with the rest of your analysis!
  • #1
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Homework Statement


We have the circuit in the figure.I have to find v using nodal analysis only.

Homework Equations


Converted 1/6 F to -3j and 2sin2t to -2j.

The Attempt at a Solution


In node v1 we have the equation
6= -12+ [v1/2] + [( v1-v)/1]
In node v we have the equation
2j+ [(v1-v)/1]= 12 + [ v/(-3j)]

Solving these equations to find v is very easy,the crucial part is finding out if the two main equations here are correct.Are they?http://i.imgur.com/nAEsUpo.jpg
 
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  • #2
Elaia06 said:

Homework Statement


We have the circuit in the figure.I have to find v using nodal analysis only.

Homework Equations


Converted 1/6 F to -3j and 2sin2t to -2j.

The Attempt at a Solution


In node v1 we have the equation
6= -12+ [v1/2] + [( v1-v)/1]
In node v we have the equation
2j+ [(v1-v)/1]= 12 + [ v/(-3j)]

Solving these equations to find v is very easy,the crucial part is finding out if the two main equations here are correct.Are they?http://i.imgur.com/nAEsUpo.jpg

They look basically right, but I usually prefer to just sum all of the currents leaving each node, and set each sum = 0. It's confusing having 2 sides to the equations, with some currents entering and some leaving each node. At least it is confusing for me. :-)
 
  • #3
I would only question your handling of the sin() source. You've made the correct translation to a phasor value (-2j), then used +2j for it in your v-node equation on the left hand side where apparently you're summing currents flowing into the node.

I agree wholeheartedly with berkeman's suggestion about summing all currents and setting the sum to zero. Choose either in-flow or out-flow for the direction and be consistent. Do it the same way every time and you won't have to think about each current and the side of the equation to put it on and what sign to give it.
 
  • #4
Many thanks to both of you :)
I guess finally I should write them like this?
6 +12- [v1/2] - [( v1-v)/1]=0
-2j+ [(v1-v)/1]- 12 - [ v/(-3j)]=0
 
  • #5
Yes, looks good!
 

Related to Nodal analysis exercise,are my equations correct?

1. How can I tell if my nodal analysis equations are correct?

In nodal analysis, the equations are derived by applying Kirchhoff's current law (KCL) at each node in the circuit. To ensure the equations are correct, make sure that the sum of currents entering the node is equal to the sum of currents leaving the node. Also, double-check the direction of the currents in your equations to make sure they align with the direction of the voltage drops in the circuit.

2. What is the most common mistake in nodal analysis exercises?

The most common mistake in nodal analysis exercises is forgetting to include all the necessary nodes in the circuit. This can lead to incorrect equations and ultimately, incorrect solutions. It is important to carefully examine the circuit and identify all the nodes before starting the analysis.

3. Can I use nodal analysis for circuits with dependent sources?

Yes, nodal analysis can be used for circuits with dependent sources. However, the analysis may become more complex as the dependent sources will introduce additional variables in the equations. It is important to carefully define the variables and properly apply KCL at each node to account for the dependent sources.

4. How many equations do I need for a nodal analysis exercise?

The number of equations needed for a nodal analysis exercise is equal to the number of unknown node voltages in the circuit. This is based on the fact that KCL equations can be written for each node in the circuit, and each equation will have only one unknown voltage variable.

5. Are there any shortcuts or tricks for solving nodal analysis exercises?

There are some tricks and shortcuts that can be used for solving nodal analysis exercises, such as identifying symmetrical circuits or using superposition to simplify the analysis. However, it is important to have a thorough understanding of the fundamentals of nodal analysis before attempting to use these shortcuts, as they may not work in all cases.

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