Nodal analysis with 2 voltage sources

In summary, the participants are discussing how to solve a circuit and have identified two supernodes. They suggest using superposition and substituting one source at a time to find the values of i and v.
  • #1
adashiu
21
0
Can someone solve this circuit

d4bb9489359f3f85.jpg


Find v and i in the circuit.

I know that we have to make somethng with supernode, but where the supernode is here? How to develop this problem? Please help me :)

Btw it is nice forum, today i have found that. I hope I will be able to help you in other engeenering topics. Greets

My attempts:

Im not sure, but I think that reference node will be that under 3 ohm resistor ( ? ) I have no idea how to cope with a problem of 2 supernodes in this circuits ( If I am right, that there are 2 supernodes). Actually I am green... :cry:
 
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  • #2
You can solve it by using superposition. Substitute one of the sources by a short circuit and solve for the other source. You find i1 and v1.
Then solve for the second source, with the first one short-circuited. You find i2 and v2.
Your solution is i = i1 + i2; v = v1 + v2.
 
  • #3


Hello there,

Thank you for your question. I am happy to assist you in solving this circuit. First, let's define the reference node. The reference node is typically chosen as the ground or the node with the most connections in the circuit. In this case, the node under the 3 ohm resistor is a good choice for the reference node.

Next, we need to identify the supernodes. A supernode is formed when a voltage source is connected between two non-reference nodes. In this circuit, there are two voltage sources, one between the 4 ohm and 5 ohm resistors and another between the 3 ohm and 2 ohm resistors. Therefore, we have two supernodes in this circuit.

To solve this circuit, we will use nodal analysis. This method involves writing Kirchhoff's current law (KCL) at each non-reference node in the circuit. We will also use Ohm's law to relate the currents and voltages in the circuit.

First, let's label the nodes in the circuit. We can label the nodes as N1, N2, N3, and N4, with N1 being the reference node. Now, we can write KCL at each node:

At N1: (N1-N2)/4 + (N1-N3)/5 = 0
At N2: (N2-N1)/4 + (N2-N3)/6 + (N2-N4)/3 = 0
At N3: (N3-N1)/5 + (N3-N2)/6 + (N3-N4)/2 = 0
At N4: (N4-N2)/3 + (N4-N3)/2 + (N4-0)/3 = 0

Next, we can use Ohm's law to relate the currents to the voltages. We know that the current through a resistor is equal to the voltage across it divided by its resistance. Therefore, we can write the following equations:

At N1: (N1-N2)/4 = (N1-N3)/5
At N2: (N2-N1)/4 = (N2-N3)/6 = (N2-N4)/3
At N3: (N3-N1)/5 = (N3-N2)/6 = (N3-N4)/2
At N4:
 

FAQ: Nodal analysis with 2 voltage sources

What is nodal analysis with 2 voltage sources?

Nodal analysis with 2 voltage sources is a method used to analyze electrical circuits with two voltage sources. It involves determining the voltage at each node in the circuit and using Kirchhoff's Current Law to write equations for each node, which can then be solved to find the unknown voltages.

How is nodal analysis with 2 voltage sources different from nodal analysis with 1 voltage source?

The main difference between nodal analysis with 2 voltage sources and nodal analysis with 1 voltage source is the number of independent equations that need to be written. With 2 voltage sources, there are more unknown voltages and therefore more equations need to be written to solve for each node. Additionally, the presence of multiple voltage sources can create additional complexities in the circuit.

What are the steps for performing nodal analysis with 2 voltage sources?

The steps for performing nodal analysis with 2 voltage sources are as follows:

  • Identify all the nodes in the circuit and assign a variable for each node's voltage.
  • Apply Kirchhoff's Current Law to each node to write equations.
  • Set up a system of equations using the nodal equations and any additional equations for known values.
  • Solve the system of equations to find the unknown node voltages.

What are some common mistakes to avoid when using nodal analysis with 2 voltage sources?

Some common mistakes to avoid when using nodal analysis with 2 voltage sources include:

  • Forgetting to include all the nodes in the circuit or writing incorrect equations for the nodes.
  • Not properly labeling the voltage sources and their polarities in the circuit diagram.
  • Incorrectly setting up or solving the system of equations.
  • Not considering the impact of dependent sources in the circuit.

In what types of circuits is nodal analysis with 2 voltage sources most useful?

Nodal analysis with 2 voltage sources is most useful in circuits with multiple voltage sources, such as circuits with batteries or power supplies. It can also be used in circuits with dependent sources, but may require additional steps in the analysis. Nodal analysis is a general method that can be used for any type of circuit, but it is particularly useful for circuits with many nodes and voltage sources.

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