Can someone please explain a step to a solution? It's about nodal analysis

In summary, the conversation is about solving nodal equations using Ohm's Law to find the voltage across a 2mA current source and then using algebra to solve for the voltage at node V2.
  • #1
naivy
40
0

Homework Statement



4wzrz.png


Homework Equations



V=IR, Nodal Analysis

The Attempt at a Solution



1 and 2 in the diagram are the nodal equations. Considering that the left node is V1 and that the right node is V2. I don't know how to get from the nodal equations to step 3. I know that you go from step 3 to step 4 using V=IR.

I tried solving the nodal equations to get to step 3...

Can someone please work it out for me? Thank you

Please help
 
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  • #2
I assume from the picture that the 1kR label next to the 10kR on the left should actually be the resistance of the 2mA current source, which is interesting, since by Ohms Law the voltage across it would then be 2V, as shown by the 1st equation current of -2/K, yet this voltage is not V1 ... somehow, despite sharing terminals ... ?

Anyway, you know what the voltage and resistance are for Ix, so substitute that in and then do the algebra (solving simultaneous equations) and you should get the value for V2.
 

FAQ: Can someone please explain a step to a solution? It's about nodal analysis

What is nodal analysis and why is it important in science?

Nodal analysis is a mathematical method used in circuit analysis to determine the voltage and current values at different nodes (connection points) in a circuit. It is important in science because it allows us to understand and predict the behavior of complex electrical systems, which is essential in many fields such as engineering, physics, and electronics.

How do I perform nodal analysis?

To perform nodal analysis, follow these steps:
1. Identify all the nodes in the circuit and label them.
2. Choose a reference node and assign it a voltage of 0.
3. Write Kirchhoff's Current Law (KCL) equations for each node, using the currents flowing into and out of the node.
4. Solve the system of equations to find the voltage values at each node.
5. Use Ohm's Law to calculate the current values at each branch.
6. Check your solution by ensuring that the sum of currents entering a node is equal to the sum of currents leaving the node.

What are the limitations of nodal analysis?

Nodal analysis is based on the assumption that all the elements in the circuit are linear (i.e. they follow Ohm's Law). Therefore, it cannot be used for circuits with nonlinear elements such as diodes or transistors. Additionally, nodal analysis becomes more complex and time-consuming for larger circuits with many nodes.

Can nodal analysis be used for AC circuits?

Yes, nodal analysis can also be used for AC circuits. However, the equations used in AC nodal analysis are more complex and involve the use of complex numbers and phasors.

How does nodal analysis differ from other circuit analysis methods?

Nodal analysis is a method based on Kirchhoff's Laws, while other methods such as mesh analysis use Ohm's Law and Kirchhoff's Voltage Law (KVL). Additionally, nodal analysis is more suitable for circuits with multiple voltage sources, while mesh analysis is more efficient for circuits with multiple current sources. Ultimately, the choice of method depends on the complexity and type of circuit being analyzed.

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