Find Io in the network nodal analysis

In summary, the student is trying to solve a homework problem involving voltages and currents, but is having difficulty understanding the equation. He needs help determining which direction the currents flow and labeling the junctions.
  • #1
Color_of_Cyan
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"Find Io in the network" nodal analysis

Homework Statement

http://img189.imageshack.us/img189/8807/homeworkprob22.jpg Find Io in the network

Homework Equations


V = IR

current division, voltage division,

KCL, KVL

Nodal Analysis (or mesh)

The Attempt at a Solution



So I think I need to use nodal analysis for this problem but not sure where to start with that.I think it goes something like

24V - 12V = (2Ω)(I2), but not sure at all. Do you use KVL / KCL at all? If yes, then how can I apply it here?

Tips for more places to start would also be helpful.Thank you
 
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  • #2


No need to invoke nodal analysis here. Just work backwards from the output and fill in voltages and currents as you go. For example, with 24V at the output, what's the current through the 4Ω resistor? What then is the current through the 2Ω resistor? What's the potential change across the 2Ω resistor? So then the potential at the top of the 18Ω resistor is... continue in that vein. Employ KVL, KCL, Ohm's Law, as required.
 
  • #3


so redrawing it like this:

http://imageshack.us/a/img96/8173/homeworkprob22edit.jpg I can't really tell which direction goes which and if I add or subtract that good with KVL but would this be on the correct track? :24V - (4Ω)(I1) = 0

(4Ω)(I1) - (2Ω)(I2) - (18Ω)(I3) = 0

(18Ω)(I3) - 12V = 0

(2Ω)(I4) + (4Ω)(I5) = 0

Io = 2A + I5 + I3 + I1 ?

Where would I go from here or are there mistakes?(and this was meant to go in the Engineering forum not physics forums by the way, because I was tired, heh)
 
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  • #4


Color_of_Cyan said:
(4Ω)(I1) - (2Ω)(I2) - (18Ω)(I3) = 0
That doesn't look right in relation to the arrows shown for the currents. Try again.
 
  • #5


I can't really tell which would be negative / positive in the equation though, any tips?

How about (2Ω)(I2) - (18Ω)(I3) + (4Ω)(I1) = 0, for the one you said?
 
  • #6


Labelling the junctions T1 to T4 in the top row and B1 to B4 in the bottom row, the diagram shows two routes from T3 to B4. The voltage drop must be the same in both routes.
 
  • #7


So, you can say (4Ω)(I5) = (2Ω)(I4) = 12 V then ?

Would that make I4 = 6A and I5 = 3A?Not sure what to do with 2 voltage sources in regards to finding current through a resistor.. (ie how would I find the current through the 2Ω resistor ? )
 
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FAQ: Find Io in the network nodal analysis

How do you perform nodal analysis to find Io in a network?

Nodal analysis is a method used in circuit analysis to determine the current flowing through a particular node in a network. To find Io, or the current at a specific node, you would follow these steps:

  • Identify the node where Io is located.
  • Create a reference node and assign it a voltage of 0.
  • Write a KCL equation for the node in terms of the incoming and outgoing currents.
  • Solve the equation for Io.

What is the purpose of nodal analysis in circuit analysis?

The purpose of nodal analysis is to determine the current flow at a particular node in a network. This is important in circuit analysis as it allows us to understand how current is distributed throughout the circuit and how different components are affecting the overall current flow.

What are the key assumptions made in nodal analysis?

There are three key assumptions made in nodal analysis:

  • The voltage at the reference node is 0.
  • The voltage at each node is known.
  • The current flowing into and out of a node is equal.

These assumptions allow us to simplify the equations and solve for the unknown currents at each node.

What types of circuits can nodal analysis be used for?

Nodal analysis can be used for both DC and AC circuits, as well as linear and nonlinear circuits. It is a versatile method that can be applied to a wide range of circuit configurations.

Can nodal analysis be used for complex networks?

Yes, nodal analysis can be used for complex networks, but it may become more difficult to solve as the number of nodes and components increases. In these cases, it may be more efficient to use other circuit analysis methods such as mesh analysis or superposition. However, nodal analysis can still be a useful tool for understanding the current flow in a complex network.

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