Nodal analysis trying to find Voc

In summary, the conversation was about finding the voltage Voc using nodal equations. The person was confused about why the 60 ohm and 10 ohm resistors were combined in the VB nodal equation, but not the 25 ohm and 10 ohm resistors in the VA nodal equation. The expert explained that it was because the terminal b was open and no current could flow through it. They also suggested adding a node at b to determine the voltage Voc.
  • #1
jdawg
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Homework Statement


Find Voc

Homework Equations

The Attempt at a Solution


This is what I have:

(VA-9)/5 +VA/5 + 1.8 = 0
VA=0

-1.8 + VB/(60+10) +(VB-9)/20
VB=35

What I'm confused about is why you combine the 60 ohm and 10 ohm resistors for the VB nodal equation, but not the 25 ohm and 10 ohm resistor for the VA nodal equation. Is it because the grounding symbol is directly below the 25 ohm resistor? Thanks!
 

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  • #2
By adding the 60 and 10 ohm resistors together you've treated them as an isolated branch, ignoring the "tap" that is the terminal "b". This is okay as far as it goes because terminal b is open and no current can flow into or out of it. So it's not really a matter of the ground symbol being directly below VA that prevents you from combining the 25 and 10 ohm resistors, but rather that it is a node that happens to be there. It just happens to be the reference node with a defined potential (0 V).

Note that what you have found is the potential at VB with respect to the reference (ground) node, not the voltage Voc.

To remedy this you could add a node at b, maybe call it VC. Then redo your node equations accordingly and solve for Voc = VB - VC. Alternatively, knowing the potential across the branch you can determine the current in the branch and hence determine the potential drop across the 60 ohm resistor.
 
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  • #3
Thanks, great explanation!
 

1. What is nodal analysis?

Nodal analysis is a method used to analyze electrical circuits in order to determine the voltage at each node or connection point in the circuit. It is based on the principle of conservation of energy, which states that the sum of voltages around a closed loop in a circuit must equal zero.

2. How does nodal analysis work?

Nodal analysis involves writing equations for each node in the circuit, using Kirchhoff's Current Law (KCL) to relate the currents entering and leaving the node, and Ohm's Law to relate the voltage across each component to its current. These equations can then be solved simultaneously to find the voltage at each node.

3. What is the purpose of using nodal analysis to find Voc?

The purpose of using nodal analysis to find Voc (open circuit voltage) is to determine the maximum possible voltage that can be obtained from a circuit. This is useful in designing and analyzing circuits to ensure that they are capable of providing the desired voltage output.

4. What are the steps involved in performing nodal analysis to find Voc?

The steps involved in performing nodal analysis to find Voc are as follows:

  • Identify the nodes in the circuit and label them.
  • Write equations for each node using KCL and Ohm's Law.
  • Solve the equations simultaneously to find the voltage at each node.
  • Identify the node with the highest voltage, which is the open circuit voltage (Voc).

5. Are there any limitations to nodal analysis when trying to find Voc?

Yes, there are some limitations to nodal analysis when trying to find Voc. Nodal analysis assumes that the circuit is linear, meaning that the relationship between current and voltage is constant. This may not always be the case in practical circuits, where components may exhibit non-linear behavior. Additionally, nodal analysis can become complex and time-consuming for circuits with a large number of nodes.

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