KCL to Find Voltage Between a and b

In summary, the conversation discusses finding the voltage between nodes A and B using KVL and KCL. It is noted that only two essential nodes, V and VOC, are present in the circuit and that the node at the top of the 20 V supply is already "solved" due to its fixed potential. The use of KCL equations to sum the currents at a given node is also mentioned. The conversation concludes with a question about why the node at the top of the 20 V supply is considered "solved", to which the response is that the potential at that node is already known and can be used to determine potential differences and currents in the rest of the circuit.
  • #1
Gbox
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Homework Statement


Find the voltage between a and b
BrEokIV.jpg

2. Homework Equations

KVL, KCL

The Attempt at a Solution


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I did not understand how they have reach the result we just two equations, and how did they use KCL to get those equations
 
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  • #2
There are only two essential nodes in the circuit, and they are labeled v and voc. The node at the top of the 20 V supply is not an essential node since its potential with respect to the reference node is fixed by that voltage source. Effectively that node's potential is already "solved".

Since there are only two essential nodes, only two node equations are required in order to completely analyze the circuit.

The KCL equations that were written are node equations. They sum the currents at a given node. Look at them term by term and you should recognize the currents for each branch leading into a given node.
 
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  • #3
Why is the node on top on the 20V is "solved"? There are different currents coming out of it?
 
  • #4
Gbox said:
Why is the node on top on the 20V is "solved"? There are different currents coming out of it?
Nodal analysis determines the potentials at the nodes with respect to the reference node. The potential at that node is already known: 20 V.

Given the node potentials the potential difference across every branch in the circuit can be determined, hence the currents can be determined, too, by Ohm/s law.
 

Related to KCL to Find Voltage Between a and b

1. What is KCL?

KCL stands for Kirchhoff's Current Law, which is a fundamental law in circuit analysis that states that the sum of currents entering a node (or junction) in a circuit must be equal to the sum of currents leaving that node.

2. How is KCL used to find voltage between two points in a circuit?

KCL can be used to find the voltage between two points in a circuit by first identifying the node or junction where the voltage is to be found. Then, the currents entering and leaving that node are calculated. Finally, the voltage can be determined using Ohm's Law (V=IR) by multiplying the current by the resistance of the component between the two points.

3. Can KCL be applied to both series and parallel circuits?

Yes, KCL can be applied to both series and parallel circuits. In series circuits, the same current flows through all components, so KCL can be used to find the voltage between two points. In parallel circuits, the current splits and KCL can be used to find the total current entering and leaving a node, which can then be used to find the voltage between two points.

4. Is KCL always accurate in finding voltage between two points?

KCL is a fundamental law and is always accurate in finding the voltage between two points in a circuit. However, it is important to note that KCL assumes ideal conditions and may not be as accurate in real-world scenarios due to factors such as resistance, capacitance, and inductance.

5. Are there any limitations to using KCL to find voltage between two points?

One limitation of using KCL to find voltage between two points is that it can only be used for DC circuits. In AC circuits, the current is constantly changing and KCL may not be as accurate. Additionally, in complex circuits with multiple nodes, KCL can become more complicated and time-consuming to apply.

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