Understanding KVL and KCL for Circuit Analysis

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Discussion Overview

The discussion revolves around the application of Kirchhoff's Voltage Law (KVL) and the calculation of the voltage difference (Vab) between two points in a circuit. Participants explore the methodology for circuit analysis, particularly in relation to resistances and voltage sources, without seeking a numerical answer.

Discussion Character

  • Homework-related
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions the methodology for finding Vab, particularly regarding the potential across terminals connected to another voltage source and whether all resistors can be lumped into one.
  • Another participant clarifies that Vab is defined as the voltage difference between points Va and Vb, emphasizing that not all resistances in the loop contribute to Vab.
  • A participant seeks confirmation on whether it is correct to calculate Vab as the potential difference between Va and Vb, suggesting a specific calculation method involving certain resistors and a voltage source.
  • A later reply supports the calculated value of 12 V, indicating that the same result can be obtained by analyzing the circuit from either direction, reinforcing the principles of KVL.

Areas of Agreement / Disagreement

Participants express some agreement on the application of KVL and the calculation of Vab, but there remains uncertainty regarding the inclusion of all resistances in the analysis and how to approach the calculation methodologically.

Contextual Notes

There are limitations in the discussion regarding the assumptions made about the circuit configuration and the treatment of the terminals. The dependency on specific definitions of voltage and resistance is also noted but not resolved.

Who May Find This Useful

This discussion may be useful for students or individuals learning about circuit analysis, particularly those interested in understanding KVL and the implications of voltage differences in electrical circuits.

carlodelmundo
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Homework Statement



Basically, find Vab

[PLAIN]http://carlodelmundo.com/hw/circuit.png

Is this correct -- note: please tell me that my methodology is sound; DO NOT GIVE ME A NUMERICAL ANSWER.

The problem asks for VAB. What's weird to me is that there is a potential across two terminals? (The weird part is: the terminals are connected to another voltage source!)

I used KVL... and I'm fairly accurate that my calculation is correct. However, I am confused with finding the actual VAB. Can I simply apply Ohm's law, and "lump" all of the resistors into one resistor (composition?) Would VAB be equivalent to the sum of all the voltages (taking polarities into account)?
 
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Your current calculations look good, but I think Vab is wrong. Keep in mind Vab = Va - Vb i.e. the voltage between two different points. As you have done in the first part of your current equations, all the voltage 'gains' must equal all of the voltage 'drops' (Kirchoffs Voltage Law) in the loop, but Vab doesn't include all of the resistances in the loop.

The terminals can be disregarded also, since they merely represent a connection point, but with or without them the circuit is the same.

Check out this redrawn circuit.
 

Attachments

  • Find Vab.JPG
    Find Vab.JPG
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I see. Based on your chart, I may have gained some insight. Let me clarify-- so we're not supposed to use all of the resistances in the circuit?

Is it correct to assume that to calculate Vab, I may simply just find the potential difference between Va and Vb?

e.g.: according your chart, Vab = vr3 + V4v = 3(i) + 4 = 3(16/6) + 4 = 12V? If this is true, can I solve for the reverse and negate the answer? (the other resistors and other voltage source)
 
hi carlodelmundo! :wink:

Zryn :smile: is offline, so I'll confirm that 12 V is correct …

you calculated it via the 4 V, but if you'd gone the other way, that will give the same result …

try it and see (you've probably already done so)! :smile:

the whole point of KVL is that the potential differences (for want of a better phrase) all add to zero around a loop …

when you're asked for the potential between two points, it's exactly the same as the sum of the voltages you'd use in KVL itself :wink:
 
Thanks! this makes a lot of sense now!
 

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