Understanding KVL and KCL for Circuit Analysis

In summary, the conversation discussed finding the voltage Vab in a circuit using KVL. The problem asked for Vab, but there was confusion about whether to include all resistances or just the potential difference between two points. After clarification, it was determined that Vab can be calculated by finding the potential difference between Va and Vb, and this can be done by using all resistances or just the voltage gains and drops in the loop.
  • #1
carlodelmundo
133
0

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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  • #2
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.
 

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  • #3
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)
 
  • #4
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:
 
  • #5
Thanks! this makes a lot of sense now!
 

Related to Understanding KVL and KCL for Circuit Analysis

What is KVL (Kirchhoff's Voltage Law) and how is it used in circuit analysis?

KVL states that the sum of voltages around a closed loop in a circuit is equal to zero. This means that the sum of voltage drops across all elements in the loop must equal the sum of voltage sources. It is used in circuit analysis to calculate unknown voltages or to verify the accuracy of a circuit's design.

What is KCL (Kirchhoff's Current Law) and how is it applied in circuit analysis?

KCL states that the sum of all currents entering and exiting a node in a circuit is equal to zero. This means that the total current flowing into a node must be equal to the total current flowing out of the node. KCL is applied in circuit analysis to solve for unknown currents or to check the accuracy of current measurements in a circuit.

What are the key assumptions made when using KVL and KCL in circuit analysis?

The key assumptions made when using KVL and KCL are that the circuit is in steady state (all voltages and currents are constant), there are no magnetic fields, and the circuit is free of any internal resistance. These assumptions allow for simplified calculations and accurate results.

Can KVL and KCL be applied to all types of circuits?

Yes, KVL and KCL can be applied to all types of circuits, including DC and AC circuits. However, they are most commonly used in linear circuits with passive elements (resistors, capacitors, and inductors).

What are some common mistakes when applying KVL and KCL in circuit analysis?

The most common mistakes when applying KVL and KCL are not taking into account the direction of current flow, not considering the polarity of voltage sources, and not properly labeling and identifying nodes and loops in a circuit. It is important to follow a systematic approach and double check all calculations to avoid these mistakes.

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