KVL Confusion: Voltages & Arrows Explained

In summary, the arrows and polarity in the circuit image is confusing. Physicist3 suggests that it does not matter which one you use, as long as you are consistent.
  • #1
Physicist3
104
0
http://www.flickr.com/photos/53512951@N06/8229416013/in/photostream/

With regards to the circuit in the image linked above, I have been told to start in the bottom left hand corner and then work clockwise around the circuit, adding up all the voltages to see if they follow the KVL principle. The thing is, the arrows and polarity is confusing me a bit. Should it be -Vs + V1 + V2 = 0, or Vs - V1 - V2 = 0? Could someone explain which one is correct and what the arrows represent please? Thanks :)
 
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  • #2
The Arrow show that voltage is nominally positive at Node 'b' relative to Node 'a'.

attachment.php?attachmentid=53458&stc=1&d=1354213175.png


Hence


Vba = (Vb - Va)


and

Vab = (Va - Vb)

Therefore

Vba = -Vab



And this two equation are correct and the result will be the same

-Vs + V1 + V2 = 0 Is the same think Vs - V1 - V2 = 0

-Vs + V1 + V2 = Vs - V1 - V2 = 0.

Or

Vs = V1 + V2

And another example
attachment.php?attachmentid=53457&stc=1&d=1354212712.png
 

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  • #3
Vs - V1 - V2 = 0 ⇔ Vs = V1 + V2 ⇔ 0 = -Vs + V1 + V2

Simple algebra :)
 
  • #4
Physicist3,

Could someone explain which one is correct and what the arrows represent please?

It does not matter how you designate voltage polarities or current directions. I personally like arrows for current direction and signs to designate the polarity of the voltages. It also does not matter whether you go CW or CCW around the circuit for KVL. As long as you are consistent with everything, the results should be the same.

Ratch
 
  • #5
Forgot to add, in the circuit i linked, the current has been said to flow clockwise around the circuit, i.e. following the direction of the arrow across the cell. Because of this current direction, am i right in saying that KVL will look like:

Vs + -V1 + -V2 = 0

because if you start in the bottom left corner, when you pass through the battery going clockwise, you go from -ve to +ve therefore moving from a lower to higher potential, meaning Vs will be positive, where as the resistors have an opposite polarity and you move from +ve to -ve, therefore moving from a higher to a lower potential, making v1 and v2 negative?

is this correct?

Thanks for your help :)
 
  • #6
When first starting out it's more important that you be consistent in your method than anything else.

I was taught to place signs for voltages and arrows for current, as somebody else said above.
Then imagine yourself inside the circuit walking around the loop. Write down each voltage with the sign you encounter as you enter that circuit element.

So in your diagram, i would add signs as follows:
On battery, minus at bottom and plus at top 'cause that's how it's drawn (memory aid - the long line can be broken in half to make a + sign, the short one is already a - sign).
On upper resistor, plus on left ('cause it's to + of battery), and minus on right of course
On right-hand resistor minus on bottom ('cause it's to - of battery, ) and plus on top, of course.

now starting on lower left and going CW, i'd write:
-VS +V1 +V2 = 0

observe if you go CCW instead you get
-V2 -V1 +VS = 0
which when multiplied on both sides by -1 is the same equation, as you know it should be.

You can show yourself that even if you start someplace else in the loop you'll get the same equation.

That's a simple technique that'll keep you out of trouble and is easily remembered.

old jim
 
  • #7
jim hardy said:
When first starting out it's more important that you be consistent in your method than anything else.

I was taught to place signs for voltages and arrows for current, as somebody else said above.
Then imagine yourself inside the circuit walking around the loop. Write down each voltage with the sign you encounter as you enter that circuit element.

So in your diagram, i would add signs as follows:
On battery, minus at bottom and plus at top 'cause that's how it's drawn (memory aid - the long line can be broken in half to make a + sign, the short one is already a - sign).
On upper resistor, plus on left ('cause it's to + of battery), and minus on right of course
On right-hand resistor minus on bottom ('cause it's to - of battery, ) and plus on top, of course.

now starting on lower left and going CW, i'd write:
-VS +V1 +V2 = 0

observe if you go CCW instead you get
-V2 -V1 +VS = 0
which when multiplied on both sides by -1 is the same equation, as you know it should be.

You can show yourself that even if you start someplace else in the loop you'll get the same equation.

That's a simple technique that'll keep you out of trouble and is easily remembered.

old jim

Thanks. Thats really helpful. From what youve written I can sort of assume that you use the sign you get to first. E.g. you get to the negative of the supply first, hence -VS
 
  • #8
Yes, write the sign that's on the end you entered,, or as you said , the one you encounter first.

I see that today they use more formal language in teaching than when i studied. Perhaps that's good, for after all our thought processes are tied to the way we speak.

Practice your KVL it's a tool you'll use your whole life.
For now, as you gain confidence in KVL you'll soon see the validity of Jony's arrows and other related concepts. It's more important today that you come to believe in Kirchoff and a simple method is best for that..

old jim
 
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1. What is KVL (Kirchhoff's Voltage Law)?

KVL, or Kirchhoff's Voltage Law, states that the sum of all voltages around a closed loop in an electrical circuit must equal zero. This means that the total voltage gained in a circuit must be equal to the total voltage dropped.

2. Why is it important to understand KVL?

KVL is important because it helps to ensure that the circuit is properly designed and functioning correctly. It is also useful for troubleshooting and analyzing complex circuits.

3. What are voltage arrows and how are they related to KVL?

Voltage arrows represent the direction and magnitude of voltage in a circuit. They are related to KVL because they help to visualize the voltages and ensure that they are in balance according to KVL.

4. What is the difference between series and parallel circuits in terms of KVL?

In a series circuit, the voltage arrows must add up to zero because there is only one path for the current to flow. In a parallel circuit, the voltage arrows must add up to the same value because the total voltage drop across each branch must be equal to the total voltage gain.

5. How can KVL be applied in real-world situations?

KVL can be applied in various real-world situations, such as designing electrical circuits, analyzing power distribution systems, or troubleshooting electrical problems. It is a fundamental principle in electrical engineering and is used extensively in the design and analysis of circuits and systems.

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