# current leading or lagging the voltage

Discussion in 'Mathematics and Physics' started by PG1995, Jan 16, 2012.

1. ### PG1995Active Member

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Hi

I'm really confused when I need to know if the current is leading or lagging the voltage. Please have a look on the attachment. You can see part of my confusion there. Please help me. Thanks.

Regards
PG

2. ### RatchitWell-Known Member

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PG,

The voltage completes 340° by the time the current has completed 370°. Therefore, the current leads the voltage by 30°.

Ratch

3. ### MrAlWell-Known MemberMost Helpful Member

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Hi PG,

Leading or lagging is relative in many cases but the usual idea is to normalize to within a limit of plus or minus 180 degrees. Thus we would not say we have a phase shift of 190 degrees, we would say we have a phase shift of -170 degrees.

There are exceptions though, like when we talk about the three phase power line we usually say the phases are at 0 degrees, 120 degrees, and 240 degrees.

When we talk about electronic components though, there is a preference for labeling by how the component actually works when presented with a current or voltage such as a step or ramp (not just a sine wave). It becomes immediately apparent that the phase of the voltage lags the current or vice versa. For example with a capacitor, it is not considered possible to change the voltage of the device instantaneously so therefore the current has to come first which means the voltage has to lag. For the inductor it's just the opposite where we can not change the current instantaneously so the voltage has to come first and the current lags. To look at it another way, we can apply a large value of voltage (which means the voltage is there already) but we have to wait for the current to rise, so obviously the current lags.

The numerical value comes from the inverse tangent after considering the proper quadrant.

Long time ago before there were refrigerators people had "ice boxes". They had to wait for the guy who brings the ice to come to their house so they could replenish their ice and continue to keep their perishables cold. Somebody coined the phrase, "Eli the Ice man", which is kind of funny, but in capitals it reads:
"ELI the ICE man", in which ELI is short for voltage E leads current I for an inductor L (the E is before the I in ELI) and ICE is short for current I leads voltage E in a capacitor C.
If he didnt come that day i guess their food went bad and the electricians couldnt figure out the proper phase for their circuits that day either

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5. ### user_88Member

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See figure 5 of this web page concerning phasors... seems to be somewhat useful ...
http://www.kwantlen.ca/science/physics/faculty/mcoombes/P2421_Notes/Phasors/Phasors.html
... that is for the simple case of strictly pure components.

6. ### PG1995Active Member

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Thank you, Ratch, MrAl, User88.

@MrAl: It was good to know about Eli the Ice Man!

Best wishes
PG

7. ### PG1995Active Member

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As I was saying at t=0 the voltage has completed 340 deg of the cycle and the current has completed only 10 deg of its cycle. If you say that current has completed 360+10=370 degree of the cycle, then the same could be said of the voltage that it has completed 340+360=700 deg of its cycle. So, to me, the situation is still a bit confusing because voltage has completed more degrees. Please help me with it. Thank you.

Regards
PG

8. ### MrAlWell-Known MemberMost Helpful Member

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Hi again PG,

I dont think you got the whole point of my previous post. That could be because you didnt look at the circuits with anything but sine waves.

If i show you two sine waves (of the same frequency) that are 60 degrees apart, does sine #1 lead sine #2 by 60 degrees, or does sine #1 lag sine #2 by 300 degrees? Note that i did not show you any circuit, i just gave you a drawing (like a scope shot) of the two sine waves.
If you can answer that question definitively without seeing the circuit then you must have discovered the key to a fourth dimension that keeps track of phase angles
Seriously though, there's no way to tell so we would use the "less than 180 degrees" rule that says that we usually want to describe them using a window of 180 degrees. Also interesting is that it may not make any difference in some cases how we label the sine waves. But when there is a circuit to go with it, we can investigate more deeply to find out what is the best way to describe the phase behavior.

9. ### PG1995Active Member

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Thank you, MrAl.

Sine wave #1 (the green one) is leading. At t=0, wave #1 has only completed 0 degree of its cycle while wave #2 has completed 300 degrees of its cycle. I hope I have it correct. I'm using phasors these days so I'm more interested to know which wave is leading or lagging at t=0. And I'm more happy in only three dimensions rather four, five, or eleven dimensions for that matter!

Now please help me. I think that "180 degree window" could help me if I understand it.

Best wishes
PG

10. ### RatchitWell-Known Member

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PG,

Nope, the current crosses the 0° or 360° line first, so it leads. Whereever the voltage is, the current is 30° ahead of it.

Ratch

11. ### PG1995Active Member

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Okay. Which one is ahead of others, and which one is lagging the other two?

Wave #1 = cos(100*pi*t + 10)
Wave #2 = cos(100*pi*t + 160)
Wave #3 = cos(100*pi*t + 220)

Last edited: Jan 17, 2012
12. ### RatchitWell-Known Member

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PG,

Tell me which is the reference wave, and I will tell you its relationship to the other waves.

Ratch

13. ### PG1995Active Member

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Do we need a reference wave? How about cos(t)?

14. ### RatchitWell-Known Member

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PG,

Certainly, just as you do for a voltage measurement.

You cannot compare the phase of those three waves with cos(t), because its frequency or period is different. But remember, the phase difference between voltage and current of components in a series or parallel circuit is never more than 180°.

Ratch

15. ### PG1995Active Member

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Okay.

Reference Wave = cos(100*pi*t)

Regards
PG

16. ### RatchitWell-Known Member

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PG,

Wave #1 and #2 both lead cos(100*pi*t). You won't find wave #3 in a series or parallel circuit, because the inductive and capacitive phase currents and voltages cannot be more than 180° apart.

Ratch

17. ### PG1995Active Member

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Thank you.

But Wave #3 can also be written as: cos(100*pi*t - 140) . Right? So, is it leading or lagging? Please tell me. Thank you.

Regards
PG

18. ### RatchitWell-Known Member

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PG,

You will never encounter a current/voltage wave with a phase difference greater than +90° or -90° in a series or parallel circuit, so cos(100*pi*t - 140) does not make sense. The range of the phase difference is 180°. If a circuit is all inductance, the current phase will be -90° with reference to the voltage, and if it is all capacitance, the current phase will be +90° with respect to the voltage.

Ratch

19. ### PG1995Active Member

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Thank you, Ratch.

I'm not trying to contradict you in any way; I'm just trying to teach myself. In the attachment in my first post, i(t)=4*cos(100*pi*t + 10) and v(t)=120*cos(100*pi*t - 20). So, can't I write, v(t)=120*cos(100*pi*t + 340)? Please let me know. Thanks.

Best wishes
PG

20. ### RatchitWell-Known Member

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PG,

Yes, and while you are at it, add another 360° to make it v(t)=120*cos(100*pi*t + 700°). v(t) will look the same either way.

Ratch

21. ### MrAlWell-Known MemberMost Helpful Member

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Hi PG,

Well the blue wave lags the green wave by 60 degrees, or if you call the blue crossing zero then the green lags the blue by 300 degrees.

I'll try to get back later with some circuits to illustrate much better.