# [AC Signals] - Leading/Lagging ambiguity

Discussion in 'Homework Help' started by nDever, Mar 20, 2015.

1. ### nDever Thread Starter Active Member

Jan 13, 2011
154
4
Hey guys,

I have a general question about classifying a signal as leading or lagging another signal.

Consider the two currents,

$i_{1}=4cos(32t+145) A$
$i_{2}=5cos(32t-65) A$

We're interested in whether $i_{1}$ leads or lags $i_{2}$.

$i_{1}$ could lead $i_{2}$ because it's 210 degrees in front of $i_{2}$, but couldn't it also lag $i_{2}$ because it's 150 degrees behind?

2. ### WBahn Moderator

Mar 31, 2012
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4,788
The nearly-universal convention is that the lead/lag amount between two signals is never more than half a cycle. Thus the only ambiguous case is whether a signal that is 180° out of phase is 'leading' or 'lagging', but in that case it makes no difference.

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3. ### nDever Thread Starter Active Member

Jan 13, 2011
154
4
That makes sense. The above example was actually from my textbook, and it stated the correct answer as $i_{1}$ in the lead by 210 degrees, so, I'm guessing it doesn't go by the convention unfortunately.

4. ### WBahn Moderator

Mar 31, 2012
17,720
4,788
Where they are probably coming from is that I1 is leading a hypothetical cosine wave that has zero phase shift and I2 is lagging that same hypothetical wave. So then it makes intuitive sense that I1 is leading I2. But that is a false premise because there is no hypothetical cosine wave that is acting as a transitive reference for the other two.

We can add or subtract 360° of phase without changing the waveform, so we could write the first as having a phase of -215°. Similarly, we could write the second as having a phase of 295°. None of that affects the lead/lag relationship between them.

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