# [AC Signals] - Leading/Lagging ambiguity

#### nDever

Joined Jan 13, 2011
153
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?

#### WBahn

Joined Mar 31, 2012
30,297
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.

#### nDever

Joined Jan 13, 2011
153
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.

#### WBahn

Joined Mar 31, 2012
30,297
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.