Always remember "ELI" the "ICE"man
E=Voltage
L=inductance
I=Current
I=Current
C=Capacitance
E=Voltage
ELI means voltage leads current in an inductive circuit.
ICE means Current leads Voltage in a capacitive circuit.
When a pure inductance is represented in complex form the imaginary component will be positive. When a pure capacitance is represented in complex form the imaginary component will be negative.
This falls out of the fundamental relationship v=L (di/dt) and i = 1/C (dv/dt) and the fact that the derivative of a sin function is the cos function (the sin is out of phase by 90deg relative to the cos).
So, to answer the question, because a motor is a pure inductive load (well overwhelming so) the voltage must lead the current. Or conversely, the current must lag the voltage…
And at this moment, I feel a need to wax a little bit philosophical about the question.
The rotor current is a function of space and time, something like I = I0*cos(w*t – p/2*theta)
The definition of the angle of the rotor requires some assumptions, conventions imagination, and maybe some handwaving. (Just kidding, no handwaving). But it is not at first obvious what we mean by angle between the rotor and stator current given the continuosly varying nature of the rotor current in space and time.
The angle between rotor and stator mmf has more physical significance. I assume that the angle between the rotor and stator currents follows is the same as the angles between rotor and stator mmf's. When we talk about angle between rotor and stator currents under this assumption, it is equivalent to assuming that we have an imaginary 3-phase rotor that creates the same mmf as the actual rotor.... then we can track the phase angle of that imaginary rotor's current against our stator current.... that's the current angle we're talking about.
And the phasor diagram shows us that the angle is between 90 and 180 degrees as in the attachment above. It is the same answer given in several references.
Now you might ask why don't we just assign a different phase of the rotor and flip the whole rotor by 120 degrees to give an angle between –30 and 60 degrees (that's something I asked myself). The answer is that we have a balanced rotor and balanced stator and so we should be able to present them on per-phase single-phase equivalent circuit. When we do that as in the attachment, we get the 90 to 180 degrees. So while the assingment of phases may on the surface appear arbitrary, the assumptions and conventions that go into that assignment of phases are the same ones that go into our per-phase equivalent circuit.
At least that's the way I look at it. But I'm always interested to learn if someone has a different slant on it.
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And it is probably important to note, there is nowhere in my discussion that I concluded rotor current lags stator current by exactly 90 degrees (that lag angle is always more than 90 degrees by my analysis).
Where did the 90 degree lag idea come from?
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