# Instantaneous current in stator of 3 phase IM

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I am studying induction motors and i have equation for instantaneous value of current flowing in each phases.(please check to image below).I can see that its it the form Im.cosωt
But isnt it supposed to be Im.sinωt ?because thats how we find all instantaneous parameters like voltage and power.we have homework regarding the same. Please explain it carefully considering im first year engineering student.

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anorlunda
Staff Emeritus
The only difference between sin and cos is the reference phase (what we call angle zero). So if you are talking about the "form", sin and cos are the same thing.

The only difference between sin and cos is the reference phase (what we call angle zero). So if you are talking about the "form", sin and cos are the same thing.
Please explain this to me in more detail if possible.sorry for inconvinience.

cnh1995
Homework Helper
Gold Member
I can see that its it the form Im.cosωt
But isnt it supposed to be Im.sinωt ?because thats how we find all instantaneous parameters like voltage and power.
As anorlunda said, they are just shifted by 90 degrees. It doesn't make any difference if you use cos instead of sine. All the other equations will change accordingly.
For example, if the current through an inductor is Imsin(ωt), the voltage across the inductor will be Ldi/dt=ωLImcos(ωt). Here the current is lagging the voltage by 90° (which is expected.)
If the current were Imcos(ωt), the voltage across the inductor would be -ωLImsin(ωt). The current still lags the voltage by 90° .

Work out some examples on your own and you'd realize the importance of sine wave in ac electricity. The derivatives and integrals of a sine wave are also sine waves with a phase-shift (cos is sine with 90 degrees phase shift). This important property simplifies the math required to analyse ac circuits. (Although it "simplifies" the math, it's called "complex" analysis ).

Last edited:
• rishi kesh