Electrical circuits lecture notes b. Tech

Phase Difference Equation 
Where:
A
m
- is the amplitude of the waveform.
ωt - is the angular frequency of the waveform in radian/sec.
Φ (phi) - is the phase angle in degrees or radians that the waveform has
shifted either left or right from the reference point 
Phase Relationship of a Sinusoidal Waveform: 

---

Two Sinusoidal Waveforms 
–
 
“in
-
phase”
 
Phase Difference of a Sinusoidal Waveform: 
The voltage waveform above starts at zero along the horizontal reference axis, but at that 
same instant of time the current waveform is still negative in value and does not cross this 
reference axis until 30
o
later. Then there exists a Phase difference between the two 
waveforms as the current cross the horizontal reference axis reaching its maximum peak and 
zero values after the voltage waveform. 
As the two waveforms are no longer “in-phase”, they must therefore be “out-of-phase” by an 
amount determined by phi, Φ and in our example this is 30
o
. So we can say that the two 
waveforms are now 30
o
out-of phase. The current waveform can also be said to be “lagging” 
behind the voltage waveform by the phase angle, Φ. Then in our example above the two 
waveforms have a Lagging Phase Difference so the expression for both the voltage and 
current above will be given as. 
where, i lags v by angle Φ 

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Likewise, if the current, i has a positive value and crosses the reference axis reaching its 
maximum peak and zero values at some time before the voltage, v then the current waveform 
will be “leading” the voltage by some phase angle. Then the two waveforms are said to have 
a Leading Phase Difference and the expression for both the voltage and the current will be. 
where, i leads v by angle Φ