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Alternating Quantity

Alternating Quantity:

Any quantity that changes its magnitude with respect to time is called alternating quantity.In electrical engineering it is known as alternating voltage or current and is defined as below 
"If the polarity of the voltage changes with time, it is known as alternating voltage and the current caused by such a voltage is called an alternating current."
Consider the following figure.
The above figure explains that voltage or current increases with time to a certain specific value which is called peak or maximum value and after that it decreases even to reach starting position i.e 0 in our case. As time goes on the quantity reverses its direction and increases to again that maximum value which it reached out in the positive half cycle but with negative sign. After that it again follow decreasing and finally reaches the starting position again.This is the way that alternating quantity repeat itself again and again.
Mathematically,
    v= Vm Sinϑ as ϑ= ωt so v=Vm Sinωt
  where;
  v= instantaneous voltage i.e. value of voltage at any instant t.
  Vm=maximum or peak voltage 
  ω= angular velocity of coil
  t= time
  Similarly,

  i= Im  Sinωt
      One thing is important to keep in mind that alternating current has the same frequency as that of applied alternating voltage.

Relationship between T & f:

Time period and frequency are reciprocal to each other.
T= 1/f or f=1/T

Relationship between Angular Velocity and Frequency: 

         Suppose a coil is rotating with an angular velocity of ω rad/sec in a uniform magnetic field. one revolution will be completed in a certain time period T and is called frequency.As we know one revolution =2Π. So by basic relation        Velocity = displacement/time. Thus,
       ω= 2Π/T
       ω= 2Πf

Relationship between Frequency and Speed:

       Consider a coil rotating at speed of N r.p.m in the field of P poles.As the coil moves from north to south and then back to north one revolution is completed.So in one revolution P/2 cycles will be generated. As we know
         frequency,f=No.of cycles /sec
                            =(No.of cycles/ revolution)*(No.of revolution/sec)
          =(P/2)*(N/60)  
f=NP/120
                     where P=No. of poles

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