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Power and power factor
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Power and Power Factor.
The power is defined as the rate at which work is being done in the circuit.
In dc circuits power is given by P = Vi. But in ac circuits, since there is some phase angle between voltage and current, therefore power is defined as the product of voltage and that component of the current which is in phase with the voltage.
Thus p= V I cos Æ ; where V and i are r.m.s. value of voltage and current.
(1) Types of power
There are three terms used for power in an ac circuit
(i) Instantaneous power : Suppose in a circuit V= V0 sin wt and i = i0 sin(wt + Æ ) then Pinsstantance = Vi = V0 i0 sin (wt + Æ
(ii) Average power (True power) : The average of instantaneous power in an ac circuit over a full cycle is called average power. It's unit is watt i.e.
Pav = `Pinst Þ Pav = Vrms irms cosÆ = (V0 /Ö2) .(i0/Ö2) cosÆ = 1/2 V0 i0 cos Æ = i2rms R = (V2rmsR/Z2)
(iii) Apparent or virtual power : The product of apparent voltage and apparent current in an electric circuit is called apparent power. This is always positive
Papp = Vrms irms = (V0i0/2)
(2) Power factor : It may be defined as
(i) Cosine of the angle of lag or lead
(ii) The ratio(R/Z) = (Resistance/Impedance)
(iii) The ratio (True Power/ Apparent Power ) = (W/VA) = (kW/kVA) = cos Æ
Note : Power factor is a dimensionless quantity and it's value lies between 0 and 1.
For a pure resistive circuit R = Z Þ p.f. = cosÆ = 1
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