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# AC BASIC AND NETWORKS

How to find out of Power in Iron-Cored choking Coil ?

The power drawn by a choking Coil is used up to supply the iron losses in the core in addition to that used up for heating the coil.

Power Consumed by a choking Coil.
P = Iron losses ( Hysteresis and Eddy Current loss ), Pi + power loss in ohmic resistance i.e., I×I R ( R being the DC resistance or true resistance of the coil)

OR  P = Pi  +  I^2×R

P            Pi
OR   ------       ------. + R
I^2           I^2
P
--------  is called the effective resistive of
I^2
The choking Coil and it is equal to the True resistance plus resistance
Pi
representing Iron loss ----------
I^2

P                Pi
So, R eff =  -------  =  R + ------
I^2             I^2

R-C Series Circuit.

Consider an AC Circuit consisting or resistance of R ohms and capacitance of C farad's connected in series as shown in Fig. a)
Let's the supply frequency be of f Hz and current flowing through the Circuit be of I amperes ( rms Value ).
The applied voltage, being equal to phasor sum of Vr and Vc, is given in megnitude by

Only for Understanding
I          R                      C
l->---^^^^^^^----•------||-----l
l<-----VR------>|------Vc----l
l--------------•V•-------------l
a) Circuit Diagram

VR = I × R
l-------l-----------l------------>
l  Ï€/2  l        Î¦       l
l------\                 l
l             \              l
l                 \          l
l                     \      l
l                         \  l
l-------------------l  V = I × Z
l  Vc = I × Xc
l
V
b) Phasor Diagram

V = √ ( VR )^2 + (Vc)^2  = √ ( I×R )^2
+ ( I × Xc )^2
=  I √ R^2 + Xc^2 = IZ
Where Z^2 = R^2 + Xc^2

The applied voltage lags behind the current by an angle Î¦
Vc       I×Xc     Xc         1
Where tan Î¦ = ----- = ----- = ----- = -----
VR       I×R       R       2Ï€fRC

1
Or Î¦ = tan^-1 --------
R2Ï€fC
R
Power factor, Cos Î¦ = -----
Z
If instantaneous Voltage is Represented by  v = V max sin 2Ï€ft
Then instantaneous Current will be expressed as
i = I max sin ( 2Ï€ft + Î¦ )
And power Consumed by the Circuit is given by  P = V × I COS Î¦