Choke coil
A choke coil is simply an inductor with large value of self-inductance.
The choke coil consists of a large number of turns of thick copper wire bound closely over a laminated soft iron core. The inductive reactance offered by the coil is XL = ωL becomes large. Therefore, magnitude of a.c. is reduced.
In an ideal choke coil, ohmic resistance = 0. Therefore, no electrical energy/power is wasted. A phase angle of π/2 is introduced between current and voltage through an ideal inductor.
∴ Average power over a complete cycle is
P = EvIv cos Φ = EvIv cos 90°
However, in actual practice, a choke coil of inductance L is linked with a small resistance r. It may be treated as a series combination of L and r. [Fig. b]. Therefore, average power consumed over a complete cycle in the practical choke coil is
P = EvIv cos Φ
or P = EvIv \(\frac{r}{\sqrt{r^2+\omega^2+L^2}}\)
In practice, a low frequency choke is made of insulated copper wire wound over a soft iron core [laminated] called low frequency choke or audio frequency choke Fig. (c) and a high frequency choke has air as core material [Fig. (b)] to eliminated eddy current losses. High frequency chokes are also called radiofrequency chokes.
Air is used as core material because, the virtual value of a.c. is given by
Iv = \(\frac{E_v}{\omega L } = \frac{E_v}{2\pi vL}\)
So as v is very high. so L should not be large. hence air cored choke is used.
Importance of choke coil over ohmic reistance
In running an arc lamp on a continuous current of 10A, about 40V are required. So that the effective resistance of the arc lamp from Ohm's law, R = \(\frac{V}{I}\) = \(\frac{40}{10}\) = 4 ohm. To get a current of 10 A from 220 V mains, the resistance to be included in series with the circuit is \(\frac{220 - 40}{10}\) = 18 ohm. By so doing, there will be wastage of power
I2R = 102 x 18 = 1800 watt
and useful power available in the arc = 102 x 4 = 400 watt.
So that, out of the total power of 2200 watt
(= VI = 220 x 10 supplied by the source AC generator), 1800 watt are wasted. Thus the use of a pure resistance to reduce current in a circuit involves huge wastage of power.
In case of AC supply, there is an alternative more economical method in which an inductance called choke, is introduced in series with the arc instead of resistance. Let L be the inductance and R be the resistance of the choke, then
\(\frac{I_0}{\sqrt2}\) = \(\frac{\frac{E_0}{\sqrt2}}{\sqrt{\omega^2 L^2 + R^2}}\)
and cos Φ = \(\frac{R}{\sqrt{\omega^2 L^2 + R^2}}\)
In the above example \(\frac{I_0}{\sqrt2}\) = 10A,
or 10 = \(\frac{220}{\sqrt{\omega^2 L^2 + R^2}}\)
Squaring, we get
ω2L2 + 16 = 22 x 22 = 484
ω2L2 = 484 - 16 = 468
ωL = 21.63
Let v = 50 Hz
ωL = 2π x 50 L
= 100πL = 21.63
L = \(\frac{21.63}{100\pi}\) = 0.06887 H
Total Power = \(\frac{I_0}{\sqrt2} \times \frac{E_0}{\sqrt2}\) cosϕ
= 10 x 220 x \(\frac{R}{\sqrt{R^2+L^2\omega^2}}\)
= 10 x 220 x \(\frac{4}{22}\) = 400 W
∴ The chief advantage of choke is that there is no wastage of power. The only energy wastage is due to Hysteresis loss in iron core of the choke. Since the reactance of an inductance is proportional to frequency choke usually has a space.
