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Physics · Ch 13 — AC Circuits

Choke Coil

13.10

Choke Coil

If the goal is simply to REDUCE the amount of AC current flowing through some part of a circuit (for example, to safely limit the current through a fluorescent tube or a fan), an obvious approach would be to insert a plain resistor in series. But this wastes a substantial amount of electrical energy as heat through ordinary Joule (I2RI^2R) heating -- energy that is simply lost, not put to any useful purpose. A choke coil offers a far more efficient alternative: it reduces the current just as effectively, but with only a small fraction of the energy loss.

A choke coil is, physically, an inductor -- constructed from thick, insulated copper wire wound in a large number of closely-spaced turns around a soft-iron core that is LAMINATED (built up from many thin, mutually insulated sheets rather than a single solid block of iron). Its large inductance L gives it a correspondingly large inductive reactance XL=ωLX_L=\omega L, which reduces the AC current through the circuit exactly as intended. Crucially, though, the AVERAGE power it dissipates, Pav=erms irmscos⁡ϕP_{av}=e_{rms}\,i_{rms}\cos\phi with power factor cos⁡ϕ=RR2+XL2\cos\phi=\dfrac{R}{\sqrt{R^2+X_L^2}}, stays very small -- because a well-made choke coil is designed to have a LARGE L (and hence large XLX_L) together with a very SMALL ohmic resistance R (achieved using thick copper winding, which has low resistance), the ratio cos⁡ϕ\cos\phi works out to be very close to zero, so almost no power is genuinely dissipated even though the coil is effectively reducing the current. …

Misc Note.13.2Why a choke coil wastes so little power, and the role of the laminated core

Worked out. A choke coil offers a large inductive reactance XL=ωLX_L=\omega L to the flow of AC current, reducing the current in a series circuit exactly as a resistor would, but with far less energy loss. This is because the power dissipated is P=ermsirmscos⁡ϕP=e_{rms}i_{rms}\cos\phi with power factor cos⁡ϕ=R/R2+XL2\cos\phi=R/\sqrt{R^2+X_L^2}: since L (and hence XLX_L) is deliberately made very large while the coil's own ohmic resistance R is kept as small as possible (thick copper winding), cos⁡ϕ\cos\phi becomes nearly zero, so almost no power is dissipated despite the current being substantially reduced. The one remaining loss mechanism is hysteresis loss in the iron core (energy lost repeatedly magnetising and demagnetising it each cycle), which is minimised by using a LAMINATED (thin, insulated sheets rather than one solid block) soft-iron core, since lamination breaks up and greatly reduces the induced eddy currents that would o …