Choke Coil
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Direct answer
A choke coil is an inductor placed in an AC circuit to limit current through its reactance XL = ωL = 2πfL while wasting almost no power, because a pure inductor draws current a quarter-cycle out of phase with the voltage and its average power consumption is zero. A rheostat could restrict the same current, but it burns P = I²R continuously; the choke achieves current control with only the small I²r loss of its own winding resistance. A real choke therefore has impedance Z = √(r² + ω²L²) and a power factor close to (but not exactly) zero. The device is why fluorescent tube circuits and rectifier filters control current without heat — and why the same coil is useless for DC, across which it is merely its small resistance.
What you must remember
- Reactance, not resistance: XL = ωL = 2πfL ohms; at 50 Hz, a 1 H choke presents 314 Ω of reactance while its winding may be only a few ohms.
- Average power in a pure inductor: zero — current lags voltage by 90 degrees, and cos 90° = 0 kills P = VI cos φ; energy oscillates between source and magnetic field each quarter-cycle.
- Real choke accounting: with winding resistance r, P = I²r only; impedance Z = √(r² + ω²L²); power factor cos φ = r/Z, small when ωL >> r.
- The rheostat comparison: to limit 0.5 A at 200 V a resistor needs 400 Ω and dissipates 100 W; a choke of reactance 400 Ω (L ≈ 1.3 H at 50 Hz) dissipates nearly nothing for the same current.
- DC behaviour: at f = 0 the reactance vanishes and the choke passes DC almost unimpeded — current limiting is an AC-only service, which is why a choke in a DC line does nothing but add its winding resistance.
- Frequency selectivity: since XL ∝ f, the same choke impedes high frequencies more — the basis of the smoothing choke in power-supply filters that blocks AC ripple while passing DC.
Designing a low-loss current limiter
A 200 V, 50 Hz supply must drive 0.5 A through a device while wasting no more than 10 W. A series rheostat would need R = 400 Ω and burn I²R = 100 W — ten times the budget. Use a choke with winding resistance r: the 10 W constraint forces r = P/I² = 10/0.25 = 40 Ω, and the impedance must be Z = V/I = 400 Ω, so ωL = √(400² − 40²) = √(158400) ≈ 398 Ω, giving L = 398/(2π × 50) ≈ 1.27 H. The same current flows as with the resistor, but nine-tenths of the waste has disappeared into the phase shift. Push the design further with thicker wire — r falls, L stays — and the loss drops toward zero, which is why real chokes for tube lights are wound with generous copper.
The phase story explains where the missing power went. Voltage across an inductor leads its current by a quarter period; when current and voltage have the same sign, energy flows into the magnetic field, and during the other part of the cycle it returns to the source. The source is not cheated — it lends and reclaims energy every quarter-cycle, and only the winding resistance converts any of it to heat. That lending is also the safety hazard: interrupt a choke's current suddenly and the collapsing field throws a large voltage across the switch (V = L di/dt), the familiar spark when a fluorescent fitting is switched off cheaply.
Where the exam probes
JEE Main's version is comparative and conceptual: why a choke is preferred over a rheostat (same current control, negligible power loss), what happens if the frequency rises (XL grows, current falls), and what a choke does in a DC circuit (nothing beyond its ohmic resistance). JEE Advanced numericals wrap the winding resistance in: solve simultaneously Z = V/I and r = P/I², then extract L — the worked design above with different numbers. The trap inventory: quoting zero power for a real choke (only the ideal one), and computing L from Z = ωL when r is not negligible. Assertion–reason pairs "a choke coil reduces current" with "it consumes no energy" — the first is true, the second only for the idealisation, and JEE wants both halves judged separately.
Frequently asked questions
Why is a choke coil preferred over a rheostat for limiting AC current?
Because it restricts current through frequency-dependent reactance while dissipating only I²r in its winding, whereas a rheostat burns the full I²R — the same current, a fraction of the heat.
What power does a real choke coil consume?
Only P = I²r in its winding resistance; the ideal inductive part consumes zero average power since current and voltage stay 90 degrees out of phase.
How does a choke behave in a DC circuit?
Its reactance ωL vanishes at zero frequency, so it offers only its small winding resistance and effectively passes DC — current limiting is an AC service.
What does the choke do in a fluorescent tube circuit?
It limits the running current through the ionised vapour and, with the starter interrupting the circuit, supplies the brief high-voltage surge that strikes the arc.
How do you compute the inductance needed for a given current and loss?
Set r = P/I² from the allowed loss, Z = V/I from the circuit, then L = √(Z² − r²)/(2πf) — the reactance carries what the resistance cannot.