Reactance of a capacitor is

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Correct — A, Inversely proportional to frequency. Capacitive reactance is defined by X_C = 1 / (ωC) = 1 / (2πfC), where f is the frequency of the supply in hertz and C the capacitance in farads. The frequency sits in the denominator, so doubling the frequency halves the reactance: the relationship is inverse, and the exponent on f is exactly minus one. The physics behind the algebra is worth holding on to, because it is what the formula is describing. A capacitor does not conduct through its dielectric at all; current 'flows' in the circuit only while the plates are charging or discharging. At a high supply frequency the voltage reverses so often that the plates never approach full charge, charge keeps sloshing in and out, and a large alternating current is sustained — which is another way of saying the opposition is small. At a low frequency the plates have time to charge fully, the current falls away as they do, and the opposition is large. Push that to the limit: at f = 0, which is direct current, X_C becomes infinite and the capacitor blocks the circuit completely. That single limit is the memory hook, because it is a fact everybody already knows — a capacitor blocks DC and passes AC — and it can only be true if reactance rises as frequency falls. Since option (a) states the relation exactly, the escape option (d) has nothing to do.

Why the other options are wrong — (b) This is the inductor's behaviour, not the capacitor's. Inductive reactance is X_L = ωL = 2πfL, with frequency in the numerator, so an inductor opposes high frequencies and passes low ones — exactly opposite to a capacitor. The two are deliberately mirrored, and swapping them is the standard error this option is built to catch.  (c) A square-root dependence appears nowhere in the reactance formulae. It is imported from the resonance condition of an LC circuit, where f = 1 / (2π√(LC)) puts a square root on the product of inductance and capacitance — a different quantity in a different equation. In X_C = 1/(2πfC) the power of f is one.  (d) This escape is correct only if all three named statements fail, and the first one is the textbook definition. The temptation is to read 'reactance' as 'impedance' and object that the total opposition of an RC circuit, Z = √(R² + X_C²), is not a clean inverse function of frequency — true, but the stem asks for reactance, not impedance.

Concept: In a direct-current circuit the only opposition to current is resistance, R, measured in ohms and set by the material and dimensions of the conductor. In an alternating-current circuit two further kinds of opposition appear, and both come from energy being stored and given back rather than dissipated as heat. A capacitor stores energy in the electric field between its plates and opposes a *change* of voltage; an inductor stores energy in the magnetic field around its coil and opposes a *change* of current. The opposition each offers is called reactance, is also measured in ohms, and unlike resistance it depends on the frequency of the supply: X_C = 1/(2πfC) for the capacitor and X_L = 2πfL for the inductor. Combined with resistance they give the impedance Z = √(R² + (X_L − X_C)²), the total opposition of an AC circuit. When X_L equals X_C the two cancel, impedance falls to R alone and the circuit is at resonance — the principle every radio tuner works on.

State PCS 2025 Q55 — Science & Technology PYQ with Answer

State PCS 2025 Q55 — Science & Technology PYQ with Answer