Frequency dependence of capacitive reactance: Is the statement “capacitive reactance (Xc) is inversely proportional to frequency” correct for linear capacitors, where Xc = 1 / (2π f C)?

Introduction / Context:Reactance quantifies opposition to AC current due to energy storage in reactive elements. For capacitors, reactance falls as frequency rises, which is why capacitors can pass high-frequency components more easily than low-frequency ones. This question confirms the textbook formula and its proportionality.

Given Data / Assumptions:

• Ideal capacitor of capacitance C farads.
• Sinusoidal steady-state analysis.
• Xc defined as the magnitude of the reactive part of impedance.

Concept / Approach:The standard relation is Xc = 1 / (2π f C). As f increases, the denominator grows, making Xc smaller. This inverse proportionality underpins the behavior of coupling capacitors, differentiators, and high-pass filters, where high-frequency signals encounter less opposition.

Step-by-Step Solution:

Verification / Alternative check:Measure current through a capacitor at two frequencies with the same applied voltage. The higher-frequency current increases in proportion to f, consistent with Xc declining as 1/f.

Why Other Options Are Wrong:Only true above cutoff / only for electrolytics: the relation is universal for ideal capacitors across frequencies where the component remains linear and parasitics are negligible.

Common Pitfalls:Confusing reactance with impedance magnitude when resistive elements are in play; ignoring ESR and ESL at very high frequencies where the simple model breaks down.

Final Answer:Correct