Capacitive Reactance

As described in NCERT Class 12, Chapter 7 (Alternating Current), a capacitor opposes alternating current through its capacitive reactance $X_C=\frac{1}{\omega C}=\frac{1}{2\pi fC}$, which decreases with frequency because a rapidly alternating voltage keeps the capacitor charging and discharging without fully blocking flow. Substituting $f=50\text{Hz}$ and $C=25\times 10^{-6}\text{F}$: the denominator is $2\pi fC=2\times 3.14\times 50\times 25\times 10^{-6}=7.85\times 10^{-3}$, giving $X_C=\frac{1}{7.85\times 10^{-3}}\approx 127\Omega$. The option 318 ohm forgets the factor of 2 in $2\pi$. The option 63.7 ohm doubles the frequency incorrectly. The option 254 ohm multiplies the true value by two. A sanity check confirms units of $\frac{1}{({\text{s}}^{-1})(\text{F})}=\Omega$, and unlike an inductor, a capacitor's reactance falls as frequency rises, so it blocks DC but readily passes high-frequency AC. This behaviour is the exact opposite of an inductor, whose reactance grows with frequency, and this complementary property is what allows LC combinations to select particular frequencies. Physically, the reactance is not a true resistance because the capacitor dissipates no energy; it merely stores charge and returns it, imposing an opposition that depends on how quickly the applied voltage reverses. At the given 50 Hz mains frequency, a reactance of about 127 ohm means this capacitor would limit the current substantially, which is why capacitors of this size are common in power-line filtering and phase-correction applications.