Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

$\frac{1}{2\pi fC}$

Quick Summary: Capacitive reactance ($X_C$) is the opposition offered by a capacitor to the flow of alternating current. It is inversely proportional to both the frequency of the supply and the capacitance of the capacitor.

💡 Explanation

Capacitive reactance ( $X_C$ ) is the opposition offered by a capacitor to the flow of alternating current. It is inversely proportional to both the frequency of the supply and the capacitance of the capacitor.

🔢 Key Formulas

$X_C = \frac{1}{2\pi fC}$ — Formula for capacitive reactance in ohms ( $\Omega$ )

$I_C = \frac{V}{X_C}$ — Current flow through a pure capacitive circuit

⚙️ Working Principle

In an AC circuit, a capacitor continuously charges and discharges as the voltage polarity changes. The opposition to current arises because the voltage across a capacitor lags the current by $90°$ . As frequency ( $f$ ) increases, the capacitor charges and discharges faster, leading to lower impedance; similarly, higher capacitance ( $C$ ) allows more charge storage per cycle, further reducing reactance.

📌 Key Points

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Capacitive reactance ( $X_C$ ) is measured in Ohms ( $\Omega$ ).
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For a D.C. circuit ( $f=0$ ), the reactance becomes infinite, behaving as an open circuit.
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Reactance decreases linearly as either frequency or capacitance increases.

✅ Advantages

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Useful for frequency-dependent filtering (High-pass filters).
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Essential for power factor correction in industrial AC systems.

❌ Disadvantages / Limitations

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Causes leading current, which can lead to voltage instability if over-compensated.
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High frequency sensitivity can lead to unexpected circuit behavior in noise-prone environments.

🛠️ Applications / Uses

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Coupling capacitors in signal processing.
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Bypass capacitors for noise filtering in power supplies.

🔄 Comparison Table

Feature	Inductive Reactance ($X_L$)	Capacitive Reactance ($X_C$)
Relationship	Directly proportional	Inversely proportional

📄 Additional Information

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Option A ( $2\pi fL$ ) represents Inductive Reactance ( $X_L$ ).
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Option B ( $\frac{1}{2\pi fL}$ ) is dimensionally inconsistent with reactance.
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Option C ( $2\pi fC$ ) is the formula for capacitive susceptance ( $B_C$ ).

📊 Diagram / Illustration

✅

D is correct — Capacitive reactance is defined by the mathematical expression $X_C = \frac{1}{2\pi fC}$ .

Core Concepts Used

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AC Circuit Theory Frequency Response Capacitor Impedance

💡 EXAM TIP

Always remember that $X_L$ increases with frequency while $X_C$ decreases; these two reactances cancel each other out at resonance, a critical concept in tuning circuits.

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