Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option B

$X_C$

Quick Summary: In an A.C. circuit, capacitive reactance ($X_C$) is inversely proportional to frequency ($f$). As the frequency of the supply voltage increases, the rate of charging and discharging of the capacitor increases, leading to a decrease in the opposition to current flow.

💡 Explanation

In an A.C. circuit, capacitive reactance ( $X_C$ ) is inversely proportional to frequency ( $f$ ). As the frequency of the supply voltage increases, the rate of charging and discharging of the capacitor increases, leading to a decrease in the opposition to current flow.

🔢 Key Formulas

$X_C = \frac{1}{2\pi f C}$ — Capacitive reactance

$X_L = 2\pi f L$ — Inductive reactance

⚙️ Working Principle

The capacitive reactance is defined by the formula $X_C = \frac{1}{2\pi f C}$ . Since frequency ( $f$ ) appears in the denominator, any increase in $f$ results in a mathematical reduction of the total reactance $X_C$ . Conversely, inductive reactance ( $X_L = 2\pi f L$ ) increases linearly with frequency.

📌 Key Points

▸
Capacitive reactance decreases as frequency increases ( $X_C \propto \frac{1}{f}$ ).
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Inductive reactance increases as frequency increases ( $X_L \propto f$ ).
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Resistance ( $R$ ) is generally considered independent of frequency in ideal conditions.
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At $f = 0$ (DC), a capacitor acts as an open circuit ( $X_C = \infty$ ).

✅ Advantages

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Used in high-pass filter designs.
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Helps in frequency-selective circuits.

❌ Disadvantages / Limitations

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High frequencies can lead to excessive current in capacitive circuits if not controlled.
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Non-linear behavior requires careful frequency management.

🛠️ Applications / Uses

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Coupling capacitors in amplifiers.
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Tuning circuits and oscillators.

📄 Additional Information

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Standard unit for reactance is Ohms ( $\Omega$ ).
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Option A ( $X_L$ ) increases with frequency.
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Option C ( $R$ ) remains constant in an ideal resistor.

📊 Diagram / Illustration

✅

B is correct — Capacitive reactance ( $X_C$ ) is inversely proportional to frequency, so it decreases as frequency increases.

Core Concepts Used

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Capacitive Reactance Frequency Response AC Circuit Theory

💡 EXAM TIP

Remember that capacitors act as 'DC blocks' because at zero frequency, reactance becomes infinite; always visualize the $1/f$ relationship to avoid confusion.

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