Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option C

$V = iX_C$

Quick Summary: In a pure capacitor circuit under AC conditions, the voltage across the capacitor is calculated using the product of the current and the capacitive reactance. Capacitive reactance represents the opposition offered by the capacitor to the flow of alternating current.

💡 Explanation

In a pure capacitor circuit under AC conditions, the voltage across the capacitor is calculated using the product of the current and the capacitive reactance. Capacitive reactance represents the opposition offered by the capacitor to the flow of alternating current.

🔢 Key Formulas

$V = I X_C$ — Voltage across a capacitor

$X_C = \frac{1}{2\pi fC}$ — Capacitive reactance formula

⚙️ Working Principle

The opposition to current in a capacitor is defined as $X_C = \frac{1}{2\pi fC}$ . Because the voltage in an AC circuit follows Ohm's law in phasor form, the magnitude of the voltage drop across the pure capacitive element is given by $V = I \times X_C$ . This relation holds because $X_C$ acts as the frequency-dependent resistance for the capacitive circuit.

📌 Key Points

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Capacitive reactance $X_C$ is inversely proportional to frequency $f$ and capacitance $C$ .
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In a purely capacitive circuit, the current leads the voltage by exactly $90°$ ( $\frac{\pi}{2}$ radians).
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Units for $X_C$ are Ohms ( $\Omega$ ).

✅ Advantages

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Provides energy storage in electric fields
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Essential for power factor correction

❌ Disadvantages / Limitations

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High reactance at low frequencies
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Potential for dielectric breakdown under overvoltage

🛠️ Applications / Uses

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Filtering circuits in power supplies
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Coupling and decoupling in signal processing

📄 Additional Information

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Option A ( $V=iR$ ) describes a pure resistive circuit.
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Option B ( $V=iX_L$ ) describes a pure inductive circuit where $X_L = 2\pi fL$ .
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Option D ( $V=iLC$ ) is dimensionally incorrect for voltage.

📊 Diagram / Illustration

✅

C is correct — The voltage drop across a pure capacitor is the product of the RMS current and its capacitive reactance ( $X_C$ ).

Core Concepts Used

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Ohm's Law for AC Capacitive Reactance Phasor Relationships

💡 EXAM TIP

Always remember that in AC circuits, 'Resistance' generalizes to 'Impedance' ( $Z$ ). For pure components, $Z$ simplifies to $R$ , $jX_L$ , or $-jX_C$ .

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