Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

Quick Summary: In a pure capacitor circuit, the current leads the voltage by an exact phase angle of $90^{\circ}$ (or $\frac{\pi}{2}$ radians). This occurs because the capacitor opposes any change in voltage by storing energy in an electric field, creating a phase shift between the sinusoidal signals.

💡 Explanation

In a pure capacitor circuit, the current leads the voltage by an exact phase angle of $90°$ (or $\frac{\pi}{2}$ radians). This occurs because the capacitor opposes any change in voltage by storing energy in an electric field, creating a phase shift between the sinusoidal signals.

🔢 Key Formulas

$i = C \frac{dv}{dt}$ — Instantaneous current-voltage relationship

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

⚙️ Working Principle

The current in a capacitor is defined as $i(t) = C \frac{dv}{dt}$ . If voltage is $v(t) = V_m \sin(\omega t)$ , then $i(t) = C \frac{d}{dt}(V_m \sin(\omega t)) = \omega C V_m \cos(\omega t) = \omega C V_m \sin(\omega t + 90°)$ . The derivative of the sine function results in a cosine, which is inherently shifted by $90°$ leading.

📌 Key Points

▸
A pure capacitor is a non-dissipative element; it stores and releases energy.
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The power factor for a pure capacitive circuit is zero (leading).
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Average power consumed by a pure capacitor over a cycle is zero.

✅ Advantages

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Zero active power consumption in ideal conditions
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Used for power factor correction in industrial systems

❌ Disadvantages / Limitations

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Ideal pure capacitors do not exist; all have some Equivalent Series Resistance (ESR)
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Can cause resonance issues in power grids

🛠️ Applications / Uses

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Filtering circuits
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Coupling and decoupling applications
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Power factor improvement banks

📄 Additional Information

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The phase angle is defined as $\phi = 90°$ for a pure capacitor.
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Option A ( $0°$ ) represents a purely resistive circuit.
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Options B ( $30°$ ) and C ( $60°$ ) represent R-C series circuits where the phase angle depends on the values of R and C.

📊 Diagram / Illustration

✅

D is correct — In a pure capacitor, the current leads the voltage by $90°$ .

Core Concepts Used

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Phase shift in reactive elements Capacitive reactance AC circuit analysis

💡 EXAM TIP

Remember 'ELI the ICE man': In an Inductor (L), E leads I; in a Capacitor (C), I leads E.

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