Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option C

Quick Summary: In an RC series circuit, the phase angle between the total voltage and the current is strictly between $0^\circ$ and $90^\circ$. The current leads the voltage because the capacitive reactance causes the voltage to lag, but the presence of resistance prevents the phase shift from reaching a perfect $90^\circ$.

💡 Explanation

In an RC series circuit, the phase angle between the total voltage and the current is strictly between $0°$ and $90°$ . The current leads the voltage because the capacitive reactance causes the voltage to lag, but the presence of resistance prevents the phase shift from reaching a perfect $90°$ .

🔢 Key Formulas

$Z = \sqrt{R^2 + X_C^2}$ — Total impedance magnitude

$\phi = \tan^{-1}\left(\frac{X_C}{R}\right)$ — Phase angle of the circuit

⚙️ Working Principle

The impedance of an RC circuit is given by the vector sum of resistance and capacitive reactance, $Z = R - jX_C$ . The phase angle $\phi$ is determined by the ratio of the imaginary (reactive) component to the real (resistive) component, defined as $\tan(\phi) = \frac{X_C}{R}$ . As long as $R > 0$ and $X_C > 0$ , the angle $\phi$ remains in the first quadrant, specifically $0°< \phi < 90°$ .

📌 Key Points

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The circuit is capacitive, so current leads the voltage.
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A pure resistor has a phase angle of $0°$ .
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A pure capacitor has a phase angle of $90°$ .
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The phase angle depends on the frequency of the source since $X_C = \frac{1}{2\pi fC}$ .

✅ Advantages

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Used for filtering high-frequency noise.
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Essential in timing circuits and oscillators.

❌ Disadvantages / Limitations

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Performance is highly dependent on frequency.
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Power factor is always leading, which can be undesirable in power systems.

🛠️ Applications / Uses

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Coupling capacitors in amplifiers.
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Bypass capacitors in power supply circuits.

📄 Additional Information

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The phase angle $\phi$ is exactly $0°$ only if $X_C = 0$ (Purely resistive).
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The phase angle $\phi$ is exactly $90°$ only if $R = 0$ (Purely capacitive).
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Option B represents a pure capacitor, while Option A represents a pure resistor.

📊 Diagram / Illustration

✅

C is correct — In an RC series circuit, the phase angle $\phi$ is defined by $\tan(\phi) = \frac{X_C}{R}$ , which yields a value strictly between $0°$ and $90°$ .

Core Concepts Used

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Phasor Algebra Impedance Triangle Capacitive Reactance

💡 EXAM TIP

Always remember that in AC circuits, the presence of resistance ensures the phase angle never reaches exactly $90°$ or $0°$ unless one of the components is absent.

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