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Impedance of the RLC circuit depends on

$R$

$X_L$

$X_C$

All of above

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalBasic Electrical

Option D

All of above

Quick Summary:

The total impedance $Z$ of a series RLC circuit represents the opposition to the flow of alternating current. It is determined by the combined effect of resistance ( $R$ ), inductive reactance ( $X_L$ ), and capacitive reactance ( $X_C$ ).

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$Z = \sqrt{R^2 + (X_L - X_C)^2}$ — Total impedance in terms of R, $X_L$ , and $X_C$

$X_L = 2\pi fL$ — Inductive reactance formula

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

⚙️ Working Principle

In an RLC series circuit, the total opposition is a complex quantity because $R$ is in phase with current, while $X_L$ leads the current by $90°$ and $X_C$ lags the current by $90°$ . The impedance is calculated as the phasor sum of these components, resulting in a magnitude determined by the vector relationship $Z = \sqrt{R^2 + (X_L - X_C)^2}$ . Thus, any change in $R$ , $X_L$ , or $X_C$ directly alters the total impedance of the circuit.

📌 Key Points

▸
Impedance is measured in Ohms ( $\Omega$ ).
▸
At resonance, $X_L = X_C$ , so $Z = R$ (the minimum impedance).
▸
The phase angle $\phi$ is given by $\tan^{-1}(\frac{X_L - X_C}{R})$ .

✅ Advantages

▸
Used in tuning circuits for radio and telecommunications.
▸
Essential for power factor correction in industrial loads.

❌ Disadvantages / Limitations

▸
High sensitivity to frequency changes near resonance.
▸
Potential for high voltage magnification across components at resonance.

🛠️ Applications / Uses

▸
Band-pass and band-stop filters.
▸
Oscillator circuits and radio receivers.

📄 Additional Information

▸
If $X_L > X_C$ , the circuit is inductive and current lags voltage.
▸
If $X_C > X_L$ , the circuit is capacitive and current leads voltage.

📊 Diagram / Illustration

✅

D is correct — The total impedance $Z$ is a phasor combination of $R$ , $X_L$ , and $X_C$ , meaning it depends on all three parameters.

Core Concepts Used

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Phasor Algebra Resonance Complex Impedance

💡 EXAM TIP

Always remember that resonance occurs when $X_L = X_C$ ; this is a high-frequency question topic in GATE and JE exams.

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