Impedance of the RLC circuit depends on

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Examoogle · Accepted Answer

All of above

Explanation: The impedance ($Z$) of an RLC series circuit represents the total opposition to the flow of alternating current. It is a complex quantity that incorporates the resistive, inductive, and capacitive components of the circuit.

Working Principle: In an RLC series circuit, impedance is calculated as the vector sum of resistance ($R$) and net reactance ($X = X_L - X_C$). Since $X_L = 2\pi fL$ and $X_C = \frac{1}{2\pi fC}$, the impedance magnitude depends directly on the resistance $R$, the inductive reactance $X_L$, and the capacitive reactance $X_C$.

Key Formulas: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ — Total impedance magnitude; $X_L = 2\pi fL$ — Inductive reactance; $X_C = \frac{1}{2\pi fC}$ — Capacitive reactance

Key Points: Impedance is measured in Ohms ($Omega$).; At resonance, $X_L = X_C$, so impedance equals $R$ (minimum impedance).; Impedance is frequency-dependent due to the reactance terms.

Advantages: Used in tuning circuits for radio receivers; Essential for analyzing power factor in AC systems

Disadvantages: Susceptible to frequency variations; Phase shift between voltage and current depends on these parameters

Applications: Band-pass and band-stop filters; Oscillators and communication transmitters

Additional Info: The resistance $R$ represents real power dissipation, while $X_L$ and $X_C$ represent reactive power storage.. Option D is correct because $Z$ is a function of the real and imaginary parts of the circuit impedance, which are $R$, $X_L$, and $X_C$ respectively.

Answer: D is correct — The impedance of an RLC circuit is determined by the combination of resistance, inductive reactance, and capacitive reactance.

Exam Tip: Remember that at resonance ($X_L = X_C$), the phase angle is zero and the circuit behaves purely as a resistor; this is a highly tested concept in competitive exams.

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