Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option C

$X_L = X_C$

Quick Summary: In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, i.e., $X_L = X_C$. At this frequency, the net reactance of the circuit becomes zero, causing the circuit to behave as a purely resistive circuit where the current and voltage are in phase.

💡 Explanation

In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, i.e., $X_L = X_C$ . At this frequency, the net reactance of the circuit becomes zero, causing the circuit to behave as a purely resistive circuit where the current and voltage are in phase.

🔢 Key Formulas

$X_L = 2\pi f L$ — Inductive Reactance

$X_C = \frac{1}{2\pi f C}$ — Capacitive Reactance

$f_r = \frac{1}{2\pi \sqrt{LC}}$ — Resonant Frequency

⚙️ Working Principle

The impedance of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$ . When $X_L = X_C$ , the reactive component $(X_L - X_C)$ becomes zero, resulting in minimum impedance $Z = R$ . Consequently, the current in the circuit reaches its maximum value, $I_{max} = \frac{V}{R}$ , and the power factor becomes unity.

📌 Key Points

▸
At resonance, the phase angle between voltage and current is $0°$ .
▸
The power factor of the circuit is unity at resonance.
▸
The circuit current is maximum because the impedance is at its minimum value (equal to R).
▸
Series resonance is also known as acceptor resonance because it allows maximum current flow.

✅ Advantages

▸
High current amplification at resonant frequency.
▸
Used in radio tuning circuits to select a specific frequency.

❌ Disadvantages / Limitations

▸
Dangerously high voltages can develop across the inductor and capacitor, potentially causing insulation failure.
▸
Requires precise component matching to maintain a specific frequency.

🛠️ Applications / Uses

▸
Radio and television tuning circuits.
▸
Oscillators and filter networks.

📄 Additional Information

▸
Resonance frequency $f_r$ is measured in Hertz (Hz).
▸
Wrong Options: Option A and B define specific component reactances rather than the cancellation condition. Option D suggests the inductive element is non-existent, which is incorrect.

📊 Diagram / Illustration

✅

C is correct — Series resonance is defined by the condition where inductive reactance perfectly cancels out capacitive reactance, $X_L = X_C$ .

Core Concepts Used

Click any tag to open in AI Tutor

RLC Series Circuit Reactance Cancellation Unity Power Factor

💡 EXAM TIP

Always remember that in series RLC resonance, current is maximum, whereas in parallel resonance (tank circuit), impedance is maximum and current is minimum.

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Related Questions

Discussion (0)