What is the frequency in resonance condition?

Question

Examoogle · Accepted Answer

Maximum

Explanation: In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance ($X_L = X_C$). At this condition, the total circuit impedance is purely resistive and reaches its minimum value, causing the circuit current to reach its maximum peak.

Working Principle: At resonance, the phase angle between voltage and current is zero, meaning the circuit operates at unity power factor. Since the total impedance $Z = \sqrt{R^2 + (X_L - X_C)^2}$ reduces to $Z = R$ (the minimum possible value), the current $I = V/Z$ becomes maximum for a given supply voltage.

Key Formulas: $f_r = \frac{1}{2\pi\sqrt{LC}}$ — Resonant frequency formula; $Z = \sqrt{R^2 + (\omega L - \frac{1}{\omega C})^2}$ — Impedance formula

Key Points: At resonance, $X_L = X_C$.; The circuit becomes purely resistive at resonance.; Power factor is unity ($cos \phi = 1$).; Current is inversely proportional to impedance, hence maximum when $Z$ is minimum.

Advantages: Used in radio tuning circuits to select specific frequencies.; Maximizes power transfer in communication systems.

Disadvantages: Can lead to dangerous voltage magnification across L and C components.; Requires high precision components to maintain stability.

Applications: Radio and TV receivers.; Oscillators and filter circuits.

Additional Info: Resonance in series RLC circuits is known as voltage resonance.. Option A is incorrect because current, not impedance, is maximized, and at resonance, impedance is at its minimum.

Answer: B is correct — At resonance, the circuit impedance is at its minimum, which leads to the maximum current flow in a series RLC circuit.

Exam Tip: Always remember that in series resonance, impedance is minimum (maximum current), whereas in parallel resonance, impedance is maximum (minimum current).

Related Questions

Discussion (0)