What is the resonance condition?

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Examoogle · Accepted Answer

When XL = XC

Explanation: Resonance in an AC circuit occurs when the inductive reactance ($X_L$) of the circuit is equal to the capacitive reactance ($X_C$). At this state, the phase angle between voltage and current becomes zero, making the circuit purely resistive. Working Principle: In an RLC series circuit, $X_L = 2\pi fL$ and $X_C = \frac{1}{2\pi fC}$. When $X_L = X_C$, the imaginary parts of the impedance cancel each other out, resulting in the minimum possible impedance $Z = R$. Consequently, the circuit draws maximum current for a given supply voltage. Key Formulas: $X_L = 2\pi fL$ — Inductive Reactance; $X_C = \frac{1}{2\pi fC}$ — Capacitive Reactance; $f_r = \frac{1}{2\pi \sqrt{LC}}$ — Resonant Frequency Key Points: At resonance, the power factor of the circuit is unity (1).; The total impedance of a series RLC circuit is minimum ($Z = R$).; Current is at its maximum value in a series resonant circuit.; The voltage drops across the inductor and capacitor are equal in magnitude but opposite in phase. Advantages: Maximum power transfer; High selectivity in communication circuits Disadvantages: Potential for dangerous over-voltage across components; High current may damage components if not damped Applications: Radio and Television tuning circuits; Induction heating; Filters in signal processing Additional Info: Resonance is primarily observed in RLC circuits.. Option A ($X_L > X_C$) represents an inductive circuit.. Option B is incomplete and mathematically invalid.. Option D is incorrect as infinite capacitive reactance occurs at DC (0 Hz). Answer: C is correct — Resonance occurs when inductive reactance equals capacitive reactance, resulting in a purely resistive circuit impedance. Exam Tip: Always remember that in series resonance, the circuit behaves like a resistor, whereas in parallel resonance, the circuit impedance becomes maximum at the resonant frequency.

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