What is the resonance condition?

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When XL=XC Explanation: Resonance in an RLC series circuit occurs when the inductive reactance ($X_L$) is exactly equal to the capacitive reactance ($X_C$). At this condition, the net reactance of the circuit becomes zero, causing the circuit to behave as a purely resistive load. Working Principle: In an RLC circuit, $X_L = 2\pi fL$ and $X_C = \frac{1}{2\pi fC}$. As frequency varies, these reactances change in opposite directions. When $X_L = X_C$, the imaginary parts of the impedance cancel out, leaving only the resistance $R$. This results in unity power factor and maximum current flow for a given voltage source. Key Formulas: $X_L = 2\pi fL$ — Inductive reactance formula; $X_C = \frac{1}{2\pi fC}$ — Capacitive reactance formula; $f_0 = \frac{1}{2\pi \sqrt{LC}}$ — Resonant frequency formula Key Points: At resonance, impedance $Z$ is minimum ($Z = R$).; Current is maximum in a series RLC circuit at resonance.; The power factor is unity ($\cos\phi = 1$).; Voltage across inductor and capacitor are equal in magnitude but opposite in phase. Advantages: Maximum power transfer; Voltage magnification; Selective frequency filtering Disadvantages: High current can damage components; High voltage stress across $L$ and $C$ Applications: Radio frequency tuning; Band-pass and band-stop filters; Oscillators Additional Info: Option A ($X_L > X_C$) corresponds to an inductive circuit.. Option B ($X_L. Resonance is a frequency-dependent phenomenon. Answer: C is correct — Resonance occurs when the inductive reactance equals the capacitive reactance ($X_L = X_C$). Exam Tip: Always remember that in series resonance, the circuit is purely resistive, whereas in parallel resonance, the circuit presents a high impedance and acts as an open circuit.

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