Frequency for series resonance is given by

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Examoogle · Accepted Answer

f0=1/2π√LC

Explanation: In an RLC series circuit, resonance occurs when the inductive reactance equals the capacitive reactance, resulting in a purely resistive impedance. The resonant frequency $f_0$ is the specific frequency at which these reactances cancel each other out. Working Principle: At resonance, the inductive reactance $X_L = 2\pi fL$ and capacitive reactance $X_C = \frac{1}{2\pi fC}$ are equal in magnitude and opposite in phase. Equating $2\pi fL = \frac{1}{2\pi fC}$ leads to $f^2 = \frac{1}{4\pi^2 LC}$, which, when solved for $f$, yields the resonant frequency $f_0 = \frac{1}{2\pi \sqrt{LC}}$. Key Formulas: $X_L = X_C$ — Condition for resonance; $f_0 = \frac{1}{2\pi \sqrt{LC}}$ — Resonant frequency formula Key Points: At resonance, power factor is unity ($\cos\phi = 1$).; Impedance is minimum and equal to resistance ($Z = R$).; Current in the circuit is maximum ($I = V/R$).; The circuit behaves purely as a resistive network. Advantages: Used in tuning circuits for radio and TV receivers.; Allows selection of a specific frequency from a range of signals. Disadvantages: Potential for very high voltages across L and C, which may damage components.; High currents at resonance require components with high current ratings. Applications: Tuned amplifiers; Band-pass filters; Oscillators Additional Info: Standard unit for $f_0$ is Hertz (Hz), L is Henry (H), and C is Farad (F).. Option A is incorrect as it lacks the inverse relation and root; Option B is incorrect due to placement of constants; Option D is an incomplete expression. Answer: C is correct — The frequency for series resonance is given by the formula $f_0 = \frac{1}{2\pi \sqrt{LC}}$. Exam Tip: Always remember that at resonance, the phase angle between voltage and current is zero, making the circuit purely resistive regardless of the values of L and C.

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