Frequency for parallel resonance is given by

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f = 1/(2π √L/C)

Explanation: The resonant frequency for a parallel LC circuit is the frequency at which the inductive reactance ($X_L$) equals the capacitive reactance ($X_C$), causing the reactive components of the currents to cancel out. This results in the circuit appearing purely resistive to the source. Working Principle: In a parallel circuit containing an inductor and a capacitor, the impedance is at its maximum at resonance. The condition for resonance is defined by setting $X_L = X_C$, which leads to $2\pi f L = \frac{1}{2\pi f C}$. Solving this algebraic equation for $f$ yields the formula $f = \frac{1}{2\pi\sqrt{LC}}$. Key Formulas: $X_L = 2\pi f L$ — Inductive Reactance; $X_C = \frac{1}{2\pi f C}$ — Capacitive Reactance; $f_r = \frac{1}{2\pi\sqrt{LC}}$ — Parallel Resonant Frequency Key Points: At resonance, parallel impedance is maximum.; The total line current is at a minimum at resonance.; The power factor of the circuit is unity (1.0) at resonant frequency.; Parallel resonance is often referred to as 'anti-resonance'. Advantages: High impedance at resonant frequency; Effective in band-pass and band-stop filtering Disadvantages: High circulating currents between L and C; Sensitive to component value variations (Q-factor dependence) Applications: Tuned circuits in radio receivers; Oscillator circuits; Signal filtering Additional Info: The formula applies to an ideal parallel LC tank circuit.. Option A ($f = 2\pi\sqrt{LC}$) is incorrect as it lacks the reciprocal and inverse root relationship.. Option B ($f = 2\pi\sqrt{L/C}$) is dimensionally inconsistent for frequency.. Option D ($f = \sqrt{L/C}$) is missing the frequency-determining constant factors. Answer: C is correct — The frequency at which inductive reactance equals capacitive reactance in a parallel circuit is given by $f = \frac{1}{2\pi\sqrt{LC}}$. Exam Tip: Always remember that for both series and parallel LC circuits, the resonant frequency formula is the same; however, the impedance behavior (minimum vs maximum) is opposite.

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