Q factor of parallel circuit is given by

Question

Examoogle · Accepted Answer

R√C/L

Explanation: The Q-factor (Quality factor) of a parallel RLC circuit represents the ratio of the energy stored in the reactive elements (inductor or capacitor) to the energy dissipated in the resistor per cycle. For a parallel resonant circuit, it is defined as $Q = R\sqrt{\frac{C}{L}}$. Working Principle: In a parallel resonant circuit, at resonance, the inductive susceptance equals the capacitive susceptance ($B_L = B_C$). The Q-factor signifies the sharpness of resonance; a higher Q-factor indicates a narrower bandwidth and higher selectivity. Since $Q = \frac{R}{X_L} = R\sqrt{\frac{C}{L}}$ at resonance, the circuit current is minimal at resonance, making the impedance maximum. Key Formulas: $Q = R\sqrt{\frac{C}{L}}$ — Q factor of parallel RLC circuit; $BW = \frac{f_r}{Q}$ — Relationship between Bandwidth and Q factor Key Points: Q factor is a dimensionless quantity representing selectivity.; Higher Q factor results in a narrower bandwidth (sharper resonance).; In parallel circuits, the Q factor is directly proportional to the resistance R.; Parallel resonance occurs when the reactive part of the admittance is zero. Advantages: High selectivity for filtering specific frequencies.; Provides high impedance at resonant frequency. Disadvantages: High Q circuits are sensitive to component tolerance variations.; Prone to instability in some oscillator applications. Applications: Radio frequency (RF) tuning circuits.; Band-pass filters and oscillators. Additional Info: For a series RLC circuit, the Q factor is $\frac{1}{R}\sqrt{\frac{L}{C}}$, which is the inverse relationship of the parallel circuit.. Option A is simply the reciprocal dimension, Option C is a ratio of reactances at resonance, and Option D is incorrect. Answer: B is correct — The quality factor for a parallel RLC circuit is expressed as $Q = R\sqrt{\frac{C}{L}}$. Exam Tip: Always remember that Q-factor for series is inversely proportional to R ($Q = \frac{1}{R}\sqrt{\frac{L}{C}}$), while for parallel it is directly proportional to R ($Q = R\sqrt{\frac{C}{L}}$).

Related Questions

Discussion (0)