What is the Q of a parallel RLC circuit, if it is resonant at 14.128 MHz, L is 2.7 microhenrys and R is 18 kilohms?

The Quality factor (Q) of a parallel RLC circuit describes how 'sharp' the resonance is and is calculated using the formula Q = R / X_L, where X_L is the inductive reactance. This is the exact inverse of the formula used for a series RLC circuit. First, calculate the inductive reactance using X_L = 2 π f L. Plugging in the values yields X_L = 2 × π × 14.128 × 10⁶ Hz × 2.7 × 10⁻⁶ H. The megahertz and microhenry terms cleanly cancel, resulting in approximately 239.7 ohms. Next, divide the parallel resistance by this reactance. The resistance is given as 18 kilohms, or 18,000 ohms. Dividing 18,000 by 239.7 gives a Q factor of approximately 75.1.