What is the Q of a parallel RLC circuit, if it is resonant at 14.128 MHz, L is 4.7 microhenrys and R is 18 kilohms?

To determine the Q of a parallel RLC circuit, use the formula Q = R / X_L. It is vital to remember that the parallel Q formula places resistance in the numerator, distinguishing it from the series Q formula. Begin by finding the inductive reactance (X_L = 2 π f L). Multiply 2 × π × 14.128 × 10⁶ Hz × 4.7 × 10⁻⁶ H. The megahertz (10⁶) and microhenry (10⁻⁶) terms cancel each other out cleanly, resulting in an X_L of approximately 417.2 ohms. Finally, take the resistance of 18 kilohms (18,000 ohms) and divide it by the inductive reactance. 18,000 / 417.2 yields a Q factor of approximately 43.1.