What is the Q of a parallel RLC circuit, if it is resonant at 14.225 MHz, L is 3.5 microhenrys and R is 10 kilohms?

To find the Q (quality factor) of a parallel RLC circuit, use the formula Q = R / X_L (where X_L is the inductive reactance). This is the inverse of the formula used for a series RLC circuit, which is a common point of confusion for students. First, calculate the inductive reactance using X_L = 2 * π * f * L. Substituting the given values (f = 14.225 MHz and L = 3.5 µH), we get X_L = 2 * 3.1416 * 14.225 * 3.5 ≈ 312.8 ohms. Note that MHz and µH cancel out their powers of 10 (10^6 and 10^-6), making the math simpler. Next, convert the resistance R to basic units (10 kilohms = 10,000 ohms) and divide it by the reactance. Q = 10,000 / 312.8 ≈ 31.9.