What is the Q of a parallel RLC circuit, if it is resonant at 7.125 MHz, L is 8.2 microhenrys and R is 1 kilohm?

The Q factor of a parallel RLC circuit is found by dividing the parallel resistance by the inductive reactance (Q = R / X_L). This relationship means that in a parallel circuit, a higher resistance leads to a higher Q, unlike in a series circuit. First, find the inductive reactance (X_L) at the resonant frequency using the formula X_L = 2 * π * f * L. With f = 7.125 MHz and L = 8.2 µH, the megahertz and microhenrys cancel out their magnitude differences. X_L = 2 * 3.1416 * 7.125 * 8.2 ≈ 367.1 ohms. Then, convert the resistance to ohms (1 kilohm = 1,000 ohms) and divide it by the reactance. Q = 1000 / 367.1 ≈ 2.73.