How much is Z_T for a 100 ? R in series with a 100 ? inductor? A) 100 ? B) 1000 ? C) 1410 ? D) 141 ?

Question

Quizplus · Accepted Answer

The impedance (Z) of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = 2\pi fL$ is the inductive reactance, $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance, and $R$ is the resistance. For a circuit with only a resistor (R) and an inductor (L), $X_C = 0$ because there's no capacitor. Given R = 100 ohms and $X_L = 100$ ohms (since the inductor is specified as 100 ? inductance, implying an inductive reactance of 100 ohms at the given frequency), the impedance $Z = \sqrt{100^2 + 100^2} = \sqrt{20000} = 141.42$ ohms, which rounds to 141 ?.

How Much Is ZT for a 100 ? R in Series

How Much Is Z_T for a 100 ? R in Series