Question 3-18B1

In a series AC circuit, resistance (R) and reactance (X) are out of phase and do not add arithmetically. Resistance represents energy dissipation, while reactance represents energy stored and released. Inductive reactance (XL) causes current to lag voltage, while capacitive reactance (XC) causes current to lead voltage. The magnitude of the total impedance (Z) in a series RLC circuit is calculated using the Pythagorean theorem: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ Given: Resistance (R) = 6 ohms Inductive Reactance (XL) = 17 ohms Capacitive Reactance (XC) = 0 ohms Plugging in the values: $Z = \sqrt{6^2 + (17 - 0)^2}$ $Z = \sqrt{6^2 + 17^2}$ $Z = \sqrt{36 + 289}$ $Z = \sqrt{325}$ $Z \approx 18.03 \text{ ohms}$ Therefore, the magnitude of the impedance is approximately 18 ohms. Option C is correct because it results from the vector sum of resistance and reactance. Options A, B, and D are incorrect as they do not apply the correct formula for combining resistance and reactance in a series AC circuit. For instance, D (23 ohms) would be the arithmetic sum (6 + 17), which is incorrect because resistance and reactance are 90 degrees out of phase.