Question 6A111

In a series AC circuit, the total impedance (Z) is the vector sum of the resistance (R) and the net reactance ($X_L - X_C$). This vector sum is necessary because resistance and reactance are 90 degrees out of phase with each other. Resistance dissipates energy, while reactance stores and releases it. The formula for total impedance in a series RLC circuit is: $Z = \sqrt{R^2 + (X_L - X_C)^2}$ Given values: R = 6 ohms $X_L$ = 17 ohms $X_C$ = 0 ohms Substituting these values into the formula: $Z = \sqrt{6^2 + (17 - 0)^2}$ $Z = \sqrt{6^2 + 17^2}$ $Z = \sqrt{36 + 289}$ $Z = \sqrt{325}$ $Z \approx 18.03$ ohms Therefore, 18 ohms is the correct total impedance. Options A, B, and D result from incorrect arithmetic or simple addition/subtraction, which does not account for the phase difference between resistance and reactance.