Question 3-17B2

In a series circuit composed of a resistor (R) and an inductor (L), the total impedance (Z) is the vector sum of the resistance and the inductive reactance ($X_L$). Impedance in polar coordinates is represented by its magnitude and phase angle. 1. **Magnitude of Impedance (|Z|):** The magnitude is calculated using the Pythagorean theorem: $|Z| = \sqrt{R^2 + X_L^2}$ Given R = 100 ohms and $X_L$ = 100 ohms: $|Z| = \sqrt{100^2 + 100^2} = \sqrt{10000 + 10000} = \sqrt{20000} \approx 141.4$ ohms. 2. **Phase Angle ($\theta$):** The phase angle for an RL circuit is found using the arctangent function: $\theta = \arctan(\frac{X_L}{R})$ $\theta = \arctan(\frac{100}{100}) = \arctan(1) = 45^\circ$. Since it's an inductive circuit, the phase angle is positive. Combining these, the impedance in polar coordinates is approximately 141 ohms, at an angle of 45 degrees ($141 \angle 45^\circ$ ohms). This corresponds to option B. The other options have incorrect magnitudes or phase angles.