Question 3-16B2

The impedance ($Z$) of a series circuit in rectangular coordinates is expressed as $Z = R + jX$, where $R$ is the resistance and $X$ is the reactance. For an inductor, the reactance is inductive ($X_L$), and it's positive, so the form is $Z = R + jX_L$. First, calculate the inductive reactance ($X_L$): $X_L = 2\pi f L$ where $f$ is the frequency and $L$ is the inductance. $f = 5 \text{ MHz} = 5 \times 10^6 \text{ Hz}$ $L = 0.1 \text{ microhenry} = 0.1 \times 10^{-6} \text{ H}$ $X_L = 2 \times \pi \times (5 \times 10^6 \text{ Hz}) \times (0.1 \times 10^{-6} \text{ H})$ $X_L = 2 \times \pi \times 0.5$ $X_L = \pi \text{ ohms}$ Approximating $\pi \approx 3.14$, $X_L \approx 3.14$ ohms. Given the answer choices, the value for $X_L$ is simplified to 3 ohms. Now, combine the resistance ($R = 30 \text{ ohms}$) and the inductive reactance ($X_L \approx 3 \text{ ohms}$) in series. $Z = R + jX_L = 30 + j3 \text{ ohms}$. This matches option D. Options A and C have a negative 'j' component, which would be correct for a capacitor. Options B and C swap the resistance and reactance values.