Question 3-16B1

To determine the impedance of a series RL circuit, we first need to calculate the inductive reactance ($X_L$). The formula for inductive reactance is $X_L = 2 \pi f L$, where $f$ is the frequency and $L$ is the inductance. Given: * Frequency ($f$) = 30 MHz = $30 \times 10^6$ Hz * Inductance ($L$) = 0.1 µH = $0.1 \times 10^{-6}$ H $X_L = 2 \pi (30 \times 10^6 \text{ Hz}) (0.1 \times 10^{-6} \text{ H})$ $X_L = 2 \pi (30 \times 0.1)$ $X_L = 2 \pi (3)$ $X_L = 6 \pi \approx 18.85 \text{ ohms}$ Rounding to the nearest whole number, $X_L \approx 19 \text{ ohms}$. For a series circuit composed of a resistor and an inductor, the total impedance ($Z$) in rectangular coordinates is given by $Z = R + jX_L$, where $R$ is the resistance and $jX_L$ represents the inductive reactance. Given: * Resistance ($R$) = 20 ohms Substituting the values: $Z = 20 + j19 \text{ ohms}$ Therefore, option C is correct. Options A, B, and D are incorrect because they represent miscalculations of the inductive reactance, incorrect signs for inductive reactance, or an incorrect combination of the real and imaginary parts.