Question 3-16B3

The impedance ($Z$) of a series circuit in rectangular coordinates is given by $Z = R + jX$, where $R$ is the resistance and $X$ is the reactance. First, we need to calculate the inductive reactance ($X_L$) of the 10-microhenry inductor at 500 MHz using the formula: $X_L = 2\pi f L$ where: $f = 500 \text{ MHz} = 500 \times 10^6 \text{ Hz}$ $L = 10 \text{ microhenries} = 10 \times 10^{-6} \text{ H}$ Plugging in the values: $X_L = 2 \times \pi \times (500 \times 10^6) \times (10 \times 10^{-6})$ $X_L = 2 \times \pi \times 500 \times 10$ $X_L = 10000 \pi$ $X_L \approx 31415.9 \text{ ohms}$ Rounding to the nearest significant figures provided in the options, $X_L \approx 31400 \text{ ohms}$. For an inductor, the reactance is positive, so it's $jX_L$. The total impedance is the sum of the series resistance and the inductive reactance: $Z = R + jX_L$ $Z = 40 \text{ ohms} + j31400 \text{ ohms}$ Therefore, the impedance is $40 + j31400$. Options B, C, and D are incorrect because they either show a negative reactance (which would be capacitive), swap the real (resistance) and imaginary (reactance) components, or both.