In rectangular coordinates, what is the impedance of a network consisting of a 0.1-microhenry inductor in series with a 30-ohm resistor at 5 MHz?

• A. 30 - j3
• B. 3 + j30
• C. 3 - j30
• D. 30 + j3

Answer: (D)

When a resistor and an inductor are in series, their impedances add: Z = R + jωL. The resistor contributes 30 Ω to the real part, and the inductor contributes the reactive part jωL, where ω = 2πf. With f = 5 MHz, ω = 2π × 5×10^6 ≈ 31.4159×10^6 rad/s. The inductive reactance is X_L = ωL = (31.4159×10^6)(1×10^-7) ≈ 3.1416 Ω. So Z ≈ 30 + j3.1416 Ω, i.e., about 30 + j3. The positive imaginary part confirms inductive reactance. The option showing 30 + j3 Ω best matches this result.