What is the magnitude of the impedance of a series circuit with a 0.1 microhenry inductor and a 30-ohm resistor at 5 MHz?

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Multiple Choice

What is the magnitude of the impedance of a series circuit with a 0.1 microhenry inductor and a 30-ohm resistor at 5 MHz?

In a series circuit, the total impedance combines the resistor and the inductor as Z = R + jωL, so the magnitude is |Z| = sqrt(R^2 + (ωL)^2). Convert the values: L = 0.1 μH = 1×10^-7 H, f = 5 MHz gives ω = 2πf ≈ 31.4159×10^6 rad/s. The inductive reactance is X_L = ωL ≈ 31.4159×10^6 × 1×10^-7 ≈ 3.1416 Ω. Then |Z| ≈ sqrt(30^2 + 3.1416^2) ≈ sqrt(900 + 9.87) ≈ sqrt(909.87) ≈ 30.2 Ω. This rounds to 30.0 Ω in the options. The inductive part is only about 3.1 Ω, so the impedance stays just slightly above the 30 Ω resistance.

In a series circuit, the total impedance combines the resistor and the inductor as Z = R + jωL, so the magnitude is |Z| = sqrt(R^2 + (ωL)^2). Convert the values: L = 0.1 μH = 1×10^-7 H, f = 5 MHz gives ω = 2πf ≈ 31.4159×10^6 rad/s. The inductive reactance is X_L = ωL ≈ 31.4159×10^6 × 1×10^-7 ≈ 3.1416 Ω. Then |Z| ≈ sqrt(30^2 + 3.1416^2) ≈ sqrt(900 + 9.87) ≈ sqrt(909.87) ≈ 30.2 Ω. This rounds to 30.0 Ω in the options. The inductive part is only about 3.1 Ω, so the impedance stays just slightly above the 30 Ω resistance.

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