In rectangular coordinates, what is the...

Question 1 of 27070Ijq7ObIgZnTteWYHN65z

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

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Question 1 of 27070

Q

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

🔍 Key Concepts

• Series RL circuit impedance is expressed as resistance plus j times reactance in rectangular form • Inductive reactance formula: X_L = 2π f L (ohms) where f is frequency and L is inductance • Know the sign of j for inductive reactance vs capacitive reactance in rectangular impedance

💭 Think About

• First calculate the inductive reactance X_L at 5 MHz using the given inductance; keep track of powers of ten carefully • Once you have X_L, combine it with the series resistor to form Z = R + jX; which term (real or imaginary) comes from which component? • Decide whether the imaginary part should be positive or negative for an inductor at this frequency

✅ Before You Answer

• Verify your unit conversions: microhenry to henry and megahertz to hertz (µH to H, MHz to Hz) • Check that your computed reactance is reasonable in size compared to 30 ohms and matches one of the answer choices • Confirm the correct sign of the imaginary term (±j) for an inductor before picking between similar-looking options