In rectangular coordinates, what is the...

Question 1 of 27070XNcpX9u73cbqsriz9Ouk

In rectangular coordinates, what is the impedance of a network composed of a 10-microhenry inductor in series with a 40-ohm resistor, at 500 MHz?

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Question 1 of 27070

Q

In rectangular coordinates, what is the impedance of a network composed of a 10-microhenry inductor in series with a 40-ohm resistor, at 500 MHz?

🔍 Key Concepts

• Impedance of an inductor: Z_L = j 2π f L • Series R-L circuit impedance: Z_total = R + jX_L in rectangular form • Unit conversions: microhenry to henry, megahertz to hertz

💭 Think About

• First, convert 10 microhenry and 500 MHz into base SI units, then compute the inductive reactance X_L • Use the formula for inductive reactance and carefully calculate the numerical value before adding the resistor • Check the sign and placement of the real and imaginary parts when writing impedance in rectangular form

✅ Before You Answer

• Confirm that 10 microhenry is correctly converted to henry before using it in the formula • Confirm that 500 MHz is correctly converted to hertz before substituting into 2π f L • Verify that the real part of impedance corresponds to resistance and the imaginary part corresponds to inductive reactance (positive j for inductors)