What is the impedance of a network composed...

Question 1 of 27070fr4rF2jrN1MGVD2a3lxG

What is the impedance of a network composed of a 0.1-microhenry inductor in series with a 20-ohm resistor, at 30 MHz? Specify your answer in rectangular coordinates.

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Question 1 of 27070

Q

What is the impedance of a network composed of a 0.1-microhenry inductor in series with a 20-ohm resistor, at 30 MHz? Specify your answer in rectangular coordinates.

🔍 Key Concepts

• Impedive of an inductor: X_L = 2π f L and that this is an imaginary (j) quantity • Series circuits: resistances and reactances in series add directly as complex numbers • Rectangular form of impedance: Z = R + jX

💭 Think About

• First compute the inductive reactance at 30 MHz for a 0.1 µH inductor. What numerical value do you get? • Once you know the reactance, how do you write the total series impedance combining a real part (resistor) and an imaginary part (inductor)? • Is the reactance of an inductor positive j or negative j in the impedance expression?

✅ Before You Answer

• Convert 0.1 microhenry to henries correctly before using it in the formula. • Convert 30 MHz to hertz correctly before calculating reactance. • Check the sign and placement of the real part (R) and imaginary part (jX) in the rectangular form: Z = R ± jX.