What is the impedance of a network composed...

Question 1 of 27070L4txSWmJ4O2ABpAlqOei

What is the impedance of a network composed of a 100-picofarad capacitor in parallel with a 4000-ohm resistor, at 500 KHz? Specify your answer in polar coordinates.

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Question 1 of 27070

What is the impedance of a network composed of a 100-picofarad capacitor in parallel with a 4000-ohm resistor, at 500 KHz? Specify your answer in polar coordinates.

🔍 Key Concepts

• Impedance of a capacitor: $X_C = \frac{1}{2\pi f C}$ and its phase angle • How to combine a resistor and capacitor in parallel using admittance ( $Y = 1/Z$ ) • Converting from rectangular form (real + j imaginary) to polar form (magnitude ∠ angle)

💭 Think About

• First, compute the capacitive reactance of the 100 pF capacitor at 500 kHz. Is it large or small compared to 4000 ohms? What does that suggest about current paths? • Write the admittance of the resistor and capacitor separately (conductance and susceptance). How do you add them to get total admittance, and then return to impedance? • Once you have the complex impedance, how do you find its magnitude and sign of the angle, based on whether the reactive part is inductive (+) or capacitive (−)?

✅ Before You Answer

• Confirm the unit conversions: picofarads to farads, kHz to Hz before calculating $X_C$ • Check whether the imaginary part of the total impedance is positive or negative (inductive vs capacitive) to determine the sign of the angle • Verify that the magnitude of the impedance makes sense given a 4 kΩ resistor in parallel with a reactive branch—should the total magnitude be greater or less than 4 kΩ?