In rectangular coordinates, what is the...

Question 1 of 27070ObGk8asxcIIgHpsl2eu5

In rectangular coordinates, what is the impedance of a network composed of a 0.01-microfarad capacitor in parallel with a 300-ohm resistor, at 50 kHz?

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Question 1 of 27070

In rectangular coordinates, what is the impedance of a network composed of a 0.01-microfarad capacitor in parallel with a 300-ohm resistor, at 50 kHz?

🔍 Key Concepts

• Impedive of a capacitor: Xc = 1 / (2πfC) and it is always negative imaginary in rectangular form • Impedance of a resistor is purely real: Zr = R + j0 • For parallel components, use admittance (Y = 1/Z): total admittance is the sum of individual admittances, then invert to get total impedance

💭 Think About

• First, compute the capacitive reactance at 50 kHz and express the capacitor impedance as a complex number in rectangular form • Convert the resistor and capacitor impedances to admittances, add them, and then take the reciprocal to get the total impedance • After you find the total impedance in rectangular form, compare both the real and imaginary parts with the answer choices, paying attention to the sign of the imaginary part

✅ Before You Answer

• Check that the sign of the imaginary part matches the fact that this is a capacitor (not an inductor) in the circuit • Verify that when combining parallel components, you added admittances, not impedances • Confirm that the units and frequency were used correctly when computing Xc: f = 50,000 Hz and C = 0.01 microfarad = 0.01 × 10⁻⁶ F