Subelement B: Electrical Math— Topic 16: Impedance Networks-1
Question 3-16B6
Element 3 (GROL)In rectangular coordinates, what is the impedance of a network composed of a 0.001-microfarad capacitor in series with a 400-ohm resistor, at 500 kHz?
Explanation
The impedance (Z) of a series circuit in rectangular coordinates is expressed as Z = R ± jX, where R is the resistance and X is the reactance. For a series RC circuit, the formula is Z = R - jXc, with the negative sign indicating capacitive reactance.
1. **Calculate the capacitive reactance (Xc):**
The formula for capacitive reactance is Xc = 1 / (2πfC).
Given:
* f = 500 kHz = 500,000 Hz
* C = 0.001 microfarads = 0.001 × 10⁻⁶ F = 1 × 10⁻⁹ F
Xc = 1 / (2 * π * 500,000 Hz * 1 × 10⁻⁹ F)
Xc ≈ 1 / (3.14159)
Xc ≈ 318.3 ohms
2. **Form the impedance:**
The resistor (R) is 400 ohms.
Substituting R and Xc into the impedance formula for an RC circuit:
Z = R - jXc
Z = 400 - j318.3 ohms
Rounding Xc to 318, the impedance is 400 - j318 ohms.
Options B and C are incorrect because the positive 'j' would represent inductive reactance. Option A incorrectly swaps the resistance and reactance values.
Related Questions
3-16B4 In rectangular coordinates, what is the impedance of a network composed of a 1.0-millihenry inductor in series with a 200-ohm resistor, at 30 kHz?3-16B5 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?3-17B1 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.3-17B2 In polar coordinates, what is the impedance of a network composed of a 100-ohm-reactance inductor in series with a 100-ohm resistor?3-17B3 In polar coordinates, what is the impedance of a network composed of a 400-ohm-reactance capacitor in series with a 300-ohm resistor?