Resistance, Reactance, Impedance 電阻、電抗、阻抗

Electrical Impedance:

Z = R + jX    or     R + jX_c

where

Z = impedance in ohms (Ω) 阻抗，單位為歐姆(Ω)
R = resistance in ohms (Ω) 電阻，單位為歐姆(Ω) real part 實部
X = reactance in ohms (Ω) 電抗，單位為歐姆(Ω) imaginary part 虛部

Z = V/I

X = 1/ωC = 1/2πf

ideal resistor with purely real impedance => resistive impedance

ideal inductor/capacitor with purely imaginary impedance => reactive impedance

phasor / phase vector 相量
阻抗可用相量表示

阻抗可以magnitude和phase來表示

magnitude 強度 |Z| = √(R² + X²)
phase 相位 θ = tan^-1(X/R)

Question: What's the reactance of a 2.2µF capacitor with 100Hz frequency?

Answer:

X = 1/ωC = 1/2πf = 1/(2×3.1416×100×2.2×10^-6) = 723.4 Ω

Question: Circuit configuration:

Function Generator ---- C ----- V_out ----- R ---- GND
where C = 1µF and R = 2.2 kΩ

Z_c = 1/jωC = j/j2ωC = - j(1/ωC) => -90°

A 2.2kΩ resistor and a  capacitor are in series. with 100Hz frequency?