In an AC circuit, what is the impedance of a capacitor with capacitance C and angular frequency ω?

• A. Z_C = 1/(jωC)
• B. Z_C = jωC
• C. Z_C = R
• D. Z_C = -jωC

Answer: (A)

Capacitors in AC respond with a current that leads the voltage by 90 degrees, and their impedance reflects the inverse relationship with frequency. From i = C dv/dt, converting to phasors gives I = j ω C V. The impedance Z is V divided by I, so Z = V/I = 1/(j ω C) = -j/(ω C). This shows the impedance is purely imaginary, with magnitude 1/(ω C) and a phase of -90 degrees. That exact form matches the correct option. The other forms correspond to different elements or incorrect relationships: j ω C would be the inductive reactance, R is the resistor’s impedance, and -j ω C would not describe a capacitor’s behavior, as it implies impedance growing with frequency rather than shrinking.