Calculate Reactance XC, C or f

Calculator and formulas for calculating the reactance of a capacitor

Calculate Reactance

Capacitive Reactance

This function allows you to calculate the reactance of a capacitor, or the capacitance or the corresponding frequency. Two values must be known to calculate the third.

Results
Capacitance C:
Frequency f:
Reactance XC:

Capacitive Reactance

What is XC?

The capacitive reactance XC is the AC resistance of a capacitor. It is frequency-dependent and decreases with increasing frequency. For DC (f = 0), XC is infinitely large.

Basic Formula
\[X_C = \frac{1}{2\pi fC}\]

Reactance of a capacitor in AC.

Frequency Behavior
  • Low frequencies: High reactance
  • High frequencies: Low reactance
  • DC (f=0): Infinite resistance
  • Phase shift: Current leads voltage by 90°

Capacitive Reactance - Theory and Formulas

What is capacitive reactance?

The capacitive reactance XC describes the resistance of a capacitor to alternating current. Unlike ohmic resistance, it is frequency-dependent and causes a phase shift between current and voltage.

Calculation formulas

Reactance
\[X_C = \frac{1}{2\pi fC}\]

The reactance can be calculated from frequency f and capacitance C.

Capacitance
\[C = \frac{1}{2\pi fX_C}\]

The capacitance is calculated from frequency f and reactance XC.

Frequency
\[f = \frac{1}{2\pi X_C C}\]

The frequency is derived from reactance XC and capacitance C.

Characteristic Properties

Frequency Dependence
  • f → 0: XC → ∞ (DC block)
  • f → ∞: XC → 0 (Short circuit)
  • Reciprocal proportionality: XC ∝ 1/f
  • Capacitance dependence: XC ∝ 1/C
Phase Behavior
  • Phase shift: φ = -90°
  • Current: Leads voltage by 90°
  • Power: Only reactive power (Q = UI)
  • Energy: Stored in the electric field

Practical Applications

Frequency Filters:
• Low-pass filter
• High-pass filter
• Band-pass filter
• Notch filter
Energy Storage:
• Power supplies
• Buffer capacitors
• Power supply
• Voltage smoothing
AC Coupling:
• Amplifier coupling
• DC decoupling
• Signal transmission
• Impedance transformation

Important Parameters

Reactance Properties
  • Unit: Ohm (Ω), like ohmic resistance
  • Complex representation: ZC = -jXC
  • Impedance: Magnitude of the complex resistance
  • Reactance: Imaginary part of the impedance
  • Loss factor: Real capacitors have additional ESR
  • Quality factor: Q = XC/ESR for real capacitors

Mathematical Relationships

Complex Representation
\[\underline{Z}_C = -j \cdot X_C\] \[|\underline{Z}_C| = X_C\]

Capacitive resistance in the complex plane

Angular Frequency
\[\omega = 2\pi f\] \[X_C = \frac{1}{\omega C}\]

Alternative representation with angular frequency ω

Related Functions

More Capacitor Calculations

Calculation Examples

Example 1: Reactance

Given: C = 10µF, f = 50Hz

\[X_C = \frac{1}{2\pi \cdot 50 \cdot 10 \times 10^{-6}} = 318.3\Omega\]

Result: The reactance is about 318Ω.

Example 2: Capacitance

Given: f = 1kHz, XC = 159Ω

\[C = \frac{1}{2\pi \cdot 1000 \cdot 159} = 1\mu F\]

Result: The required capacitance is 1µF.

Design Guidelines

Practical Considerations
  • Frequency range: Reactance is highly frequency-dependent
  • Tolerances: Capacitors often have large tolerances (±20%)
  • Temperature effect: Capacitance can be temperature dependent
  • Voltage rating: Observe maximum operating voltage
  • ESR: Real capacitors have additional series resistance
  • Self-resonance: Parasitic inductance at high frequencies

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Capacitor functions

Series connection with capacitors  •  Series connection with 2 capacitors  •  Reactance Xc of a capacitor  •  Time constant of an R/C circuit  •  Capacitor charging voltage  •  Capacitor discharge voltage  •  R/C for the charging voltage  •  Series circuit R/C  •  Parallel circuit R/C  •  Low pass-filter R/C  •  High pass-filter R/C  •  Integrator R/C  •  Differentiator R/C  •  Cutoff-frequency R,C  •  R and C for a given impedance  •