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Fill in any two of \( f \), \( C \), \( X_C \) — the third is solved. \( R \) is optional: if provided, \( |Z| \) and \( \phi \) are computed as additional outputs. \( \phi \) can also be used as an input together with \( R \) to replace one of the three main variables.
A capacitor resists changes in voltage. At AC, this opposition is called capacitive reactance \( X_C \) and depends on both the capacitance and the signal frequency: \[ X_C = \frac{1}{2\pi f C} \] Where:
Unlike resistance, reactance is frequency-dependent: \( X_C \) decreases as frequency increases. At DC (\( f = 0 \)) a capacitor blocks current entirely — \( X_C \to \infty \). At very high frequencies it approaches a short circuit — \( X_C \to 0 \). This is the basis for using capacitors as high-pass or low-pass filter elements. In an LC circuit, resonance occurs at the frequency where \( X_C \) equals the inductive reactance — see the LC resonance frequency calculator.
Given any two of \( f \), \( C \), \( X_C \), the calculator solves for the third. The rearranged formulas are:
A real capacitor or RC circuit also has a series resistance \( R \). The total impedance magnitude and phase angle are: \[ |Z| = \sqrt{R^2 + X_C^2} \] \[ \phi = -\arctan\!\left(\frac{X_C}{R}\right) \] The phase angle \( \phi \) is always negative for a capacitor, meaning the current leads the voltage. It ranges from \( 0° \) (purely resistive, \( X_C \ll R \)) to \( -90° \) (purely capacitive, \( X_C \gg R \)).
If \( \phi \) and \( R \) are known instead of \( X_C \), the reactance can be recovered: \[ X_C = -R \cdot \tan(\phi) \]
More calculators: blog.hirnschall.net/tools/.
