RC time constant

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In an RC circuit, the value of the time constant (in seconds) is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e. <math>\tau</math> = R · C. It is the time required to charge the capacitor, through the resistor, to 63.2 (~ 63) percent of full charge; or to discharge it to 36.8 (~ 37) percent of its initial voltage. (Those values are derived from the mathematical constant e, specifically 1-e^-1 and e^-1 respectively.)

The time constant <math>\tau</math> is related the cutoff frequency f_c, an alternative parameter of the RC circuit, by

<math>\tau = R \cdot C = \frac{1}{2 \pi \cdot f_c}</math>.

or, equivalently,

<math>f_c = \frac{1}{2 \pi \cdot R C} = \frac{1}{2 \pi \cdot \tau}</math>,

Short conditional equations:

(f_c in Hz) = 159155 / (τ in µs)

(τ in µs) = 159155 / (f_c in Hz)

Other useful equations are:

rise time (20% to 80%) <math>t_r \approx 1.4 \tau</math>

rise time (10% to 90%) <math>t_r \approx 2.2 \tau</math>

Standard time constants and cutoff frequencies
for pre-emphasis/de-emphasis RC filters:

See also

• Time constant and exponential decay
• RC circuit and RL circuit
• Filter (signal processing) and transfer function
• Cutoff frequency and frequency response
• Emphasis, preemphasis, deemphasis
• High-pass filter, low-pass filter, band-pass filter

External links

• Conversion time constant <math> \tau </math> to cutoff frequency f_c and back
• RC time constantde:Zeitkonstante