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. $τ$ = 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 $τ$ is related to the cutoff frequency f_c, an alternative parameter of the RC circuit, by

$\tau = RC = \frac{1}{2 \pi f_c}$ .

or, equivalently,

$f_c = \frac{1}{2 \pi R C} = \frac{1}{2 \pi \tau}$

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%) $t_r \approx 1.4 \tau$

rise time (10% to 90%) $t_r \approx 2.2 \tau$

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

Organization	Time constant $τ$ in µs	Cutoff frequency f_c in Hz
RIAA	7958	20
RIAA, NAB	3183	50
—	1592	100
RIAA	318	500.5
—	200	796
—	140	1137
MC	120	1326
—	100	1592
MC	90	1768
RIAA	75	2122
FM	70	2274
NAB, PCM	50	3183
DIN	35	4547
—	25	6366
AES	17.5	9095
PCM	15	10610
RIAA	3.18	50000