RC Time Constant

The RC time constant, denoted τ (lowercase tau), the time constant (in seconds) of a resistor–capacitor circuit (RC circuit), is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.:

τ = R C [seconds]

It is the time required to charge the capacitor, through the resistor, from an initial charge voltage of zero to approximately 63.2% of the value of an applied DC voltage, or to discharge the capacitor through the same resistor to approximately 36.8% of its final charge voltage. These values are derived from the mathematical constant e, where 63.2% ≈ 1 − e⁻¹ and 36.8% ≈ e⁻¹. The following formulae use it, assuming a constant voltage applied across the capacitor and resistor in series, to determine the voltage across the capacitor against time:

• Charging toward applied voltage (initially zero voltage across capacitor, constant V₀ across resistor and capacitor together) V₀ : V(t) = V₀ ( 1 − e^−t/τ)
• Discharging toward zero from initial voltage (initially V₀ across capacitor, constant zero voltage across resistor and capacitor together) V₀ : V(t) = V₀(e^−t/τ)

The time constant τ is related to the cutoff frequency, f_c, an alternative parameter of the RC circuit, by

τ = RC = 1 / 2 π f_c

where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in Hz.