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): 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 initial charge voltage.

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: The time constant

is related to the RC circuit's cutoff frequency fc, by or, equivalently, where resistance in ohms and capacitance in farads yields the time constant in seconds or the cutoff frequency in hertz (Hz).

: Other useful equations are: In more complicated circuits consisting of more than one resistor and/or capacitor, the open-circuit time constant method provides a way of approximating the cutoff frequency by computing a sum of several RC time constants.

When the feature size becomes smaller and smaller to increase the clock speed, the RC delay plays an increasingly important role.

Charge spreads by diffusion in such a wire, as explained by Lord Kelvin in the mid nineteenth century.

[2] Until Heaviside discovered that Maxwell's equations imply wave propagation when sufficient inductance is in the circuit, this square diffusion relationship was thought to provide a fundamental limit to the improvement of long-distance telegraph cables.

That old analysis was superseded in the telegraph domain, but remains relevant for long on-chip interconnects.