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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 ...
The time required for the voltage to fall to V 0 / e is called the RC time constant and is given by, [1] τ = R C . {\displaystyle \tau =RC\,.} In this formula, τ is measured in seconds, R in ohms and C in farads.
Similarly, in an RC circuit composed of a single resistor and capacitor, the time constant (in seconds) is: = where R is the resistance (in ohms ) and C is the capacitance (in farads ). Electrical circuits are often more complex than these examples, and may exhibit multiple time constants (See Step response and Pole splitting for some examples.)
The constant = is called the relaxation time or RC time constant of the circuit. A nonlinear oscillator circuit which generates a repeating waveform by the repetitive discharge of a capacitor through a resistance is called a relaxation oscillator.
For a simple one-stage low-pass RC network, [18] the 10% to 90% rise time is proportional to the network time constant τ = RC: t r ≅ 2.197 τ {\displaystyle t_{r}\cong 2.197\tau } The proportionality constant can be derived from the knowledge of the step response of the network to a unit step function input signal of V 0 amplitude:
Figure 1: Simple RC circuit and auxiliary circuits to find time constants. Figure 1 shows a simple RC low-pass filter. Its transfer function is found using Kirchhoff's current law as follows. At the output, = , where V 1 is the voltage at the top of capacitor C 1. At the center node:
In the case of AM, φ(t) (the phase component of the signal) is constant and can be ignored. In AM, the carrier frequency is also constant. Thus, all the information in the AM signal is in R(t). R(t) is called the envelope of the signal. Hence an AM signal is given by the function
An RC circuit sets the output pulse's duration as the time in seconds it takes to charge C to 2 ⁄ 3 V CC: [16] = (), where is the resistance in ohms, is the capacitance in farads, is the natural log of 3 constant.