Question

What is the time constant of an RC circuit?

Answer 1

The time constant (

τ) of an RC circuit, which stands for Resistor-Capacitor circuit, is a fundamental parameter that determines the rate at which the circuit charges or discharges. It is defined as the product of the resistance (

R) and the capacitance (

C) in the circuit:


=

⋅

τ=R⋅C

The time constant represents the time it takes for the voltage across the capacitor to charge or discharge to approximately 63.2% (1 - 1/e) of its final value in response to a step change in voltage.

For charging, the voltage across the capacitor (


V
C
    ​

) approaches the source voltage (

source
V
source
    ​

) according to the equation:



(

)
=

source
⋅
(
1
−

−

/

)
V
C
    ​

(t)=V
source
    ​

⋅(1−e
−t/τ
)

For discharging, the voltage across the capacitor decreases from its initial value (

0
V
0
    ​

) towards zero according to the equation:



(

)
=

0
⋅

−

/

V
C
    ​

(t)=V
0
    ​

⋅e
−t/τ

The time constant is crucial in understanding the behavior of RC circuits in various applications, such as signal filtering, time delay, and waveform shaping. It helps determine how quickly a capacitor charges or discharges in response to changes in the input voltage.