Time Constant 1/RC: Origin & Meaning

[akj_akj_akj]

where is this equation from?
what does it equal?

 

[chroot]

Well, presumably you're talking r as an electrical resistance, and c as an electrical capacitance. (Note that people ordinarily use the capital letters R and C for these quantities.) Also, you're not describing an equation, you're describing an expression.

The expression RC has units of seconds. It is known as the "time constant" of a circuit formed by a resistor and capacitor. Imagine giving this circuit a step input, perhaps from 0V to 1V. The time constant is the length of time needed for the circuit's step response to be within a factor of 1/e of its final value. The factor 1/e is around 37%. Thus, after one time constant, the output voltage is about 63% of its final value.

- Warren

 

[ogb p]

The time constant 1/RC is a term commonly used in electrical engineering and physics. It is derived from the equation for the exponential decay of a capacitor charging through a resistor, which is given by V(t) = V0 * e^(-t/RC). In this equation, V(t) represents the voltage across the capacitor at time t, V0 is the initial voltage, R is the resistance of the circuit, and C is the capacitance of the capacitor.

This equation is derived from the fundamental principles of circuit analysis and is used to understand and predict the behavior of circuits involving capacitors and resistors. It is also used in various applications such as filtering, signal processing, and time-domain reflectometry.

The time constant 1/RC has a unit of time and represents the time it takes for the voltage across the capacitor to reach 63.2% of its final value. It is equal to the product of the resistance and capacitance in the circuit, and its value can be adjusted by changing either of these parameters. The time constant is an important concept in understanding the behavior of circuits and is widely used in the design and analysis of electronic systems.