Electrical

1. RC circuit used to produce time constants

RC circuit

A resistor-capacitor circuit (RC circuit) is an electric circuit gather of resistor and capacitor driven by a voltage or current source. It will be in the form of circuit if consists of one resistor and one capacitor. RC circuits are usually used to filter signal waveform, altering the proportional amount of low frequency and high frequency information in their output signal proportional to their input signal. There couple of type of filters which are low-pass filter and high-pass filter and band-pass filters too. The exact purpose of it is for smoothing a signal. To calculate the time constant of the RC circuit is by t=RC, while for fully charged or discharge is t=5RC. Just at the start of charging, potential difference across capacitor is zero, therefore putting Vc=0, eventually gets:- V=CR dv/dt Initial rate of rise of voltage across the capacitor is = (dv/dt) = V/CR = V/λ volt/second. If this rate of rise is maintained, then time taken to reach voltage (V) would have been V+V/CR=CR. This time is known as time constant (λ) of the circuit. Hence, time constant of an R-C circuit is defined as the time during which voltage across capacitor would have reached its maximum value (V) had it maintained its initial rate of rise.

Example in an equation if t=λ, then

Vc=V(1-℮^(-t⁄λ) )=V(1-℮^(-t⁄λ) )=V(1-℮^(-1) )=V[1-1/℮]=V[1-1/(2.718)]=0.632 V

Hence, time constant may be defined as the time during which capacitor voltage actually rises to 0.632 of its final steady value. In another example equation, by putting t=λ, gets

i_c=I_0 ℮^((-λ)⁄λ)=I_0 ℮^(-1)=I_0/2.718≅0.368

Hence, the constant of a circuit is also the time during which the charging current falls to 0.37 of its initial maximum value (or falls by 0.632 of its initial value).

Since the overcome voltage and the values of R and C in a circuit known as universal time constant chart (Figure 1) can be used to find the time constant of the circuit. Curve A is a...