RC circuits are normally referred to as RC charging circuits. The circuit consist of a resistor, or R, in series with a capacitor, or C. The result is a circuit where, once a supply voltage is applied, the voltage across the capacitor will slowly increase to the value of the power supply. The speed in which it reaches the value of the supply voltage is based on the RC time constant.
Find the source voltage, or "Vs," for the circuit. Refer to circuit diagrams or specifications. As an example, assume Vs is 120 volts.
Determine the RC time constant, or T, using the formula: T = R x C where the R stands for resistance and C stands for capacitor. Refer to the circuit diagram or specification to get the value of R and C for the RC circuit. For example, if R is 30 ohms and C is 15 microfarads, T is 450 microseconds: (30)(15)
Calculate the voltage in the RC circuit using the formula: V = Vs x (1-e^-t/T) where t is the time from when the supply voltage, Vs, is applied to the circuit. V will change with time until the circuit reaches steady state or until the capacitor is completely charged and V = Vs. Consider the example calculations below using Vs at 120-volts and T at 450 microseconds:
At t = 0 microsecond
e^-t/T = e^-0/450 = e^0 = 1
V = Vs x (1-e^-t/T) = 120 x (1-1) = 120 x 0 = 0
At t = 1 microsecond
e^-t/T = e^-1/450 = e^-0.0022 = 0.9978
V = Vs x (1-e^-t/T) = 120 x (1- 0.9978) = 120 x .0022 = 0.264 volts
At t = 100 microsecond
e^-t/T = e^-100/450 = e^-0.222= 0.801
V = Vs x (1-e^-t/T) = 120 x (1- 0.801) = 120 x 0.199 = 23.8 volts
At t = 1000 microsecond or 1 millisecond
e^-t/T = e^-1000/450 = e^-2.22= 0.108
V = Vs x (1-e^-t/T) = 120 x (1- 0.108) = 120 x 0.892 = 107 volts
As you can see, as t increases, V trends toward the steady state where V = Vs. In fact, as t increases, e^-t/T will get smaller and smaller and 1-e^-t/T will reach 0.99999 or effectively 1 where V = Vs = 120.
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