The time required to charge a capacitor to
63 percent (actually 63.2 percent) of full charge or to
discharge it to 37 percent (actually 36.8 percent) of its
initial voltage is known as the TIME CONSTANT (TC) of the
circuit. The charge and discharge curves of a capacitor are
shown in figure 3-11. Note that the charge curve is like the
curve in figure 3-9, graph (D), and the discharge curve like
the curve in figure 3-9, graph (B).
Figure 3-11. - RC time constant.
The value of the time constant in seconds is equal to the
product of the circuit resistance in ohms and the circuit
capacitance in farads. The value of one time constant is
expressed mathematically as t = RC. Some forms of this
formula used in calculating RC time constants are:
Q.14 What is the RC time constant of a series RC circuit
that contains a 12-megohm resistor and a 12-microfarad
capacitor?
UNIVERSAL TIME CONSTANT CHART
Because the impressed voltage and the values of R and C or R
and L in a circuit are usually known, a UNIVERSAL TIME
CONSTANT CHART (fig. 3-12) can be used to find the time
constant of the circuit. Curve A is a plot of both capacitor
voltage during charge and inductor current during growth.
Curve B is a plot of both capacitor voltage during discharge
and inductor current during decay.
Figure 3-12. - Universal time constant chart for RC and RL
circuit.
The time scale (horizontal scale) is graduated in terms of
the RC or L/R time constants so that the curves may be used
for any value of R and C or L and R. The voltage and current
scales (vertical scales) are graduated in terms of
percentage of the maximum voltage or current so that the
curves may be used for any value of voltage or current. If
the time constant and the initial or final voltage for the
circuit in question are known, the voltages across the
various parts of the circuit can be obtained from the curves
for any time after the switch is closed, either on charge or
discharge. The same reasoning is true of the current in the
circuit. |