is 20 usec, 99.9 percent of the steadystate value is reached in 140
usec or 7 time constants. If the time constant is 50 usec, 99.9
percent of the steadystate value is reached in 350 usec. At the end
of 7 time constants, the voltage across the capacitor always equals
99.9 percent of the steadystate value, regardless of the value of
the time constant.
12.
EFFECT OF VARYING R AND C.
a. The larger the capacitance, the larger is the amount of charge
necessary for the voltage drop across the capacitor to reach the
applied voltage. Increasing the capacitance increases the time
required to reach a steadystate condition, thereby increasing the
time constant. Decreasing the capacitance decreases the time
constant.
b. Since the capacitor must charge through the resistor,
increasing the value of the resistance decreases the charging current
in the circuit, and, therefore, increases the time required for the
capacitor to charge. Increasing the value of R, therefore, increases
the time constant. Decreasing the value of R increases the charging
current in the circuit, and, therefore, decreases the time required
for the capacitor to charge. Decreasing the value of R, therefore,
decreases the time constant.
c. Circuits with the same time constants require the same period
of time to reach the steadystate condition. For example, if C is
equal to 0.001 uf and R is equal to 10,000 ohms, the time constant is
equal to 10 usec. If the capacitance is decreased to 0.0001 uf and
the resistance is increased to 100,000 ohms, the time constant is
still 10 usec. In both cases, 7 time constants or 70 usec are
required to reach the steadystate condition.
UNIVERSAL RC TIME CONSTANT CHART
a. When a positive step voltage is applied to a series RC
circuit, it is possible to determine the values of It, ER, and EC
through the use of the universal time constant chart (Figure 20).
The horizontal axis is plotted in time constants. The vertical axis
is plotted in terms of relative voltage or current, where 100 percent
corresponds to the applied voltage or maximum attainable current.
The rising Curve A represents the charging of the capacitor. Curve B
represents the current flowing in the circuit and voltage appearing
across the resistor.
b. The following discussion illustrates how the time constant
chart can be used. In a series RC circuit, if C is equal to 1000
uuf, R is equal to 10,000 ohms, and the applied voltage is equal to 1
volt, 1 time constant is equal to 10 usec, and the voltage drop
across the capacitor will reach 63.2 percent of the
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