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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