The curves for ER and It are identical to Curve B, but opposite in
polarity. At the end of 1 time constant, the capacitor voltage has
decreased to 36.8 percent of its maximum value, while ER (which is
the negative value of Ec) has decreased the same amount and It has
decreased proportionately. The reduced current flow causes less
charge to be drawn from the capacitor and the rate of discharge
decreases. After five time constants, the rate of change of Ec, ER,
and It is small. It can be seen that the Ec, ER, and It curves
change gradually as they did when the positive step was applied.
Section IV. TIME CONSTANTS
11.
THEORY OF RC TIME CONSTANTS.
a. An RC time constant is the time required for the capacitor
voltage, in a series RC circuit, to reach 63.2 percent of the applied
or steadystate voltage. 1 time constant, in addition to
representing the time required for the capacitor to charge to 63.2
percent of the applied voltage, also represents the time required for
the voltage across the resistor and the current in the circuit to
fall to 36.8 percent of their maximum values. During the second time
constant, the capacitor voltage will increase to 63.2 percent of the
remaining 36.8 percent (100 percent 63.2 percent) or 86.4 percent
of its maximum value, and the voltage across the resistor and the
current in the circuit will fall to 36.8 percent of their remaining
36.8 percent, or 13.6 percent of their maximum values. During each
succeeding time, constant Ec will increase to 63.2 percent of its
remaining value, while ER and It will decrease to 36.8 percent of
their remaining values. The formula for computing an RC time
constant is TC = RC, where R is in ohms, C is in farads, and the time
constant is in seconds. For example, if C is equal to 1,000 uuf and
R is equal to 10,000 ohms, the time constant is equal to 0.001 x 106
x 104 or 10 usec. When the time constant is short, the capacitor
charges rapidly to its steadystate value. When the time constant is
long, the capacitor charges slowly to its steadystate value.
b. Figure 20 indicates that, after 7 time constants, the
capacitor has charged to 99.9 percent of its maximum value. The
period of time required for any capacitor in a series RC circuit to
charge to 99.9 percent of the steadystate value can be expressed in
terms of the time constant. If the time constant of a circuit
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