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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