counter emf in the inductor which acts as the source of voltage in

the circuit. EL is now equal to ER (Figure 17D), but opposite in

polarity. Since the counter emf of the inductor opposes any change

in current flow in the circuit, current continues to flow in the same

direction as it did when the applied voltage was present.

b. At the instant the applied voltage falls to zero, EL becomes

equal to its maximum value but opposite in polarity (Figure 17E).

The current and, therefore, ER are at their maximum values. As the

counter emf of the inductor gradually decreases to zero, the current

and the voltage across the resistor decrease in exactly the same

manner. This decrease is rapid at first, but gradually declines

until, at the end of five time constants, the rate of decrease is

practically zero.

Section II. RL TIME CONSTANTS

5.

THEORY OF RL TIME CONSTANTS.

a. An RL time constant can be defined as the time requited for

the current flowing through an RL circuit to increase to 63.2 percent

of its maximum value. The formula for an RL time constant is TC =

L/R, where TC represents the time constant in seconds, L represents

the inductance in henries, and R represents the resistance in ohms.

The ratio L/R also represents the time required for the voltage

across the resistor to rise to 63.2 percent of the applied voltage,

and the time required for the voltage across the inductor to fall to

36.8 percent of the applied voltage. (These values are determined by

detailed mathematical calculations. However, since these

calculations do not necessarily increase one's understanding of

practical RL circuit response, they are not included in this text.)

For example, if L is equal to 10 mH and R is equal to .1,000 ohms,

the TC is equal to 10 x 103/103 or 10 usec. If the applied voltage

is 10 volts, then the maximum current in the circuit is equal to 10

volts/l,000 ohms or 10 mA. 10 usec (1 time constant) after the

voltage is applied to the circuit, It is equal to 6.32 mA, ER is

equal to 6.32 volts, and EL is equal to 3.68 volts. At the end of 20

usec (two time constants), It will have increased to 63.2 percent of

the remaining 3.68 mA (10 mA 6.32 mA) or a total of 8.64 mA. ER

will have increased to 8.64 volts, and EL will have decreased to 36.8

percent of the

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