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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