MM0704, Lesson 1
the coil. Each time, if the voltage across the coil is halved, the current increase would be halved. Theoretically, the
current would never reach maximum. For all practical purposes, however the voltage across the coil becomes zero, and
the current reaches a steady state. This increase of current through an inductor is very similar to the increase of voltage
across a charging capacitor
RL Time Constants. The rate of increase of current through a coil is directly proportional to the voltage across it and
indirectly proportional to the inductance. The larger the inductance, the smaller the rate of increase. Therefore, since it
must take longer for the current to reach maximum through a larger inductance, the time for the current to reach
maximum is proportional to the inductance in the circuit.
The maximum current is equal to the applied voltage divided by the resistance in the circuit. The greater the resistance,
the smaller the maximum current. Since it takes less time for the increasing current to reach a low value than it does to
reach a high value, the time required must be inversely proportional to the resistance in the circuit.
It may be shown that something else in the RL circuit could affect the time required for the current through the coil to
reach maximum. If the applied voltage is increased, the maximum current will be higher. This would appear to
increase the time required but, at the same time, the rate of increase would be greater, tending to shorten the time.
Thus, an increase in voltage would not affect the time required for the current to reach maximum value. It remains that
the only factors affecting the time required for the current to reach maximum are the resistance and the inductance in
the circuit.
In RC circuits, it was shown that both resistance and capacitance were directly proportional to the time required for
completion of the transient action. In a series RL circuit, on the other hand, inductance is directly proportional to the
transitory time, and resistance is inversely proportional. This relationship is shown in the following equation:
This value L/R represents a period of time proportional to the transitory time in the RL circuit and is like the product of
R and C in the RC circuit. Therefore, it is also termed a time constant. The relationship holds true when expressed in
the following units:
At the end of the first TC in a series RL circuit, the current will have reached 63.2 percent of its maximum value. At
the end of the second TC, the current will have increased to 86.5 percent of its maximum value; at the end of the third
TC, 95.1 percent; at the end of the fourth TC, 98.2 percent; and at the end of the fifth TC, 99.3 percent of its maximum
value.
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