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

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.

Integrated Publishing, Inc. |