Effect on Time Constant of Varying L and R

Timing Circuits
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remaining 3.68 volts or 1.36 volts. Using this same method, the

value of It at the end of 30 usec (three time constants) is found to

be 9.5 mA, ER is 9.5 volts, and EL is 0.5 volts. This process may be

repeated for any number of time constants.

b. The period of time required for the current in any RL circuit

to rise to 99.9 percent of the steadystate value is found to be

equal to 7 time constants. If the time constant is 10 usec, 99.9

percent of the steadystate value is reached in 70 usec or 7 time

constants later. If the time constant is 50 usec, 99.9 percent of

the steadystate value is reached in 350 usec, again 7 time constants

later. Regardless of the value of the time constant, 7 time

constants will always represent the time required for the current to

reach 99.9 percent of the steadystate value. When the time

constant is short, the current rises rapidly to its steadystate

value. When the time constant is long, the current rises slowly to

its steadystate value.

EFFECT ON TIME CONSTANT OF VARYING L AND R.

a. Varying L only. Inductance in a circuit prevents the current

from rising immediately to its steadystate value. The larger the

inductance, the greater the opposition to a change in current, and

the longer the period of time required to reach the steadystate

value. Increasing the value of L, therefore, increases the time

constant. Decreasing the value of L decreases the time constant.

b. Varying R only. If the value of the resistance is increased

without varying the inductance, the steadystate is reached in a

shorter period of time. Increasing the value of R decreases the

maximum value of current in the circuit. Since the rate of current

increase remains the same, the steady state will be reached in a

shorter period of time, thus decreasing the time constant of the

circuit. Decreasing the value of R increases the time constant.

c. Effect of varying R and L proportionately. Circuits with the

same time constants require the same period of time to reach the

steadystate condition. For example, if L is equal to 10 mH and R is

equal to 1,000 ohms, the time constant is equal to 10 usec. If the

values of L and R are doubled so that the values increase to 20 mH

and 2,000 ohms respectively, the time constant remains 10 usec. In

both cases, 70 usec or 7 time constants are required to reach the

steadystate condition.

UNIVERSAL TIME CONSTANT CHART.

a. When a step voltage is applied to a series RL circuit, it is

possible to determine the values of It, ER, and EL through