9.2 LR Time Constant

Last week we began Module 9, "Relationships of Current, Counter EMF, and Voltage in LR Circuits." These modules are part of the Navy Basic Electricity and Electronics series from the 1970s.

9.1 Rise and Decay of Current and Voltage

1. The second unit for this week is called "LR Time Constant." L of course stands for inductance and R for resistance. "In a purely resistive circuit, current reaches its maximum value the instant the circuit is energized" (30). On the other hand, we have seen that inductance in a circuit creates a counter-EMF when a circuit is powered up, meaning that current will take a moment to reach its maximum value.

2. Now enter the notion of a "time constant." The time constant is defined as the inductance in henrys divided by the resistance in ohms, the result of which is in time.

TC = L/R

As it turns out, this constant approximates one fifth of the amount it takes for an LR circuit to energize up to its full current value. So it takes a circuit five time constants to power up. For each passing time constant, a circuit will move 63.2% of its remaining current amount.

So the first TC period, the circuit will go from zero amps to 63.2% of its final amp value. Similarly, when powering down, a circuit will go from 100% to 36.8% of its maximum value. In the second TC period, it will power up 63.2% of its remaining amount or another 23.3% to 86.5% of its maximum value (or down to 13.5% its maximum value if it is decreasing).

From T2 to T3, it will reach 95% of its maximum (or 5% if de-energizing). From T3 to T4 it will reach 98% (or 2%). Then by T5 it will be approximately to its maximum (or zero if de-energizing).

3. The section ends here, but I can mention the mathematical basis for this peculiar set of percentages. The underlying formula from which 63.2% comes is (1 - 1/e).