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AC Components and Circuits

Section 1-6 The L/R Time Constant

The L/R Time  Constant


When switch S is open, there can be no current flowing through the circuit. The entire source voltage, VT, is across the open switch contacts--there is no voltage across R and L.

The instant the switch is closesthe very instant--there is still virtually no current flow through the circuit, and the full source voltage shifts from  the switch to the inductor. There is, at that instant, no voltage across R.

As time passes, the energy from the source  begins to shift from the inductor and to the resistor. As a result, the voltage across the inductor drops and the resistor increases. As long as the switch remains closed, VR + VL = VT.  Also, the current through the circuit is  increasing.

After a certain length of time, there is no longer any voltage  across the inductor, and the full  amount  of  source voltage can be found across the resistor.


Energy stored in the inductor's magnetic field is  W =


Energy converted to heat in the resistor is P = I2R


Time Constant of a Series RL Circuit

t =



= time constant in Seconds
L = inductance
R = resistance
t is the Greek letter "tau." Think of it as t for time.


Current through the inductor in an RL circuit does not increase at a steady rate. Rather, the rate of increase is rapid at first, but then slows as it reaches the maximum level.

During each time constant, the current builds 63.2% of the remaining distance to the maximum current level.



Inductor current build-up is considered complete at the end of 5 time constants.







0.632 x Vs/R


0.865 x Vs/R


0.950 x Vs/R


0.981 x Vs/R


0.992 x Vs/R

This table shows how to calculate the build-up current through an inductor at the end of each time constant. 

T = number of time constants that have passed in seconds
Vs = voltage of the DC source in volts 
R = value of the series resistor in ohms 

 The ratio Vs / R is actually an expression of Ohm's Law for maximum current through the circuit. You can always replace the ratio Vs / R with Imax

Vs / R = Imax





Charge curve for an R/L circuit

vC = VT(1 etR/L)


Discharge curve  for an R/L  circuit

vC = VT etR/L








David L. Heiserman, Editor

Copyright   SweetHaven Publishing Services
All Rights Reserved

Revised: June 06, 2015