Contact Us - Tell A Friend - Free-Ed.Net Home  

AC Components and Circuits
Inductance

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 closes�the 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, V_R + V_L = V_T.  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 converted to heat in the resistor is P = I²R

Equation Time Constant of a Series RL Circuit   t = L R Where: 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.

 

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

 

T	iL
0	0
1	0.632 x Vs/R
2	0.865 x Vs/R
3	0.950 x Vs/R
4	0.981 x Vs/R
5	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 V_s / R is actually an expression of Ohm's Law for maximum current through the circuit. You can always replace the ratio Vs / R with I_max. 

Vs / R = Imax

 

 

Examples

 

Charge curve for an R/L circuit

v_C = V_T(1 � e^�tR/L)

 

Discharge curve  for an R/L  circuit

v_C = V_T e^�tR/L