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Lesson 4-2 RL Time Constant

RL Time Constant

\Before starting this module, you should be able to:

When you complete this module, you should be able to:

Explain self-inductance.
Define inductance in terms of induced voltage.
Cite the units of measure for inductance.

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Describe the equation for determining the time constant of a series RL circuit.
Calculate the L/R time constant of a circuit.
Explain the significance of the percentage value 63.2% while current is building through an RL circuit.
Explain why the build-up current of an inductor reaches its steady state the end of 5 time constants.
Calculate the build-up current through an inductor after a given number of time constants.
Explain the significance of the percentage value 63.2% while current is decaying through an RL circuit.
Explain why the decaying current of an inductor reaches a steady state at the end of 5 time constants.
Calculate the amount of decay current through an inductor after a given number of time constants.

L/R Time Constant

The time constant of a series RL circuit equal to the value of inductance divided by the resistance:

T = L / R

where

T = time constant in seconds
L = inductance in henries
R = resistance in ohms

The time constant for an RL circuit is nothing more than the value of the inductor divided by the value of the resistor..

You will also find the Greek letter t (tau) used as the math symbol for time constant. For instance:

t = L / R

What is the time constant of a series RL circuit where R = 1 kW and L = 1 mH?

Ans: 1 ms

RL Build-Up Curve

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.

RL Current Build-Up Table

T	i_L
0	0
1	0.632 x V_s/R
2	0.865 x V_s/R
3	0.950 x V_s/R
4	0.981 x V_s/R
5	0.992 x V_s/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 V_s / R with I_max.

V_s / R = I_max

Vs = 6 V
R = 100 W
L = 100 mH

Ans: T = 1 ms, i_L = 51.9 mA

Step 1

T = L / R
T = 100 mH / 100 W
T = 1 ms

Step 2
At the end of two time constants:

i_L = 0.865 x Vs/R
i_L = 51.9 mA

RL Decay Curve

Inductor current does not drop off at a steady rate. Rather, the rate of current decay is discharge is rapid at first, but slows considerably as the charge approaches zero.

During each time constant, the current decays 63.2% of the remaining distance to the minimum current level.

Inductor current decay is considered complete at the end of 5 time constants.

RL Current Decay Table

T	i_L
0	Vs/R
1	0.368 x Vs/R
2	0.135 x Vs/R
3	0.05 x Vs/R
4	0.019 x Vs/R
5	0.008 x Vs/R

This table shows how to calculate the decay 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 steady-state maximum current through a 1.2 H inductor is 12 A. When this inductor is switched from the power source to a 1 W resistor, what is the current at the end of 3 time constants.

Ans: i_L = 600 mA

Step 1

T = L / R
T = 1.2 s

Step 2
At the end of 3 time constants:
i_L = 0.05 x Vs / R, but remember that Vs / R = I_max:

i_L = 0.05 x 12 A
i_L = 600 mA

Author and Content Provider: David L. Heiserman
Publisher: SweetHaven Publishing Services

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