1. Basic Electronics Ninth Edition Grob Schultz
©2002 The McGraw-Hill Companies

2. RC and L/R Time Constants
Basic Electronics
Ninth Edition 23
CHAPTER
RC and L/R Time Constants
©2003 The McGraw-Hill Companies

3. Topics Covered in Chapter 23
High Voltage Produced by Opening an RL Circuit
RC Time Constant
RC Charge and Discharge Curves
High Current Produced by Short-circuiting RC Circuit
RC Waveshapes

4. Topics Covered in Chapter 23
(continued)
Long and Short Time Constants
Charge and Discharge with Short RC Time Constant
Long Time Constant for RC Coupling Circuit
Universal Time Constant Graph
Comparison of Reactance and Time Constant

5. Transient Response of an Inductor
The transient response of an inductor has a time constant T = L / R.
T is in seconds
L is in henries
R is in ohms
The time (T) required for a change in current of 63 % is one time constant, T.
Inductor current reaches its steady-state value in five time constants.

6. Transient Response of an Inductor (charge)10 L
1 H 8
10 V 6 R
1 kW
iC in mA 4 2
T = L/R = 1/1 x 103 = 1 ms
ISS = 10 V/1 kW = 10 mA
T in ms
Steady state circuit current (ISS) = 10 mA

7. Interrupting Inductor Current
The instant an inductive circuit is opened, a high voltage is generated across the inductor.
Opening the circuit causes a rapid decrease in current.
In an inductive circuit, the faster the rate of change of current, the higher the amount of induced voltage: vL = L(di/dt).

8. Interrupting Current Flow in an Inductive Circuit
Large di/dt generates a very high voltage.

9. Shorting a Charged Capacitor
The instant a charged capacitor is shorted with a very low resistance, considerable discharge current flows through the short.
Shorting the capacitor causes a rapid decrease in capacitor voltage.
In a capacitor circuit, the faster the rate of change of voltage, the higher the amount of current: iC = C(dv/dt).

10. Shorting a charged capacitor
With large capacitors,
this can be dangerous!

11. Transient Response of a Capacitor
The transient response of a capacitor has a time constant T = RC.
T is the time in seconds
C is the capacitance in farads
R is the resistance in ohms
The time required for a change in voltage of 63 % is one time constant, T.
Capacitor voltage reaches its steady-state value in five time constants.

12. Transient Response of a Capacitor (charge)10
1 kW 8 R
10 V 6
1 mF C
vC in Volts 4
Initial charge = 0 V 2
T in ms
T = RC = 1 x103 x 1 x 10-6 = 1 ms

13. Transient Response of a Capacitor (discharge)10 8
1 kW R 6
vC in Volts
1 mF C 4 2
Initial charge = 10 V
T in ms
T = RC = 1 x103 x 1 x 10-6 = 1 ms

14. Short Time Constants
A short time constant is 1/5 or less of the pulse width of the applied voltage.
RC Circuits: Produces sharp voltage spikes for vR and rounded edges for vC at the leading and trailing edges of an applied rectangular wave.
L/R Circuits: Produces rounded edges for vR and sharp voltage spikes for vL.

15. Short Time Constant in an RC CircuitVS
1 kW R VS
100 Hz
1 mF C vC
Pulse width = 5 ms
T = RC = 1 ms vR

16. Long Time Constants
A long time constant is 5 or more times longer than the pulse width of the applied voltage.
RC Circuits: vR is very nearly the same as the applied waveform, and the capacitor blocks the average dc level of the applied waveform.
L/R Circuits: vR resembles the average dc level of the applied waveform.

17. Long Time Constant in an RC CircuitVS
1 kW R VS
2.5 kHz
1 mF C vC
Pulse width = 0.2 ms
T = 1 ms vR

18. Output Waveshapes With long time constants: With short time constants:
vC and iL rise slowly to the steady-state value.
The output waveform is said to be integrated.
With short time constants:
vC and iL rise rapidly to the steady-state value.
The output waveform is said to be differentiated.

19. Integrators and DifferentiatorsVS
vOUT
vOUT C
Integrators use a relatively long time constant. C
vOUT VS R
vOUT
Differentiators use a relatively short time constant.

20. Universal Time Constant Graphs
Rising curve:
Value increases 63% with each time constant.
Can represent:
Capacitor charging voltage, vC
Rising inductor current, iL
Falling curve:
Value decrease 63% with each time constant.
Can represent:
Capacitor discharging voltage, vC
Decaying inductor current, iL

21. Universal Rising CurveT
0.5
39.3 %
1.0
63.2 %
1.5
77.7 %
2.0
86.5 %
2.5
91.8 %
3.0
95.0 %
3.5
97.0 %
4.0
98.2 %
4.5
98.9 %
5.0
99.3 %
100 %
80 %
60 %
40 %
20 %
0 % T

22. Universal Falling CurveT
100 %
0.5
60.7 %
1.0
36.8 %
1.5
22.3 %
2.0
13.5 %
2.5
8.21 %
3.0
4.98 %
3.5
3.02 %
4.0
1.83 %
4.5
1.11 %
5.0
0.674 %
100 %
80 %
60 %
40 %
20 %
0 % T