ch7-response of first-order rl and rc circuits

8/12/2019 CH7-RESPONSE OF FIRST-ORDER RL AND RC CIRCUITS

1/34

ECE 2132 CIRCUIT

ANALYSIS

Dr Hasmah Mansor

E2-2-13.1

[email protected]
mailto:[email protected]:[email protected]


2/34


3/34

CONTENTS

7.1 The Natural Response of an RLCircuit7.2 The Natural Response of an RCCircuit

7.3 The Step Response of RLand RCCircuits


4/34

7.1 The Natural Response of

an RLCircuit

RLcircuit RCCircuit


5/34

7.1 The Natural Response of

an RLCircuit

A first-order circuitmay be reduced to a

Thvenin (or Norton) equivalent connected toeither a single equivalent inductor or

capacitor.


6/34

7.1 The Natural Response

of an RLCircuit

An inductor connected toa Thvenin equivalent

An inductor connected to

a Norton equivalent


7/34


of an RCCircuit

An capacitor connected to

a Norton equivalent

An capacitor connected toa Thvenin equivalent


8/34


of an RLCircuit

The natural response is the currents and

voltages that exist when stored energy is

released to a circuit that contains noindependent sources.

Natural response of an RLcircuit

0,)()(

0

teitit

L

R


9/34


of an RLCircuit

The time constant of an RLcircuitequals the

equivalent inductance divided by the Thvenin

resistance as viewed from the terminals of theequivalent inductor.

R

L

Time constant for RLcircuit


10/34

Value of for tequalto integral multiples of


of an RLCircuit

t

e


11/34

A graphic interpretation of the

time constant of the RLcircuit


of an RLCircuit


12/34


13/34


of an RCCircuit

AnRCcircuit

After

Switching


14/34


of an RCCircuit

Initial capacitor voltage

0)0()0()0( vvvvv g


15/34

The time constant of an RCcircuitequals

the equivalent capacitance times the

Thvenin resistance as viewed from the terminalsof the equivalent capacitor.


of an RCCircuit

RC

Time constant for RCcircuit


16/34


17/34

The natural response of an RC circuit


of an RCCircuit


18/34


of an RCCircuit

Calculating the natural response of an RC

circuitcan be summarized as follows:

1. Find the initial voltage, V0, across thecapacitor.

2. Find the time constant of the circuit, = RC.

3. Use,v(t) = V0e-t/, t 0 togeneratev(t)fromV0

and.


19/34

Example 7.1The switch has been closed for a long time before it is opened at t=0. Find

a) iL(t) for t 0,

b) i0(t) for t 0+

,

c) v0(t) for t 0,

d) The percentage of the total energy stored in the 2H inductor that is

dissipated in the 10 resistor


20/34

Problem 7.4

The switch in the circuit has been closed for a long time before opening at t = 0.a) Find i1(0-) and i2(0-).

b) Find i1(0+) and i2(0+).

c) Find i1(t) for t 0.

d) Find i2(t) for t 0+

e) Explain why i2(0-

) i2(0+

)


21/34

Example 7.3

The switch in the circuit shown has been in positionxfor a long time. At t=0,the switch moves instantaneously to position y. Find

a) vc(t) for t 0,

b) v0(t) for t 0+,

c) i0(t) for t 0+,

d) The total energy dissipated in the 60 kresistor.


22/34

Problem 7.23The switch in the circuit has been in position a for a long time and v2= 0 V. At t = 0,

the switch is thrown to position b. Calculate

a) i, v1and v2for t 0+.

b) The energy stored in the capacitor at t = 0.

c) The energy trapped in the circuit and the total energy dissipated in the 5 k

resistor if the switch remains in position b indefinitely.


23/34


24/34


25/34

7.3 The Step Response of

RLand RCCircuits

Step response of RLcircuit


26/34

The step response of the RLcircuit whenI0= 0.


RLand RCCircuits


27/34

Inductor voltage versus time


RLand RCCircuits


28/34

A circuit used to illustrate the stepresponse of a first-order RCcircuit


RLand RCCircuits


29/34

Step response of an RCcircuit


RLand RCCircuits

0,)( 0

teRIVRIv RCt

sSc


30/34

Example 7.6

The switch in the circuit shown has been in position 1 for a long time. At t = 0,

the switch moves to position 2. Find

a) v0(t) for t 0 and

b) i0(t) for t 0+.


31/34

Problem 7.83The voltage signal source in the circuit is generating the signal shown in (b).

There is no stored energy at t = 0.

a) Derive the expression for v0(t) that apply in the intervals t < 0; 0 t 4ms;

4ms t 8ms; and 8ms t infinity.

b) Sketch v0and vson the same axes.


32/34

Example 7.12The uncharged capacitor in the circuit is initially switched to terminal a. At t=0,

the switch is moved to position b, where it remains for 15 ms. After 15 ms

delay, the switch is moved to position c where it remains indefinitely.

a) Derive the expression for v(t).

b) Plot v(t) versus t.

c) When will the voltage on the capacitor equal to 200 V?


33/34


34/34

END OF CHAPTER 7

ch7-response of first-order rl and rc circuits

Documents