Mapua Institute of Technology
School of EECE
Department of Electrical Engineering
Experiment No. 8
FORCED AND NATURAL RESPONSE OF RL CIRCUITS WITH DC
EXCITATION
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Huerte, Leo Francis A.
CPE - 2
EE101L/B7
_Engr. Ronaldo C. Cabuang_
Professor
18 - 3 18 - 3
GRADE
WIRING DIAGRAM
TinaPro schematic diagram of RL Circuit
FINAL DATA SHEET
Experiment 8: Forced and Natural Response of RL circuits with DC excitation
Name: Huerte, Leo Francis A. Date: September 3, 2014
Crs/Sec: EE101L/ B7 Group no: 3
Table 8.1 Charging (Complete response)
TIME (ms) CURRENT (A)
30.81 256.7
68.66 488.86
84.51 562.64
132.04 735.63
172.54 826.24
235.04 915.32
261.44 936.12
286.09 953.19
320.42 967.88
355.63 979.03
394.37 987.14
419.84 990.26
470.45 994.79
Table 8.2 Discharging (Natural response)
TIME (ms) CURRENT (A)
8.80 902.73
36.97 762.91
49.30 701.59
84.51 526.28
98.59 466.74
140.85 309.79
163.73 252.70
191.02 185.59
223.59 134.79
251.76 98.20
291.37 61.66
320.42 45.80
389.96 19.52
Approved by:
Engr. R. C. Cabuang
Instructor
GRAPHS / CURVES
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CHARGING (Complete Response)
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CHARGING & DISCHARGING of RC Circuit
CHARGING
DISCHARGING
TinaPro output waveform of RL Circuit
DATA ANALYSIS / INTERPRETATION OF RESULTS
Experiment 8 deals with the forced and natural response of RL (resistance
inductor) circuits with DC (direct current) excitation. In this experiment an element
called inductor was used to obtain the result of the use of RL circuit. Also, the software
TINAPro was utilized to perform the experiment.
Like a capacitor, an inductor stores a finite amount of energy. It also resists an
abrupt change in the current through it. Charging the inductor means storing current into
it. Note that even if the voltage of the inductor is zero, energy can still be stored in it
because it acts as a short-circuit in a DC.
Table 8.1 shows the complete response of charging an inductor where as time
increases, the current (in A) also increases. But at time=235.04 ms, the current is almost
915.32 A up to time=470.45 ms where the current stays at 900+ A range, 994.79 to be
exact. This means that approximately 235.04 ms is the time when the inductor will be
fully charged having a maximum current of 900+ A range. Mathematically, the time
when the inductor will be fully charged is equal to 5 where =L/R . After 5 or at an
infinite time, there would be constant current but no voltage, meaning, the inductor will
act as a short-circuit in DC. However, at time=0, there is voltage but no current and so, it
is considered as an open-circuit in DC.
If one switch is turned off such that no current flows through a resistor, the
inductor can supply energy to it provided that it has been charged earlier. In table 8.1, we
can see that as time increases, the current (in A) decreases until the current is zero.
Having a zero current means that the current in the inductor is already drained. And so,
the resistor will stop working.
This experiment also observes the responses of a DC excited RL circuit. Natural
response corresponds to the transient response of the circuit from time 0 to 5 . And the
forced response corresponds to the steady-state response of the circuit after 5 . The
combination of natural and forced responses corresponds to the complete responses of a
dynamic RL circuit.
It can be noticed that the graph of the capacitance and inductance are the same, it
is for the reason that both have almost the same characteristics and both are energy
storing devices.
For this experiment, the circuit below was used:
CONCLUSION
Experiment 8, forced and natural response of RL circuits with DC excitation, an
inductor was used in the circuit connection. Inductor is basically a length of wire
wounded into a coil that concentrates magnetic field around a given core. It stores a finite
amount of energy in a magnetic field produced by a current through a wire coil.
Based on the graph of the inductor with respect to the current and time it can be
therefore conclude that in charging response, current, I, is directly proportional to time, t
or I < t. while, when in discharging response, current, I, is inversely proportional to time,
t or I < 1/t.
Furthermore, based on the data gathered it can be therefore conclude that an
inductor, when connected to a direct current supply, is considered short circuit to a direct
current wherein the time is equal to infinity. Also a finite amount of energy can be stored
in an inductor even if the inductor voltage across it is zero. An inductor can also resist an
abrupt change in the current through it (proven in the graph). In the graph, it can be seen
that before the peak voltage of the charging response is reach, the capacitor need some
time to reach it, same goes in the discharging response.
Lastly, an inductor is also similar to capacitor since it also demonstrates some of
the characteristics of a capacitor wherein when connected to a dc supply, inductor never
dissipates energy but only stores it.
The figure below is a simple RL Circuit;
ANSWER TO QUESTION AND PROBLEM
1. What are the factors governing inductance?
NUMBER OF TURNS IN THE COIL- the inductance can be increased by
increasing the number of turns of coil.
COIL CROSS-SECTIONAL AREA- increasing the cross- sectional area will
increase the inductance.
COIL LENGTH- reducing the length of the coil will increase the inductance.
PERMITIVITY OF THE MATERIAL- using material with higher permeability
as the core will make the inductance increase.
2. What are the characteristics of the inductor when connected a DC source?
An inductor exhibits the following characteristics when connected to a dc supply:
An inductor is considered short-circuit to dc ( t = ).
A finite amount of energy can be stored an inductor even if the inductor voltage is
zero.
An inductor resists an abrupt change in the current through it.
The inductor never dissipates energy but only stores it.
3. What are the basic applications of an RL circuit?
The frequency-dependent behavior of the series RL circuit can be very useful.
Consider what would happen if a complex audio signal, such as music or speech were
applied to a series RL circuit. The signal appearing across R would contain primarily the
lowest frequency components. If we took our output across R, the RL circuit would
behave like a low-pass filter.
4. Define the time constant of an RL circuit.
The time constant of an RL circuit is an exponential decay of the initial current. It
could be obtained by getting the quotient of the inductance divided by the resistance.
5. Discuss briefly the different types of inductors.
Coupled Inductors
- exhibit magnetic flux that is dependent on other conductors to which they are linked
- used when mutual inductance is needed
Multi-Layer Inductors
- consists of a layered coil, wound multiple times around the core
- have a high inductance level.
Ceramic Core Inductors
- unique in having a dielectric ceramic core, meaning it cannot store a lot of energy but has
very low distortion and hysteresis
Molded Inductors
- molded using plastic or ceramic insulation
- often used in circuit boards, they can assume either a cylindrical or bar formation, with
windings featuring terminations at each end
6. Determine the equivalent inductance when a 10mH inductor is placed in parallel with
series connected 12mH and 3mH inductors.
GIVEN:
Series: 12 mH and 3 mH
Parallel: 10 mH with 12 mH and 3 mH
SOLUTION:
equivalent inductance =
( )( )
7. Find the equivalent inductance when series connected 40mH and 150mH inductors are
connected in parallel with series connected 0.1H and 0.12H inductors.
GIVEN:
Series: 40 mH and 150 mH; 0.1 H and 0.12 H
Parallel: 40 mH and 150 mH with 0.1 H and 0.12 H
SOLUTION:
equivalent inductance =
(
)( )
8. Determine the time constant of an RL circuit with a resistance R=20 Ohms and a 500mH
inductor connected in series with a 10V DC source.
GIVEN:
R = 20 |
equivalent inductance = ^6 mH
equivalent inductance = ^.102 H
L = 500 mH
SOLUTION:
=
9. Determine the time constant of an RL circuit with a resistance R=1.5K and a 220mH
inductor connected in parallel with a 25V DC source.
GIVEN:
R = 1.5 K|
L = 220 mH
SOLUTION:
=
= 0.025 s
= 0.147 s
