ECEN 301Discussion #6 – Things Practical1 DateDayClass No. TitleChaptersHW Due date Lab Due date...
-
date post
19-Dec-2015 -
Category
Documents
-
view
221 -
download
0
Transcript of ECEN 301Discussion #6 – Things Practical1 DateDayClass No. TitleChaptersHW Due date Lab Due date...
Discussion #6 – Things PracticalECEN 301 1
Date Day ClassNo.
Title Chapters HWDue date
LabDue date
Exam
22 Sept Mon 6 Things Practical 2.6 – 2.8 LAB 2
23 Sept Tue
24 Sept Wed 7 Network Analysis 3.1 – 3.3
25 Sept Thu LAB 2
26 Sept Fri Recitation HW 3
27 Sept Sat
28 Sept Sun
29 Sept Mon 8 Equivalent Circuits 3.4 – 3.5
NO LAB
30 Sept Tue
Schedule…
Discussion #6 – Things PracticalECEN 301 2
Spiritual – Temporal1 Nephi 15:3232 And it came to pass that I said unto them that it was a
representation of things both temporal and spiritual; for the day should come that they must be judged of their works, yea, even the works which were done by the temporal body in their days of probation.
Mosiah 2:4141 And moreover, I would desire that ye should consider on the
blessed and happy state of those that keep the commandments of God. For behold, they are blessed in all things, both temporal and spiritual; and if they hold out faithful to the end they are received into heaven, that thereby they may dwell with God in a state of never-ending happiness. O remember, remember that these things are true; for the Lord God hath spoken it.
Discussion #6 – Things PracticalECEN 301 3
Lecture 6 – The Wheatstone Bridge
An Applications of Things Electrical
Discussion #6 – Things PracticalECEN 301 4
Wheatstone Bridge
A circuit used to find: An unknown resistance Rx
The unknown voltage vab
Another unknown value (such as a force)
vs+_
R2
R1 R3
Rx
bava vb
c
d
cR1
vs+_
R3
R2 Rx
d
a bvavb
Discussion #6 – Things PracticalECEN 301 5
Wheatstone Bridge The circuit consists of the parallel combination of 3
subcircuits with the same voltage:a) The voltage sourceb) Series combination of R1 and R2
c) Series combination of R3 and Rx
Voltage divider between:a) R1 and R2
• v2 = vad
b) R3 and Rx• vx = vbd 21
2
RR
Rvv sad
vs+_
R2
R1 R3
Rx
bava vb
c
d x
xsbd RR
Rvv
3
Discussion #6 – Things PracticalECEN 301 6
Wheatstone Bridge KVL around the bottom loop:
x
xs
bdadab
RR
R
RR
Rv
vvv
321
2
vs+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 7
Wheatstone Bridge
Example1: when is vab = 0?
vs+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 8
Wheatstone Bridge
Example1: when is vab = 0?
132
21232
2132
321
2
321
2
321
2
0
RRRR
RRRRRRRR
RRRRRR
RR
R
RR
R
RR
RRR
Rv
RR
R
RR
Rvv
x
xxx
xx
x
x
x
xs
x
xsab
vs+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 9
Wheatstone Bridge
Find Rx:
s
ab
s
ab
x
x
xsab
v
v
RRR
v
v
RRR
R
R
RR
R
RR
Rvv
21
2
21
23
321
2
1
vs
+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 10
Wheatstone Bridge Example2: find Rx
R1 = R2 = R3 = 1kΩ, vs = 12V, vab = 12mV
s
ab
s
ab
x
vv
RRR
vv
RRR
R
R
21
2
21
23
1vs
+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 11
Wheatstone Bridge Example2: find Rx
R1 = R2 = R3 = 1kΩ, vs = 12V, vab = 12mV
996501.0
499
1021
1
1021
10
121012
10210
1
121012
10210
10
1
3
33
3
3
3
3
3
33
21
2
21
23
s
ab
s
ab
x
vv
RRR
vv
RRR
R
R
vs+_
R2
R1 R3
Rx
bava vb
c
d
Discussion #6 – Things PracticalECEN 301 12
Resistance Strain Gauges Strain gauge: device bonded to the surface of an object and
whose resistance varies as a function of surface strain Used to perform measurements of:
• Strain• Stress,• Force• Torque• Pressure
NB: cylindrical resistance:
Compression/elongation will change resistance
A
LR
Compression lower resistance Stretch higher resistance
L – length of cylindrical resistorσ – conductivity of the resistorA – resistor cross-sectional area
Discussion #6 – Things PracticalECEN 301 13
Resistance Strain Gauges Gauge factor (GF): the relationship between change in
resistance and change in length value of about 2 is common
L
L
Strain (ε): the fractional change in length of an objectMax strain that can be measured is about 0.4 – 0.5 percent
• i.e. ε = 0.004 to 0.005• For a 120Ω resistor: +/– 1.2 Ω
LL
RRGF
/
/ 0
R0 – the zero strain resistance
Discussion #6 – Things PracticalECEN 301 14
Resistance Strain Gauges Change in resistance due to strain:
GFRR 0
RGCircuit symbol for a strain gauge
Discussion #6 – Things PracticalECEN 301 15
Wheatstone Bridge Wheatstone bridge commonly used to measure force
using strain gauge resistorsExample: force applied to a cantilever beam
• Two strain gauges (R1 and R4) on top• Two strain gauges (R2 and R3) on bottom• Under no strain: R1 = R2 = R3 = R4 = R0
R1
vs+_
R3
R2 R4
d
a bvavb
ia ib
c
R4
R1
R2 & R3
FL
w
h
Discussion #6 – Things PracticalECEN 301 16
Wheatstone Bridge Under the strain of force F we have:
R4
R1
R2 & R3
FL
w
h
vs+_
R0 + ∆R
bava vb
c
d
R0 + ∆R
R0 - ∆R
R0 - ∆R
ia ib
tension
tension
compression
compression
RRRR 041
RRRR 032
Discussion #6 – Things PracticalECEN 301 17
Wheatstone Bridge From elementary statics it can be shown that:
R4
R1
R2 & R3
FL
w
h
vs+_
R0 + ∆R
bava vb
c
d
R0 + ∆R
R0 - ∆R
R0 - ∆R
ia ib
Ywh
LF2
6 Y is the beam’s modulus of elasticity
Discussion #6 – Things PracticalECEN 301 18
Wheatstone Bridge Using Ohm’s Law:
vs+_
R0 + ∆R
bava vb
c
d
R0 + ∆R
R0 - ∆R
R0 - ∆R
ia ib
43 RR
vi sb
21 RR
vi sa
R1
vs+_
R3
R2 R4
d
a bvavb
ia ib
c
Discussion #6 – Things PracticalECEN 301 19
Wheatstone Bridge Using Ohm’s Law:
vs+_
R0 + ∆R
bava vb
c
d
R0 + ∆R
R0 - ∆R
R0 - ∆R
ia ib
GFv
R
Rv
RRRR
RRv
RRRR
RRv
RR
Rv
RR
Rv
RiRi
vvvvvv
s
s
ss
ss
ab
adbdabbaout
0
00
0
00
0
21
2
43
4
24
Discussion #6 – Things PracticalECEN 301 20
Wheatstone Bridge
Find vo in terms of force F:
kF
FYwh
GFLvYwh
LFGFv
GFvv
s
s
so
2
2
6
6
k is a calibration constant
vs+_
R0 + ∆R
bava vb
c
d
R0 + ∆R
R0 - ∆R
R0 - ∆R
ia ib
Discussion #6 – Things PracticalECEN 301 21
Wheatstone Bridge Example3: using the Wheatstone bridge as a strain measurement tool find the
maximum vo
the bridge measures forces ranging from 0 to 500 N L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x109N/m2, vs = 12V
NmVF
NVF
F
FYwh
GFLv
kFv
s
o
/125.0
/1025.1
1069)01.0)(05.0(
)3.0)(2)(12(6
6
4
92
2
R4
R1
R2 & R3
FL
w
h
Discussion #6 – Things PracticalECEN 301 22
Wheatstone Bridge Example3: using the Wheatstone bridge as a strain measurement tool find
the maximum vo
the bridge measures forces ranging from 0 to 500 N L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x109N/m2, vs = 12V
mV
NmVFvo
5.62
)500(1025.1
/125.0
: voltageimumMax
4
R4
R1
R2 & R3
FL
w
h
Discussion #6 – Things PracticalECEN 301 23
Practical Sources
Discussion #6 – Things PracticalECEN 301 24
Ideal Sources Ideal current source
3A source
012345678
0 1 2 3 4 5 6 7 8
v
i
Ideal voltage source6V source
012345678
0 1 2 3 4 5 6 7 8
v
i
Provides a prescribed voltage across its terminals irrespective of the current flowing through it.
Provides a prescribed current irrespective of the voltage across it.
Discussion #6 – Things PracticalECEN 301 25
Practical Sources Actual voltage sources have limitations
There is a limit to the number of total electrons any battery can motivate through a circuit
• How to measure limitations?• Total number of electrons? (huge number)• Use coulombs? (also too huge)• amp-hour – unit invented for this purpose
• 1 amp-hour = 1 amp for 1 hour = 2 amps for ½ hour
= 1/3 amp for 3 hours
Batteries have ratings indicating their current limitations• Car battery – 12V, 70 amp-hours (A-h) @ 3.5 A (for 20 hours)• D – cell (1.5V) carbon-zinc battery – 4.6 amp-hours @ 100mA (for 46 hours)• 9 – volt carbon-zinc battery – 400 mA-hours @ 8mA (for 50 hours)
1 amp = 1 coulombs/second1 amp-hour = 3600 coulombs
Discussion #6 – Things PracticalECEN 301 26
Practical Sources Actual voltage sources have limitations
As the load resistance (RL) decreases, the voltage source (vs) is required to provide increasing amounts of current (i) in order to maintain vs
+_vs v
+
_
i
Load (RL)
L
s
R
vi
As RL 0, vs has to provide an infinite amount of current!
Discussion #6 – Things PracticalECEN 301 27
Practical Sources Actual voltage sources have limitations
A series resistance rs poses a limit to the maximum current the voltage source can provide
Ls
ss Rr
vi
+_vs
+
vL
–
is
rs
Practical voltage source
Load (RL)
Discussion #6 – Things PracticalECEN 301 28
Practical Sources Actual voltage sources have limitations
A series resistance rs poses a limit to the maximum current the voltage source can provide
+_vs
+
vL
–
is
rs
Practical voltage source
Load (RL)Ls
Ls
LsL
Rr
Rv
Riv
NB: vs = vL
Discussion #6 – Things PracticalECEN 301 29
Practical Sources Actual voltage sources have limitations
+_vs
+
vL
–
is
rs
s
sS
s
ss
R
Ls
ss
r
vi
r
vi
Rr
vi
L
max
0lim
Practical voltage source
A series resistance rs poses a limit to the maximum current the voltage source can provide
Discussion #6 – Things PracticalECEN 301 30
Practical Sources Actual current sources have limitations
As the load resistance (RL) increases, the current source (is) is required to provide increasing amounts of current (v) in order to maintain is
is
+
vs
–
Load (RL)
Ls Riv
As RL ∞, is has to provide an infinite amount of voltage!
Discussion #6 – Things PracticalECEN 301 31
Practical Sources Actual current sources have limitations
A series resistance rs poses a limit to the maximum voltage the current source can provide
)||( LssS Rriv
is
+
vs
–
rs
Practical current source
Load (RL)
Discussion #6 – Things PracticalECEN 301 32
Practical Sources Actual current sources have limitations
ssS
sssR
LssS
riv
riv
Rriv
L
max
lim
)||(
A series resistance rs poses a limit to the maximum voltage the current source can provide
is
+
vs
–
rs
Practical current source
Discussion #6 – Things PracticalECEN 301 33
Practical Sources
012345678
0 1 2 3 4 5 6 7 8
v
i
012345678
0 1 2 3 4 5 6 7 8
v
i
Actual current and voltage sources have limitations
Ideal 3A current source Ideal 6V votage source
Discussion #6 – Things PracticalECEN 301 34
Practical Sources
012345678
0 1 2 3 4 5 6 7 8
v
i
012345678
0 1 2 3 4 5 6 7 8
v
i
Actual current and voltage sources have limitations
Practical 3A current source Practical 6V votage source
Discussion #6 – Things PracticalECEN 301 35
Measuring Devices
Discussion #6 – Things PracticalECEN 301 36
Ohmmeter
Ohmmeter: measures the resistance of a circuit element
NB: the resistance of an element can only be measured when the element is disconnected from all other circuit elements
Ω ΩR
Ohmmeter symbol
Ohmmeter connection setup for circuit element resistance measurement
Discussion #6 – Things PracticalECEN 301 37
Ammeter Ammeter: a device that can measure the
current flowing though a circuit element when connected in series with that circuit elementNB: 1. the ammeter must be connected in series with the circuit element 2. the ammeter should not restrict the flow of current (i.e. cause a voltage drop) – an ideal ammeter has zero resistance
A Ammeter symbol
iR2vs
+_
R1 R1
iR2
vs+_
A
Discussion #6 – Things PracticalECEN 301 38
Voltmeter Voltmeter: a device that can measure the
voltage across a circuit element when connected in parallel with that circuit element
NB: 1. the voltmeter must be connected in parallel with the circuit element 2. the voltmeter should not draw any current away from the element – an ideal voltmeter has infinite resistance
V Voltmeter symbol
vs
i
+R2
–
+_
R1 R1
i
+R2
–vs
+_ V+v2
–
Discussion #6 – Things PracticalECEN 301 39
Wattmeter Wattmeter: a device that can measure the
power dissipated by a circuit element
NB: 1. the wattmeter must be connected in parallel with the circuit element, but also in series with the circuit. – a wattmeter is simply the combination of a voltmeter and an ammeter
W Wattmeter symbol
vs
i
+R2
–
+_
R1 R1
i
+R2
–vs
+_
W
Discussion #6 – Things PracticalECEN 301 40
Practical Voltmeters and Ammeters In reality, voltmeters and ammeters have internal
resistancesPractical ammeters will always add some resistancePractical voltmeters will always draw some current
V
IdealVoltmeter
Vrm
PracticalVoltmeter
A
IdealAmmeter
PracticalAmmeter
A
rm