Schedule Date Day Class Title Chapters HW Lab Exam No. Due - PowerPoint PPT Presentation

Schedule… Date Day Class Title Chapters HW Lab Exam No. Due date Due date 2.6 – 2.8 22 Sept Mon 6 Things Practical LAB 2 23 Sept Tue 3.1 – 3.3 24 Sept Wed 7 Network Analysis 25 Sept Thu 26 Sept Fri Recitation HW 3 27 Sept Sat 28 Sept Sun 3.4 – 3.5 29 Sept Mon 8 Equivalent Circuits LAB 3 30 Sept Tue Discussion #6 – Things Practical ECEN 301 1

Spiritual – Temporal 1 Nephi 15:32 32 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 2:41 41 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 Practical ECEN 301 2

Lecture 6 – The Wheatstone Bridge An Applications of Things Electrical Discussion #6 – Things Practical ECEN 301 3

Wheatstone Bridge  R x is an unknown resistance to be determined c c R 1 R 3 R 1 R 3 v a v b + + a v b b v a v s _ v s _ a b R 2 R x R 2 R x d d Discussion #6 – Things Practical ECEN 301 4

Wheatstone Bridge  The circuit consists of the parallel combination of 3 subcircuits with the same voltage: a) The voltage source b) Series combination of R 1 and R 2 c) Series combination of R 3 and R x  Voltage divider between: a) R 1 and R 2 • v 2 = v ad R b) R 3 and R x 2 v v c • ad s v x = v bd R R 1 2 R 1 R 3 v a v b + v s _ a b R x v v R 2 R x bd s R R d 3 x Discussion #6 – Things Practical ECEN 301 5

Wheatstone Bridge  KVL around the bottom loop: v v v ab ad bd R R 2 x v s R R R R 1 2 3 x c R 1 R 3 v a v b + v s _ a b R 2 R x d Discussion #6 – Things Practical ECEN 301 6

Wheatstone Bridge  Example1 : when is v ab = 0? c R 1 R 3 v a v b + v s _ a b R 2 R x d Discussion #6 – Things Practical ECEN 301 7

Wheatstone Bridge  Example1 : when is v ab = 0? R R c 2 x v v ab s R R R R 1 2 3 x R 1 R 3 R R v a v b + v s 2 x 0 _ v a b s R R R R 1 2 3 x R R R 2 R x 2 x R R R R d 1 2 3 x R R R R R R 2 3 1 2 x x R R R R R R R R 2 3 2 1 2 x x x R R R R 2 3 1 x Discussion #6 – Things Practical ECEN 301 8

Wheatstone Bridge  Find R x : R R 2 x v v ab s R R R R 1 2 3 x c R 1 R 3  v a v b + v s _ a b R 2 R x R v 2 ab R d 3 R R v 1 2 s R x R v 2 ab 1 R R v 1 2 s Discussion #6 – Things Practical ECEN 301 9

Wheatstone Bridge  Example2 : find R x  R 1 = R 2 = R 3 = 1k Ω , v s = 12V, v ab = 12mV c R v 2 ab R R 1 R 3 3 R R v 1 2 s R v a v b + v s x _ a b v R 2 1 ab R R v 1 2 s R 2 R x d Discussion #6 – Things Practical ECEN 301 10

Wheatstone Bridge  Example2 : find R x R v 2 ab R  R 1 = R 2 = R 3 = 1k Ω , v s = 12V, v ab = 12mV 3 R R v 1 2 s R x R v 1 2 ab R R v 1 2 s 3 3 10 12 10 3 10 c 3 2 10 12 R 1 R 3 3 3 10 12 10 1 v a v b + v s 3 _ 2 10 12 a b 1 3 3 10 10 R 2 R x 2 d 1 3 1 10 2 499 0 . 501 996 Discussion #6 – Things Practical ECEN 301 11

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 L – length of cylindrical resistor L  NB : cylindrical resistance: R σ – conductivity of the resistor A A – resistor cross-sectional area  Compression/elongation will change resistance Compression lower resistance Stretch higher resistance Discussion #6 – Things Practical ECEN 301 12

Resistance Strain Gauges  Gauge factor (GF) : the relationship between change in resistance and change in length  value of about 2 is common / R R 0 GF R 0 – the zero strain resistance / L L  Strain ( ε ) : the fractional change in length of an object  Max strain that can be measured is about 0.4 – 0.5 percent • i.e. ε = 0.004 to 0.005 • For a 120 Ω resistor: +/ – 1.2 Ω L L Discussion #6 – Things Practical ECEN 301 13

Resistance Strain Gauges  Change in resistance due to strain : R R GF 0 Circuit symbol for a strain gauge R G Discussion #6 – Things Practical ECEN 301 14

Wheatstone Bridge  Wheatstone bridge commonly used to measure force using strain gauge resistors  Example : force applied to a cantilever beam • Two strain gauges ( R 1 and R 4 ) on top • Two strain gauges ( R 2 and R 3 ) on bottom c F i a L i b R 1 R 3 h R 1 + a v b b v a _ v s R 4 w R 2 R 4 R 2 & R 3 d Discussion #6 – Things Practical ECEN 301 15

Wheatstone Bridge  Under the strain of force F we have: R R R R 1 4 0 tension c R R R R compression 2 3 0 R 0 - ∆R R 0 + ∆R F v a v b a L + v s b _ i a i b h R 1 R 4 R 0 - ∆R R 0 + ∆R w compression tension R 2 & R 3 d Discussion #6 – Things Practical ECEN 301 16

Wheatstone Bridge  From elementary statics it can be shown that: 6 LF Y is the beam’s modulus of elasticity 2 wh Y c R 0 - ∆R R 0 + ∆R F v a v b a L + v s b _ i a i b h R 1 R 4 R 0 - ∆R R 0 + ∆R w R 2 & R 3 d Discussion #6 – Things Practical ECEN 301 17

Wheatstone Bridge  Using Ohm’s Law: v v s s i i a b R R R R 1 2 3 4 c c R 0 - ∆R R 0 + ∆R i a i b R 1 R 3 v a v b a + + v s a v b b b v a _ _ v s i a i b R 2 R 4 R 0 - ∆R R 0 + ∆R d d Discussion #6 – Things Practical ECEN 301 18

Wheatstone Bridge  Using Ohm’s Law: v v v v out ba b a c i R i R 4 2 b a R 0 - ∆R v R v R R 0 + ∆R s 4 s 2 R R R R 3 4 1 2 v a v b a + v s R R R R _ b 0 0 v v i a i b s s R R R R R R R R 0 0 0 0 R 0 - ∆R R 0 + ∆R R v s R 0 d v GF s Discussion #6 – Things Practical ECEN 301 19

Wheatstone Bridge  Find v o in terms of force F : v v GF o s c 6 LF v GF R 0 - ∆R s 2 wh Y R 0 + ∆R 6 v GFL v a v b a s + F v s _ b 2 wh Y i a i b kF R 0 - ∆R R 0 + ∆R d k is a calibration constant Discussion #6 – Things Practical ECEN 301 20

Wheatstone Bridge  Example3 : using the Wheatstone bridge as a strain measurement tool find v o  the bridge measures forces ranging from 0 to 500 N  L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x10 9 N/m 2 , v s = 12V v kF o F L 6 v GFL s F 2 h wh Y R 1 R 4 6 ( 12 )( 2 )( 0 . 3 ) w F 2 9 ( 0 . 05 )( 0 . 01 ) 69 10 R 2 & R 3 4 1 . 25 10 / F V N 0 . 125 / F mV N Discussion #6 – Things Practical ECEN 301 21

Wheatstone Bridge  Example3 : using the Wheatstone bridge as a strain measurement tool find v o  the bridge measures forces ranging from 0 to 500 N  L = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x10 9 N/m 2 , v s = 12V F Max imum voltage : L h 0 . 125 / R 1 v o F mV N R 4 w 4 1 . 25 10 ( 500 ) R 2 & R 3 62 . 5 mV Discussion #6 – Things Practical ECEN 301 22

Practical Sources Discussion #6 – Things Practical ECEN 301 23

Ideal Sources  Ideal current source  Ideal voltage source  3A source  6V source 8 i 8 i 7 7 6 6 5 5 4 4 3 3 2 2 1 1 v v 0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 Provides a prescribed voltage across its Provides a prescribed current terminals irrespective of the current irrespective of the voltage across it. flowing through it. Discussion #6 – Things Practical ECEN 301 24

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 amp = 1 coulombs/second 1 amp-hour = 3600 coulombs = 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) Discussion #6 – Things Practical ECEN 301 25

Practical Sources  Actual voltage sources have limitations  As the load resistance ( R L ) decreases, the voltage source ( v s ) is required to provide increasing amounts of current ( i ) in order to maintain v s v s i R i L + As R L 0, v s has to + provide an infinite amount v v s Load ( R L ) _ of current! _ Discussion #6 – Things Practical ECEN 301 26

Practical Sources  Actual voltage sources have limitations A series resistance r s poses a limit to the maximum current the voltage source can provide i s v s i s r s + r R s L + Load ( R L ) v L v s _ – Practical voltage source Discussion #6 – Things Practical ECEN 301 27