1. ECEN 301Discussion #6 – Things Practical1 DateDayClass No. TitleChaptersHW Due date Lab Due date Exam 22 SeptMon6Things Practical2.6 – 2.8 LAB 2 23 SeptTue 24 SeptWed7Network Analysis3.1 – 3.3 25 SeptThu LAB 2 26 SeptFri Recitation HW 3 27 SeptSat 28 SeptSun 29 SeptMon8Equivalent Circuits3.4 – 3.5 NO LAB 30 SeptTue Schedule…

2. ECEN 301Discussion #6 – Things Practical2 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.

3. ECEN 301Discussion #6 – Things Practical3 Lecture 6 – The Wheatstone Bridge An Applications of Things Electrical

4. ECEN 301Discussion #6 – Things Practical4 Wheatstone Bridge A circuit used to find: uAn unknown resistance R x uThe unknown voltage v ab uAnother unknown value (such as a force) vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d c R1R1 vsvs + _ R3R3 R2R2 RxRx d a b vava vbvb

5. ECEN 301Discussion #6 – Things Practical5 Wheatstone Bridge uThe 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 uVoltage divider between: a)R 1 and R 2 v 2 = v ad b)R 3 and R x v x = v bd vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

6. ECEN 301Discussion #6 – Things Practical6 Wheatstone Bridge uKVL around the bottom loop: vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

7. ECEN 301Discussion #6 – Things Practical7 Wheatstone Bridge uExample1: when is v ab = 0? vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

8. ECEN 301Discussion #6 – Things Practical8 Wheatstone Bridge uExample1: when is v ab = 0? vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

9. ECEN 301Discussion #6 – Things Practical9 Wheatstone Bridge uFind R x : vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

10. ECEN 301Discussion #6 – Things Practical10 Wheatstone Bridge uExample2: find R x ÙR 1 = R 2 = R 3 = 1kΩ, v s = 12V, v ab = 12mV vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

11. ECEN 301Discussion #6 – Things Practical11 Wheatstone Bridge uExample2: find R x ÙR 1 = R 2 = R 3 = 1kΩ, v s = 12V, v ab = 12mV vsvs + _ R2R2 R1R1 R3R3 RxRx ba vava vbvb c d

12. ECEN 301Discussion #6 – Things Practical12 Resistance Strain Gauges uStrain gauge: device bonded to the surface of an object and whose resistance varies as a function of surface strain ÙUsed to perform measurements of: Strain Stress, Force Torque Pressure uNB: cylindrical resistance: ÙCompression/elongation will change resistance Compression lower resistanceStretch higher resistance L – length of cylindrical resistor σ – conductivity of the resistor A – resistor cross-sectional area

13. ECEN 301Discussion #6 – Things Practical13 Resistance Strain Gauges uGauge factor (GF): the relationship between change in resistance and change in length Ùvalue of about 2 is common uStrain (ε): the fractional change in length of an object ÙMax 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 R 0 – the zero strain resistance

14. ECEN 301Discussion #6 – Things Practical14 Resistance Strain Gauges uChange in resistance due to strain: RGRG Circuit symbol for a strain gauge

15. ECEN 301Discussion #6 – Things Practical15 Wheatstone Bridge uWheatstone bridge commonly used to measure force using strain gauge resistors ÙExample: 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 Under no strain: R 1 = R 2 = R 3 = R 4 = R 0 R1R1 vsvs + _ R3R3 R2R2 R4R4 d a b vava vbvb iaia ibib c R4R4 R1R1 R 2 & R 3 F L w h

16. ECEN 301Discussion #6 – Things Practical16 Wheatstone Bridge uUnder the strain of force F we have: R4R4 R1R1 R 2 & R 3 F L w h vsvs + _ R 0 + ∆R b a vava vbvb c d R 0 - ∆R iaia ibib tension compression

17. ECEN 301Discussion #6 – Things Practical17 Wheatstone Bridge uFrom elementary statics it can be shown that: R4R4 R1R1 R 2 & R 3 F L w h vsvs + _ R 0 + ∆R b a vava vbvb c d R 0 - ∆R iaia ibib Y is the beam’s modulus of elasticity

18. ECEN 301Discussion #6 – Things Practical18 Wheatstone Bridge uUsing Ohm’s Law: vsvs + _ R 0 + ∆R b a vava vbvb c d R 0 - ∆R iaia ibib R1R1 vsvs + _ R3R3 R2R2 R4R4 d a b vava vbvb iaia ibib c

19. ECEN 301Discussion #6 – Things Practical19 Wheatstone Bridge uUsing Ohm’s Law: vsvs + _ R 0 + ∆R b a vava vbvb c d R 0 - ∆R iaia ibib

20. ECEN 301Discussion #6 – Things Practical20 Wheatstone Bridge uFind v o in terms of force F: k is a calibration constant vsvs + _ R 0 + ∆R b a vava vbvb c d R 0 - ∆R iaia ibib

21. ECEN 301Discussion #6 – Things Practical21 Wheatstone Bridge uExample3: using the Wheatstone bridge as a strain measurement tool find the maximum v o Ùthe bridge measures forces ranging from 0 to 500 N ÙL = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x10 9 N/m 2, v s = 12V R4R4 R1R1 R 2 & R 3 F L w h

22. ECEN 301Discussion #6 – Things Practical22 Wheatstone Bridge uExample3: using the Wheatstone bridge as a strain measurement tool find the maximum v o Ùthe bridge measures forces ranging from 0 to 500 N ÙL = 0.3m, w = 0.05m, h = 0.01m, GF = 2, Y = 69x10 9 N/m 2, v s = 12V R4R4 R1R1 R 2 & R 3 F L w h

23. ECEN 301Discussion #6 – Things Practical23 Practical Sources

24. ECEN 301Discussion #6 – Things Practical24 Ideal Sources uIdeal current source Ù3A source uIdeal voltage source Ù6V source Provides a prescribed voltage across its terminals irrespective of the current flowing through it. Provides a prescribed current irrespective of the voltage across it.

25. ECEN 301Discussion #6 – Things Practical25 Practical Sources uActual voltage sources have limitations ÙThere 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 ÙBatteries 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/second 1 amp-hour = 3600 coulombs

26. ECEN 301Discussion #6 – Things Practical26 Practical Sources uActual voltage sources have limitations ÙAs 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 + _ vsvs v + _ i Load (R L ) As R L 0, v s has to provide an infinite amount of current!

27. ECEN 301Discussion #6 – Things Practical27 Practical Sources uActual voltage sources have limitations A series resistance r s poses a limit to the maximum current the voltage source can provide + _ vsvs +vL–+vL– isis rsrs Practical voltage source Load (R L )

28. ECEN 301Discussion #6 – Things Practical28 Practical Sources uActual voltage sources have limitations A series resistance r s poses a limit to the maximum current the voltage source can provide + _ vsvs +vL–+vL– isis rsrs Practical voltage source Load (R L ) NB: v s = v L

29. ECEN 301Discussion #6 – Things Practical29 Practical Sources uActual voltage sources have limitations + _ vsvs +vL–+vL– isis rsrs Practical voltage source A series resistance r s poses a limit to the maximum current the voltage source can provide

30. ECEN 301Discussion #6 – Things Practical30 Practical Sources uActual current sources have limitations ÙAs the load resistance (R L ) increases, the current source (i s ) is required to provide increasing amounts of current (v) in order to maintain i s isis +vs–+vs– Load (R L ) As R L ∞, i s has to provide an infinite amount of voltage!

31. ECEN 301Discussion #6 – Things Practical31 Practical Sources uActual current sources have limitations A series resistance r s poses a limit to the maximum voltage the current source can provide isis +vs–+vs– rsrs Practical current source Load (R L )

32. ECEN 301Discussion #6 – Things Practical32 Practical Sources uActual current sources have limitations A series resistance r s poses a limit to the maximum voltage the current source can provide isis +vs–+vs– rsrs Practical current source

33. ECEN 301Discussion #6 – Things Practical33 Practical Sources uActual current and voltage sources have limitations Ideal 3A current sourceIdeal 6V votage source

34. ECEN 301Discussion #6 – Things Practical34 Practical Sources uActual current and voltage sources have limitations Practical 3A current sourcePractical 6V votage source

35. ECEN 301Discussion #6 – Things Practical35 Measuring Devices

36. ECEN 301Discussion #6 – Things Practical36 Ohmmeter uOhmmeter: 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 Ω R Ohmmeter symbol Ohmmeter connection setup for circuit element resistance measurement

37. ECEN 301Discussion #6 – Things Practical37 Ammeter uAmmeter: a device that can measure the current flowing though a circuit element when connected in series with that circuit element NB: 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 i R2R2 vsvs + _ R1R1 R1R1 i R2R2 vsvs + _ A

38. ECEN 301Discussion #6 – Things Practical38 Voltmeter uVoltmeter: 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 vsvs i +R2–+R2– + _ R1R1 R1R1 i +R2–+R2– vsvs + _ V +v2–+v2–

39. ECEN 301Discussion #6 – Things Practical39 Wattmeter uWattmeter: 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 vsvs i +R2–+R2– + _ R1R1 R1R1 i +R2–+R2– vsvs + _ W

40. ECEN 301Discussion #6 – Things Practical40 Practical Voltmeters and Ammeters uIn reality, voltmeters and ammeters have internal resistances ÙPractical ammeters will always add some resistance ÙPractical voltmeters will always draw some current V Ideal Voltmeter Vrmrm Practical Voltmeter A Ideal Ammeter Practical Ammeter A rmrm