1. Lab #1: Imperfections in Equipment Measure the internal resistance of a battery Measure the input impedance of the oscilloscope Measure the output impedance of the signal generator

2. Current Current: amount of charge that passes a point on the wire each second (amps = columb/second) Determined by number of charges and by their speed

3. Basic Electrical Concepts Conductors Terminal velocity depends on voltage, the geometry of the materials, and the properties of the material Resistivity Ohmic materials:

4. Resistance Material resistivity at room temp (  -m) Insulators Mica 2x10 15 Glass 10 12 -10 13 Rubber 10 13 Semi-conductors Silicon 2200 Germanium 0.45 Conductors Carbon 3.5x10 -5 Nichrome 1.2x10 -6 Copper 1.7x10 -8

5. Circuits You learned in your class how to analyze circuits using Ohm’s law and Kirchkoff’s laws. However, most of the time, you neglected to take into account the fact that the instruments you use to measure the circuit can themselves alter the performance of the circuit. We will study this in the lab, see how big the effect is, and from that get an idea of when this needs to be taken into account when comparing results to predictions.

6. Internal Resistance of a Battery Internal resistance of the battery

7. Input/Output Impedences Likewize, a realistic oscilloscope can be modeled as an ideal one in series with a resistor and a realistic signal generator can be modeled as an ideal one in series with a resistor. We will measure the internal resistance of each of these devices. We will also practice error propogation, and understanding how to

8. Estimating Errors: Review Systematic errors : sources of error that have the same size effect on every measurement that is made (or a correlated effect) a ruler that was not manufactured correctly a consistently delayed reaction when using a stop watch your inability to perfectly estimate the size of a stray magnetic field from your computer that leaks into your experimental area Random errors : sources of error whose effect varies with each measurement precision of your measuring device when using a stop watch, a reaction time that sometimes anticipates the event, some times is in retard of the event.

9. Systematic Errors Most of the time, you will treat systematic errors in the same way as random errors. Most of the time you can use standard error propogation to get the error in a quantity calculated from another that has a systematic error. However, when you are fitting, you have to handle systematic errors in a different way.

10. Error on slope and intercept Note error on intercept scales with root(N)

11. Fitting and syst errors Suppose you are measuring V using a meter that has infinite accuracy and that has no random errors, but that always reports a voltage that is always off by 0.25V? Adding points does not reduce the error. Previous formula can not work for systematic errors

12. slope How can slope be changed? If voltage is always off by a scale factor, or if current is always off by a scale factor, slope is off by the same factor.

13. intercept What if the voltage is always off by a fixed, constant amount? (see “lectures” link of class web site, kelly_SystematicErrors.pdf, for a more complete, rigorous derivation of this result.)

14. Multi-meter syst errors

15. Random and Sys errors first, fit to a straight line using only random errors get the error on the fit m and b due to random errors from the spreadsheet calculate the errors on m and b due to systematic errors as shown on previous 2 slides take the error on m due to random errors and the error on m due to systematic errors and add them in quad ditto for b

16. Fitting and Syst Errors If you don’t understand this (how to calculate the syst error on slope/intercept and then combine with the stat error), don’t leave the room today until you do! It’s important for this and future labs!

17. Linearizing This semester, we will often do a variable transformation in order to get a linear dependence that we can easily fit. When we transform variables, we also need to recalculate the errors. In this lab:

18. Lab do not do section A.3 or any of section B. Do the supplement instead do not do systematic error analysis for supplement, only for the part in the manual. do not do the second paragraph of section A in the manual do not do the first 2 sentances of section III.A in the supplement be careful with grounds when measuring the output impedence of the signal generator Some of the resistors have values that drift with temperature. It is important to measure V&I simultaneously. If you measure one, wait a minute, then measure the other, you’ll get a bad result. Random error from your ability to read the 2 meters at the same time. (Drift is biggest when using smallest resistor. Why?) You need to quote errors on all measured numbers and all numbers calculated from measured numbers. Never use the nominal value of a resistor. Always measure the resistance using an ohm meter. Always remove the resistor from the circuit before measuring its resistance (why?) all numbers should have units and be carefully labeled last line of supplement r_load -> r_out

19. What are we testing Before you leave class, tell professor Eno what this lab was testing.

20. Bureaucracy Please note lab report is due Sept 22,23. Please upload to elms and bring a paper copy to my office (slide under my door if I’m not there) No Class Sept 22,23 See you Sept 29,30 You must upload your spreadsheet before leaving class!