Lab #1: Ohm’s Law (and not Ohm’s Law)

• Measure the internal resistance of a battery

• Study the V vs I characteristics of a diode and show that it does not obey Ohm’s law

• using a diode, verify Kirchoff’s laws are satisfied even when a non-ohmic device is in the circuit

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

Basic Electric Concepts

=- ds

V=- E ds

U F

UV

q

Resulting Motion depends on material

• conductor

• insulator

• semi-conductor

F qE

Basic Electrical ConceptsConductors

Terminal velocity depends on voltage, the geometry of the materials, and the properties of the material Resistivity

Ohmic materials: AI V

l

Resistance

Material resistivity at room temp (-m)InsulatorsMica 2x1015

Glass 1012-1013

Rubber 1013

Semi-conductorsSilicon 2200Germanium 0.45ConductorsCarbon 3.5x10-5

Nichrome 1.2x10-6

Copper 1.7x10-8

Circuit Symbols

Internal Resistance of a Battery

0V V ir

Internal resistance of the battery

Question:

Why not put the ammeter next to R?

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.

Error on slope and intercept

2

2 ( )j

bj j

x

N x x

Note error on intercept scales with root(N)

Fitting and syst errorsSuppose 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

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.

2 2 2( ) ( )

measured x true

measured y true

m x y

x x

y y

m m

intercept

2 2 2 2( ) ( ) ( )

measured x true x

measured y true y

b y by bx

x x b

y y b

b m

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.)

Multi-meter syst errors

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

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!

Hints

• should we record R (the resistance of the variable resistor in your circuit)?

• For R, should we use the color-band value or should we measure it?

• big currents! Should we switch to lower scale when using smaller currents?

• open switch when not in use (try touching the resistors)

• Some of these batteries drift with temperature. Take A.1 and A.5 seriously to avoid this problem. Also, recheck results for first value of resistance used occasionally to look for drift.

• If you still have drift, it is important to measure V&I simultaneously. If you measure one, wait a minute, then measure the other, you’ll get a ba result. Random error from your ability to read the 2 meters at the same time. (Drift is biggest when using smallest resistor. Why?

LabStarts on page 11

• when measure V0 and r, need to report errors on these numbers

• take at least 5 data points

• please put text in your spreadsheet, carefully labeling all the data!

• all numbers should have units!

• Take A.1 and A.5 seriously!

• don’t do A.7 (until you take this into account during the linear fit)

• section C: use the LED

• C.2. only measure current and voltage across diode

• don’t do C.3

• don’t do C.5

• Don’t do section VII

You must upload your spreadsheet before leaving class!

diode

•Start with the volt meter on the power supply.•First, just qualitatively observe the behavior. Slowly dial it from zero volts up, watching the ammeter. Don’t dial it above 5 V.•After you have a qualitative feel, start taking data. Take a large number of data points, with both positive and negative voltages. Take the most data points where the curve is changing quickly, fewer where it is changing slowly.

•Be careful with voltage signs for this one.

Bureaucracy

• Please note lab report is due Oct 1/2

• Oct 1/2 Oscilloscope review (in class spreadsheet due, no lab report)

What are we testing

• Before you leave class, tell professor Eno what this lab was testing.