## Introduction to Electrical Measurements

Contents

Preparatory Exercise
Please review error propagation and analysis. Complete the following exercise for the two cases shown before the lab session. You may find a resistor color code table to be useful.

 Evaluate the effective resistance and estimate its uncertainty between points a and b, b and c, and a and c. Click for larger image! Case 1. Metal film resistorswith 1% tolerance. Click for larger image! Case 2. Carbon resistorswith mixed tolerances.

Equipment List
Keithley 179 digital multimeter or equivalent. (Front Panel)
Note: I recommend this meter for use as an ammeter in this exercise.
BK Precision 2906 handheld digital multimeter or equivalent. (Functions)
Note: I recommend this meter for use as a voltmeter in this exercise.
Pasco 8015 Counter/Timer used as a +12 V dc power supply (or equivalent).
Envelope of 2 selected precision resistors (1% metal film).
10 banana-plug patch cords.
General-purpose circuit board (Layout).

Objectives
Master correct use of digital multimeter as voltmeter and ammeter.
Reinforce understanding of series and parallel configurations.
Begin introduction to simple circuit diagrams.
Gain experience with wiring simple circuits.

Introduction
Historically, the study of electricity began with electrostatics, the study of stationary charges. Static devices were used in the 1700's by Franklin, Coulomb, and others. The important discoveries leading to the present widespread use of electricity came at the start of the 19th century when the battery was invented by Volta, electric currents and their effects were studied by Ampere and Oersted, and dynamic effects of changing electric and magnetic fields were investigated by Faraday, Henry, Maxwell, and others. The practical applications of electricity to human life followed with the invention in the late 1800's of light bulbs, motors, telephones, etc. which led up to the modern day development of transistors, integrated circuits, high-speed communication, and powerful yet inexpensive computers. Studying the physics behind these discoveries will occupy most of this course. The study of electric circuits, current flow, and its measurement is the subject of this laboratory exercise.

Traditionally, electric charge is introduced as the primary electrical quantity, measured in coulombs in the SI system of units. However, in actual practice the electrical unit which is defined (and measured at the National Institute of Standards and Technology) is the ampere, the unit of electrical current. Electric current, i, is the time rate of flow of charge and has the unit coulomb/second, known as the ampere (A). More typically milliamp (mA = 10-3 A) currents are encountered in laboratory instrumentation.

Many common electrical measurement instruments are based on electrical current. This first lab exercise seeks to give you some rudimentary understanding of these instruments and to demonstrate their correct and intelligent use. The course lectures may not yet have presented fully the principles behind the operation of these instruments, but do not despair --- most of the circuitry inside modern instrumentation cannot be entirely explained during any introductory course! Athough you may not understand the details of what is inside the meter, you do need to learn how to connect and use the meter properly and comprehend the meaning of the readings. (After all, most people drive safely without a detailed understanding of an internal combustion engine.) Failure to use the laboratory instruments appropriately may break them irreparably, incurring frustration on you and your laboratory instructor from waste of time and resources.

Safety
A complete circuit is needed before electric current will flow, a convenient feature for working safely with laboratory circuitry. If you do not plug in the power supply or turn it on, you can work on most circuits without fear of being shocked. (Note: Capacitors in high voltage circuits, such as in video monitors, can remain charged for long times after the power is turned off. Always discharge capacitors before handling!) Therefore, when setting up a circuit, turning on the power should be the last step, and turning off the power is the first step before touching or changing any section of the circuit.

Another safety guideline is to always work with one hand behind your back or safely out of the way; i.e., do not use both hands for wiring. Damaging current flow through your upper chest may result if your body serves to complete a circuit between your right and left hands. Most death by electrocution is caused by fibrillation, disruption of the body's nerve signals controlling rhythmic beating of the heart, induced by modest current flow through the chest area.

Circuit Diagrams and Connections
There are conventional symbols used for drawing diagrams of circuits, known as circuit schematics. It is best to learn and use the conventional symbols from the start, even with the relatively simple circuits examined in introductory physics. The schematic symbols for the circuit elements in this lab exercise (battery and resistor) are shown in Fig. 1. Conducting wires are used to connect the various circuit elements together and are represented by straight lines. Corners in schematics mean nothing; they are needed only to complete the circuit.

 Figure 1. Schematic symbols for simple circuit elements.

Conducting wires (insulated in plastic to isolate the circuit) are often referred to as "leads." The ends of these leads often have convenient attachments. The three most commonly used ends, shown in Fig. 2, are:

1. banana plugs, so called because of their shape, which are easily pushed into the banana ``jacks'' to make the connection; many instruments in introductory laboratories have this kind of connection.
2. alligator clips, having jaws (thus the name) that clamp onto bare metal to make the connection.
3. BNS (Bayonet Neill-Concelman) connector, so named after its designers and twist-lock mechanism, is prevalent in scientific instrumentation.

 Figure 3. Typical connectors used in an introductory physics laboratory.

It is expected that you are already familiar with the difference between series and parallel connections of circuit elements from discussions in class. Carefully examine Fig. 3; if still unclear ask your laboratory or recitation instructor for further explanation.

 Figure 3. Series and parallel connections.

The Ammeter
The ammeter is an instrument used to measure electrical current. To measure the current flowing through some point of a circuit, the circuit must be broken open at that point and the ammeter inserted so that the current to be measured actually flows through the meter too. (Note: Turn off the power before inserting the ammeter, then restore the power to make the current reading.) To reiterate: to measure the current flowing through a circuit element, the circuit must be opened and the ammeter put in series with it. See the top two circuits of Fig. 4 for examples of correct ammeter placement.

 Figure 4. Correct placement and use of ammeter and voltmeter.

Most meters have a number of possible settings for the maximum possible current that can be measured; for example: 2 A, 200 mA, 20 mA, 2 mA. You should always start by turning the setting to the highest possible rating (for example, 2 A). When the meter is finally situated in the circuit to take the reading, and the power is turned on to the circuit, the sensitivity of the ammeter may be increased by changing to progressively lower ranges. It is important not to overshoot the maximum value that can be read. For example, if the current is about 75 mA, then the ammeter would be set to the 200 mA scale for the most accurate reading; setting to the 20 mA scale would overload the ammeter and most likely open its internal fuse. Golden rule of multimeters: Return to voltmeter mode immediately after use as an ammeter is completed.

The Voltmeter
The potential difference, or change in electric potential, between two points is measured with a voltmeter. Current flows through a resistor because of a potential difference applied by a battery or power supply. Potential difference is commonly measured in units of volts (V) or millivolts (mV = 10-3 V). Common usage refers to a potential difference relative to ground (0.0 V) as simply the voltage, though it is prudent to call it by its correct name to emphasize the way it is measured. The potential difference across a circuit element is measured by placing the two leads of a voltmeter on the two sides of the element. Look again at the lower two diagrams in Fig. 4. The voltmeter remains "to the side"; its removal will not change the circuit. Notice the difference in ammeter use where the meter becomes an integral part of the circuit being measuring. The removal of a correctly used ammeter would stop current flow in at least part of the circuit by creating an open condition.

The Multimeter
Most of the measurement capabilities needed in this laboratory are provided by the Keithley 179 multimeter with 4 1/2 digit readout (Fig. 5) and the BK Precision 2906 handheld multimeter with 3 1/2 digit readout (Fig. ***). Most of the discussion that follows refers to the Keithley multimeter; the handheld multimeter, having lower precision, is used in essentially the same way. These instruments are basically sensitive ammeters that can be configured to measure ac and dc voltage, ac and dc current, and resistance. All measurements in this exercise are dc, standing for direct current, which refers to a constant, unvarying voltage or current. ac (alternating current) measurements, where the signal is time varying, will be considered in a later lab exercise. Be aware that in ac mode, the multimeter would give a null reading if connected to a dc signal, since there would be no time-varying component.

 Figure 5. Keithley Model 179 Multimeter: Front Panel View. Courtesy of Keithley Instruments, Inc.

With the Keithley 179 multimeter, voltages in the 2 V range can be measured with a resolution of 100 microV and an accuracy given by the numerical weight of the least significant digit (for example, 0.1 mV for a displayed reading of 123.4 mV) plus 0.04% when properly calibrated, as stated in the instruction manual. For example, a reading of 1.9837 V has a least significant digit of 0.0001 V (0.1 mV); 0.04% of the reading is 0.8 mV. The resulting uncertainty in the reading is actually about 1.0 mV and should be recorded as 1.984 +/- 0.001 V! Thus the 4 1/2 digit readout is really only good to 3 1/2 digits -- Be careful!

The measurement functions (modes) and ranges are selectable with front panel push buttons, as shown in Fig. 5. The decimal point is also positioned by the selected panel setting and polarity (+/-) of the measured signal is automatically displayed.

Use of the Keithley multimeter for measuring dc voltage is as easy as 1-2-3:

• Select DC V function and desired range.
• Connect the unknown dc voltage to the two INPUT jacks of the Model 179.

As stated before, use of the multimeter as an ammeter requires that the circuit be opened and the ammeter inserted. Note: Extreme care is required in using the ammeter function of any multimeter. If you attempt to use the multimeter as a voltmeter when it has been left in the ammeter function, the internal fuse will be destroyed! The specified shunt resistance of the multimeter is only 1 ohm for the 200 mA range and the internal fuse is rated at 2 A; it follows readily from Ohm's law that if such an ammeter is hooked across a potential difference of more than a few volts, the fuse will blow.

The Exercise
Construct each of the circuits shown in Fig. 6. For guidance in using the general-purpose circuit board, shown in Fig. 7, follow the example shown in Fig. 8 for wiring circuit b in Fig. 6.

For the following measurements, use the Keithley multimeter to measure currents and the BK Precision multimeter to measure voltages -- we hope this will avoid errors in use as described above. Measure the potential difference of the power supply (or battery) and across each resistor for both circuits. Then carefully use the ammeter function of the Keithley multimeter to measure the current flow through each circuit element. Remember: use of the multimeter as a voltmeter when the ammeter function is selected must be avoided. Also remember to turn off the power before each change of the circuit. Record all values and their estimated uncertainties.

Since the multimeters also include the option of reading the value of each resistor used in the circuit, a cross check of the above measurements can be implemented. Select the ohm function of the multimeter and place the probes securely on either side of the isolated resistor (disconnected from circuit); read by selecting progressively finer sensitivities without going over the maximum value the scale can handle. How do the resistance values calculated using Ohm's law (R = V/I) for the above measurements compare to those measured "directly" with both multimeters? Also compare your measured value with the resistor values specified by the resistor color code, commonly used by manufacturers to label the value of resistors.

Discuss all results thoroughly. Specifically, compare and contrast the relationships among the voltages and/or currents for the series and parallel resistor combinations.