Revised October 24, 1996

OHM'S LAW AND METERS

INTRODUCTION

Ohm's law is an expression of the experimental fact that in most conductors, including all those made of metals, the potential difference V, the voltage, between two points is proportional to the current I flowing between those points:

V = RI -----------------Eqn.(1)

The proportionality constant R in this equation is called the resistance and is measured in V(olts)/A(mpere). One V/A = one Ohm. The unit Ohm is usually abbreviated with the Greek letter W (Omega). In this experiment you will verify Ohm's law and study electrical meters and measuring techniques, as well as simple d(irect) c(urrent) circuits. The two most basic electrical meters are the voltmeter which measures the potential difference, or voltage, between two points in a circuit and the ampere meter or ammeter, which measures the current through a conductor. You will measure the voltage drop across several resistors as a function of current to verify Ohm's law.

REFERENCES

Read the Appendix E on electricity before you come to this lab. You may also want to look at relevant sections of your physics text book.

APPARATUS

Digital Multimeter, milliammeter, Thornton 6­range meter, 2 decade resistor boxes, 20 ohm resistor, HP 10 V power supply, precision resistors.

WHAT TO DO

1). Examine the meters: they are all multirange meters and have different scales corresponding to their different ranges. The milliammeter has three ranges, obtained by plugging the positive lead into different banana jacks. The meter will work only if the current flows into the positive and out of the negative terminal. Currents flowing in the opposite direction or currents that exceed the maximum value indicated on the scale may damage the meter. For this reason do not turn on the power in any circuit until you have checked the polarities and are sure that the meter ranges will not be exceeded. The Thornton 6­range meter has both current and voltage ranges. It can be used either as a voltmeter or as an ammeter. We will see how this is done later in the experiment. The Digital Multimeter is an electronic instrument, having an internal transistor amplifier powered by a battery. Always turn these meters OFF at the end of the session.

Figure 1:Verification of Ohm's law.

2). Put together the circuit shown in Figure 1, using the large 20 W resistor with a banana jack on each end. Use the 500 mA (1/2A) range of the milliammeter and the 20 V range of the Digital Multimeter. Note that a current meter must be connected in series to measure the flow of charge, whereas a voltmeter must be connected in parallel to measure the voltage drop across the resistor. Please ask your instructor to check your circuit before you turn on the power supply. The voltage control knob on the power supply allows its output voltage to be varied. Always start your measurements with the control set to its lowest value, then raise the voltage. Measure the current I through the resistor as a function of the voltage drop V across it from zero to 10 volts in 1 V increments. Plot the measured values of V vs. I. The slope of this plot represents the resistance R. Include this plot in your lab journal and your lab report.

NOTE: if a current I flows through a resistor R it will cause a voltage drop V and an amount of power

-----------Eqn.(2)

Figure 2: There are two ways to add resistors.

will be dissipated in the resistor. The corresponding energy will appear as heat. The 20 Ohm resistor used in this experiment is designed to absorb the full output of the power supply although it may get uncomfortably hot. The individual resistors in the boxes used in the following experiments are only rated for a maximum dissipation of 1/2 watt each. You must calculate the maximum current that is permissible in your circuit before you turn on the power.

3). Connect the two decade boxes in series, as shown in Figure 2a. The boxes contain a number of resistors that can internally be connected in series so that their total resistance is equal to the sum of the values written above the switches (rotary switches with dials in one type, or slide switches in the other). Select a convenient value, e.g. 500 ohms, in both boxes and plug the circuit in place of the 20 Ohm resistor in Figure 1. Increase the sensitivity of the ammeter as needed and measure the total resistance, Rt = V/I. Then connect the two boxes as shown in Figure 2b) and measure the resistance Rt of the parallel connection. Compare your results with those given by the formulas for the total resistance Rt in Figure 2.

Figure 3:Voltmeter and ammeter.

Figure 4: Voltmeter Circuit - figure is missing - will be fixed!

4). Build a voltmeter with full scale sensitivity of 10 V by putting a resistor in series with the Thornton 6­range meter. With the 100 mA button depressed, the input terminals are connected directly to the meter. The front panel indicates that this range is also a voltmeter with a sensitivity of 0.1 V full scale. If it takes 0.1 V to cause full scale deflection and you want to build a 10 V meter you must drop 9.9 V in the series resistor. How large a resistor must you use to drop 9.9 V with a current of 100 mA? Connect one of the decade boxes as shown in Figure 3a), and use the combination in place of the voltmeter, V, shown in Figure 4. Verify the calibration by connecting the Digital Multimeter in parallel to the home built one. Explain in your lab report, with a

circuit diagram, what must be happening inside the Thornton meter when you push the 2 V or the 10 V button.

Figure 5: Calibration of the ammeter.

5). Construct an ammeter with a full scale sensitivity of 100 mA by connecting the resistor box in parallel to the Thornton Multimeter. Since the meter itself deflects to full scale when a current of 0.1 mA flows through it you must provide a parallel resistor through which the remaining current of 99.9 mA is shunted. Calculate the resistance of the shunt that is needed to conduct 99.9 mA past the meter at a voltage of 0.1 V, thus turning the Thornton meter into milliammeter with a full scale sensitivity of 100 mA. Flick the appropriate resistor switches on a decade box and wire it in parallel with the Thornton Multimeter as shown in Figure 3b). Test your ammeter by comparing it with the Digital Multimeter as shown in Figure 5.

If there is a disagreement it is probably in the ammeter you constructed, which depends critically on the accuracy of the shunt resistance. Use the Digital Multimeter to measure the shunt resistance. Does the measured resistance explain the difference in the reading of the ammeters?

There are some precision resistors in the lab that you should use to improve the accuracy of your ammeter.

To sum up: a voltmeter is a sensitive current meter with a large resistor in series. An ammeter is a sensitive current meter with a small resistor in parallel. An ideal voltmeter will have an infinite total resistance so that it does not draw any current from the circuit under test. An ideal ammeter will have zero resistance so that it does not introduce any additional voltage drop in the circuit. It is now possible to make electronic voltmeters with a resistance as high as 1014 ohms and electronic ammeters with a voltage drop as low as 10-9 V.

If you have time, you might figure out how to use the galvanometer, a series resistor and the power supply to make an "ohmmeter" that reads near center scale when connected across a 100,000 ohm resistor; then try it out.