EFFECTS OF METERS ON CIRCUITS

PURPOSE

Determining the effect on a circuit of applying a voltmeter to that circuit, and comparing the effects of two different kinds of voltmeter.

WHAT'S THE POINT?

To see how measuring devices can change the very quantities they are designed to measure.

BACKGROUND READING:

Cutnell and Johnson 20.6, 20.7, 20.8, 20.10 and especially 20.11.

INTRODUCTION

Meters are designed to measure currents and voltages in circuits without changing the values of these variables in the circuit. Thus, since voltmeters are connected in parallel to a circuit element, we want the meter's resistance to be so large that a negligible fraction of the current in the circuit passes through it. Similarly, an ammeter is connected in series with a resistor in order to measure the current through the resistor. In order to keep the potential difference across the ammeter insignificant, it must have a resistance that is so small that it is negligible compared to the other resistances in the circuit.

Ideal voltmeters would have infinite resistance. Real voltmeters have finite resistance; thus, they may affect the circuit to which they are connected and give inaccurate readings.

PROCEDURE

This experiment involves two steps. In each step, you must build a circuit as shown in Figure 1 below.

Figure 1.

One of the pieces of equipment in your kit this week is a circuit board with 2 pairs of resistors. One pair consists of two 1,000 Ohm resistors connected in series. The other pair consists of two 100,000 Ohm resistors connected in series. Use first one pair, then the other, as described below.

There are two different voltmeters in your kit. One is a digital meter, made by Fluke. Set the knob on the digital meter to the position labelled with a V with a solid bar over it -- that causes the meter to measure voltage in a circuit with direct current. The other meter, made by Simpson, is an analog device: you must read voltages by noting the position of a needle which moves in front of a graduated dial. To use the analog meter, do the following:

• set the meter's left-hand knob to "+DC"
• set the meter's central switch to "10V"
• read the black DC scale with the smallest values -- it will indicate the voltage in units of volts
• connect the negative lead to the "- common" terminal, at lower left
• connect the positive lead to the "+" terminal, at lower left

The digital meter has a resistance of 10,000,000 Ohms. The resistance of the analog meter depends on the voltage of the current passing through it:

         resistance of analog meter = 20,000 Ohms per volt

First, you must set the power supply so that it provides exactly 10 Volts. Use the digital voltmeter, connected directly to the terminals of the power supply, to set the power supply as close to 10.00 volts as you can. Do not modify the power supply during the rest of this experiment.

Step I. Using 1,000 Ohm resistors

1. Set up the circuit as shown in Figure 1, using the pair of 1,000 Ohm resistors.

2. What is the voltage across each resistor?

3. Using the digital meter, measure the voltage across resistor R1. Does this value agree with your prediction in step 3?

4. With the digital meter in the circuit, calculate the voltage across resistor R1. You will need to incorporate the effects of the meter on the circuit. Does your calculation agree with the measurement in step 4?

5. Suppose you were to borrow another digital meter from another group and place it across resistor R2, while your digital meter is still attached across R1. What voltage should you measure across R2?

6. Borrow another digital meter from another group. Use it to measure the voltage across R2, while your meter is still attached across R1. Does this measurement agree with your calculation in step 6?

7. Remove the digital meters from your circuit.

8. Suppose you were to place the analog meter across resistor R1. What voltage should the meter display?

9. Actually measure the voltage across resistor R1 with the analog meter. Does it agree with your prediction?

10. Suppose you were to leave the analog meter connected across R1, and then place the digital meter across R2. What value should you read with the digital meter?

11. Leave the analog meter connected across R1, and then place the digital meter across R2. What value do you read with the digital meter? Does it agree with your prediction?

Step II. Using 100,000 Ohm resistors

1. Set up the circuit as shown in Figure 1, using the pair of 100,000 Ohm resistors.

   Repeat items 2-11 with this setup.

When you have finished making all measurements, turn the control knob of the digital meter to the "Off" position.

CONCLUSION

Which meter do you consider better, and why? Use the above results in your explanation. You may include other factors, too, such as ease of use, size, weight, etc.