EEE 1 Experiment No. 1 D.C. and Resistance Measurements

Objectives:

To know the different methods of making DC voltage, DC current and resistance measurements

To be able to specify the degree of accuracy of any measurements made Materials and Equipment:

1-Variable DC Voltage Supplies 1mA Movement Potentiometer Box Analog Multimeter Protoboard Resistors (to be given by the instructor) Wires, Connector Clips

Procedure: A. Determining the Internal Resistance of the 1mA Movement

1. Connect the circuit shown in Figure 1 with R2

disconnected and the power supply turned off. Ω

The voltage adjustment knob of the power supply

R2

should be set to minimum. ΚΩ

2. Turn the power supply on. Slowly increase Vs A

+ -

using the voltage adjustment knob. The R

1

milliammeter needle should start to move upscale. Vs

Continue increasing Vs until the needle indicates

full-scale (1 mA). Vs = 14V

3. Connect R2. Use a 200Ω or 500Ω potentiometer. Its initial setting is immaterial. Nevertheless, once inserted, the milliammeter reading should decrease. Adjust the shaft of R2 until the milliammeter indicates half-scale (0.5 mA). (If the current thru the ammeter does not reach half-scale using the 200 Ω potentiometer, try a larger valued potentiometer.)

4. Disconnect and measure R2. The value measured will be approximately equal to the internal resistance of the ammeter, Rm.

Rm = 80Ω

B. Errors in Current Measurements Due to Loading Effects

1. Refer to the circuit in Figure 2. For each combination of R

V and R in Table 1, compute for the value of the a

current, I, that should flow. Fill up Table 1

correspondingly.

Vs

2. For each of these same combinations, set up the circuit

of Figure 2 and measure the current that flows by

replacing the short circuit between a and b with your b

1mA movement. Complete Table 1 with your

measured values. Figure 2

Figure 1

V (volts) R (Ω) I, Ideal (mA) I, Measured (mA)

0.17 200 0.85 0.167

1 2 k 0.5 0.458

10 20 k 0.5 0.5

Table 1

C. The DC Voltmeter 1. A DC ammeter can be used to measure voltage

by simply connecting a resistor in series with it, as shown in Figure 3. Compute the value of the series resistance Rs that will allow your 1mA movement to measure DC voltages up to 10 volts. Rs = 10000Ω

2. Use the potentiometer to obtain the resistance computed in step 1 above. Set up your 10V full-scale voltmeter. Check its operation with the three calibration values indicated in Table 2. Fill up Table 2 correspondingly.

+ Rs

Vu +

Ifs

A Rm

-

-

Figure 3

Figure 5

Calibration 1mA Movement Corresponding

Voltage (V) Reading (Deflection, %) Reading of Vu (V)

2 21% 2.1

5 51% 5.1

8 81% 8.1 Table 2

D. Errors in Voltage Measurements Due to Loading Effects

1. Refer to the circuit in Figure 4. For each of the values of R given in Table 3, compute for the

R

value of Vx that should be obtained. Fill up

+ a

Table 3 correspondingly.

2. For each of the values of R in Table 3, set up 15V

R Vx

Figure 4 and measure the voltage Vx using your

just constructed voltmeter. Fill the measured

- b

values into Table 3.

Figure 4

R (Ω) Theoretical Vx (V) Measured Vx (V)

1 k 7.5 7.9

10 k 7.5 5.5

100 k 7.5 1.5

Table 3

E. The Series Ohmmeter Method

1. Set up the circuit of Figure 5. Set the power supply to 10V. Use a 10KΩ potentiometer for R2.

2. Short together terminals A and B and adjust R2 until the 1mA movement indicates full scale. Leave R2 at this setting.

3. You will be given three resistors Ra, Rb and Rc whose resistances you are supposed to determine. Connect them, one at a time, across terminals A and B. Record into Table 4 the deflection D produced by each resistance in the 1mA movement. Compute for the corresponding resistance.

Resistance Deflection (%) Corresponding Resistance (Ω)

Ra 0.70 4285.714286

Rb 0.85 1764.705882

Rc 0.10 90000 Table 4

F. The Voltmeter - Ammeter Method

1. The same resistances Ra, Rb and Rc are to be determined using the circuit of Figure 6. Use an analog multimeter as the voltmeter and the 1 mA movement as the ammeter. Vs may be set to any reasonable value provided that the 1mA movement does not go beyond full scale and the maximum power rating of Ru is not exceeded (Ru should not get too hot while in circuit). For each of the unknown resistances

connected in place of Ru, record the readings of the voltmeter and the ammeter. Fill the read values into Table 5.

Figure 6 Figure 7

Resistance V reading I reading Corresponding

Resistance (Ω)

Ra 2.5 0.5 5000

Rb 2.5 1 2500

Rc 18 0.2 90000 Table 5

2. Repeat the above procedure using the circuit of Figure 7 to fill in Table 6.

Resistance V reading I reading Corresponding

Resistance (Ω)

Ra 2.5 0.5 5000

Rb 2 0.8 2500

Rc 19 0.2 95000 Table 6

Required Discussion

1. The method used in determining the internal resistance of the milliammeter is just an

approximation. Discuss how the value of the resistor R1 affects the accuracy of the measurement.

2. Based on the meter resistance of your 1mA movement, predict the accuracy that you should obtain for each of the measurements made in Procedure B. Compare these figures with the actual accuracy of your measurements. Account for any differences.

3. Show how you computed for the value of Rs to be used to convert your 1mA movement into a 10-V voltmeter. What is the internal resistance of your 10-V voltmeter?

4. Discuss the linearity and accuracy of the 10-V voltmeter you constructed based on the calibration points given to you in Table 2. What are the possible sources of error?

5. Based on the internal resistance of your 10-V voltmeter, predict the accuracy that you should obtain for each of the measurements made in Procedure D. Compare these figures with the actual accuracy of your measurements.

6. Show that the relationship between unknown resistance Ru and deflection D for the series ohmmeter circuit of Figure 5 is given by Ru = Ro (1 - D)/D. In our case, what is Ro?

7. Compare the computed resistance in Procedures E and F with the actual values of Ra, Rb, and Rc given by your instructor. Account for any differences.

8. Given the two possible arrangements for making resistance measurements using the voltmeter-ammeter method, when should one method be used instead of the other if the resistance is to be taken as the voltage reading divided by the current reading?