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To find which of the circuits, shown below, are most suitable to measure a range of resistances, which the meters (the voltmeter and the ammeter) could be used to measure.

Extracts from this document...

Introduction

Nigel Evans

Physics Coursework – “How Do I Connect This Voltmeter”

        -  -

How do I connect this Voltmeter?

Aim

To find which of the circuits, shown below, are most suitable to measure a range of resistances, which the meters (the voltmeter and the ammeter) could be used to measure.

image00.png

Prediction

I did not know which circuit would be the most accurate, to start with so I did a preliminary investigation, which consisted of setting up the two circuits above and then just putting two resistors in each and working out the required resistance. I did not see at the time that different value of resistance would make much of a difference until I commenced with my calculations. I discovered by using resistance values of 2200Ω and 4700Ω, that Circuit Two was better.

Circuit One

2200Ω = 2105Ω by meter readings

4700Ω = 4364Ω by meter readings

Circuit Two

2200Ω = 2222Ω by meter readings

4700Ω = 4600Ω by meter readings

As you can see from these initial findings Circuit Two is the better circuit for measuring resistance values according to the labelled resistance.

Hypothesis

The manufacturers’ specifications as given on the Voltmeter and Ammeter are as follows:

Ammeter – Maximum Current 2mA, resistance 40Ω

Voltmeter – Maximum Pd 5V, Maximum current 100μA

After inspecting the above apparatus I have decided that the smallest value of the Current that I can accurately measure is         1 x 10-4 A and the maximum is 2 x 10-3 A. Any higher than 2 x 10-3A will be too high a reading for the ammeter. Also the minimum voltage that I think that I can accurately measure is 0.1V and the maximum is 5V (any higher will be to high for the voltmeter).

From the above values I have established the biggest and smallest resistance that these two meters can be used to measure:

From Ohms law it follows that image08.png

For the biggest resistance image09.png =

5 x 104 Ω

For the smallest resistance image16.png =

50Ω

...read more.

Middle

1150.0

1420

2.5

0.0018

1388.9

1435

2.8

0.002

1400.0

1470

2.9

0.002

1450.0

1500

2.8

0.0019

1473.7

1800

3.1

0.0018

1722.2

2200

4

0.0019

2105.3

2700

4.9

0.0019

2578.9

3300

4.2

0.0014

3000.0

4700

4.8

0.0011

4363.6

5600

4.5

0.0009

5000.0

6800

4.6

0.0008

5750.0

8200

4.7

0.0007

6714.3

10000

4.9

0.0006

8166.7

15000

4.3

0.0004

10750.0

22000

4.3

0.0003

14333.3

33000

3.8

0.0002

19000.0

47000

3.6

0.0001

36000.0

The first column of this table shows the resistance that was labelled on the actual resistor. The second and third columns are the actual readings that I noted from the Voltmeter and ammeter. I have then calculated the resistance from these two readings in the fourth column.

Second Set of Readings for Circuit One:

Circuit One – Second Set

Labelled Value of Resistor (Ω)

-+5%

Voltage from Voltmeter Readings (V)

Current from Ammeter Readings (A)

Resistance Obtained From Meter Readings (Ω)

56

0.1

0.0019

52.6

68

0.1

0.0017

58.8

100

0.2

0.002

100.0

150

0.3

0.0019

157.9

220

0.4

0.0017

235.3

270

0.5

0.0019

263.2

330

0.6

0.0019

315.8

680

1.3

0.0019

684.2

1000

1.9

0.0019

1000.0

1200

2.3

0.002

1150.0

1420

2.5

0.0018

1388.9

1435

2.8

0.002

1400.0

1470

2.9

0.002

1450.0

1500

2.8

0.0019

1473.7

1800

3.1

0.0018

1722.2

2200

4

0.0019

2105.3

2700

4.9

0.002

2450.0

3300

4.2

0.0014

3000.0

4700

4.8

0.0011

4363.6

5600

4.5

0.0009

5000.0

6800

4.6

0.0008

5750.0

8200

4.7

0.0007

6714.3

10000

4.9

0.0006

8166.7

15000

4.3

0.0004

10750.0

22000

4.3

0.0003

14333.3

33000

3.8

0.0002

19000.0

47000

3.6

0.0001

36000.0

The first column of this table shows the resistance that was labelled on the actual resistor. The second and third columns are the actual resistance values that were taken in the two attempts I did. The fourth column is the average of these two readings.

Average Resistance for Circuit One:

Circuit One

Labelled Value of Resistor (Ω)

-+5%

Resistance First Time (Ω)

Resistance Second Time (Ω)

Average Resistance

(Ω)

56

55.6

52.6

54.1

68

58.8

58.8

58.8

100

100.0

100.0

100.0

150

157.9

157.9

157.9

220

235.3

235.3

235.3

270

263.2

263.2

263.2

330

315.8

315.8

315.8

680

684.2

684.2

684.2

1000

1000.0

1000.0

1000.0

1200

1150.0

1150.0

1150.0

1420

1388.9

1388.9

1388.9

1435

1400.0

1400.0

1400.0

1470

1450.0

1450.0

1450.0

1500

1473.7

1473.7

1473.7

1800

1722.2

1722.2

1722.2

2200

2105.3

2105.3

2105.3

2700

2578.9

2450.0

2514.5

3300

3000.0

3000.0

3000.0

4700

4363.6

4363.6

4363.6

5600

5000.0

5000.0

5000.0

6800

5750.0

5750.0

5750.0

8200

6714.3

6714.3

6714.3

10000

8166.7

8166.7

8166.7

15000

10750.0

10750.0

10750.0

22000

14333.3

14333.3

14333.3

33000

19000.0

19000.0

19000.0

47000

36000.0

36000.0

36000.0

The first column of this table shows the resistance that was labelled on the actual resistor. The second and third columns are the actual readings that I noted from the Voltmeter and ammeter. I have then calculated the resistance from these two readings in the fourth column.

First Set of Results for Circuit Two:

Circuit 2 – First Set

Labelled Value of Resistor (Ω)

-+5%

Voltage from Voltmeter Readings (V)

Current from Ammeter Readings (A)

Resistance Obtained From Meter Readings (Ω)

56

0.2

0.0019

105.3

68

0.2

0.0019

105.3

100

0.3

0.0019

157.9

150

0.4

0.002

200.0

220

0.5

0.0018

277.8

270

0.6

0.002

300.0

330

0.6

0.0017

352.9

680

1.3

0.0018

722.2

1000

2

0.0019

1052.6

1200

2.4

0.0019

1263.2

1420

2.8

0.0019

1473.7

1435

2.5

0.0018

1388.9

1470

3

0.002

1500.0

1500

2.7

0.0018

1500.0

1800

3.5

0.0019

1842.1

2200

4

0.0018

2222.2

2700

4.9

0.0018

2722.2

3300

5

0.0015

3333.3

4700

4.6

0.001

4600.0

5600

4.9

0.0009

5444.4

6800

4.7

0.0007

6714.3

8200

4.8

0.0006

8000.0

10000

5

0.0005

10000.0

15000

4.4

0.0003

14666.7

22000

4.1

0.0002

20500.0

33000

3.2

0.0001

32000.0

47000

5

0.0001

50000.0

The first column of this table shows the resistance that was labelled on the actual resistor. The second and third columns are the actual readings that I noted from the Voltmeter and ammeter. I have then calculated the resistance from these two readings in the fourth column.

Second Set of Readings for Circuit Two:

Circuit 2 – Second Set

Labelled Value of Resistor (Ω)

-+5%

Voltage from Voltmeter Readings (V)

...read more.

Conclusion

The thing that bothered me most during the experiment was the accuracy of the two meters. They were on the whole very inaccurate. Parallax error also could have influenced my results and if this happened the resulting resistance could have been a long way off its actual value.

I think that digital meters would be have been a far better alternative to analogue, because they have a higher resistances, and human error could have been drastically reduced because the readout is digital. Parallax error would have been totally eradicated, and the reading would have been accurate to more decimal places.

Internal resistance of the components in question could have influenced my results, but I don’t think this happened because overall the readings were generally good.

I think overall the accuracy of my investigation was good, but there are numerous small factors that could have influenced a few of the anomalous results.

If I were to repeat the experiment again, I would try to find resistors that had a greater tolerance accuracy e.g. tolerances of 1% to get better resistor values. I would leave the power supply on for only a limited amount of time to prevent heating, which could change the resistance. I would like to use digital meters to record the current and voltage with. This would ensure that the results would be more accurate.

Overall though, I think my investigation did prove what I was trying to find and I could make conclusions that matched up with my evidence and my predictions. It must have meant that my results were fairly accurate and my investigation proved what I was out to find - You should connect the voltmeter without the ammeter in for low resistances up to 1435Ω for this particular circuit, but after this circuit two would give more accurate results.

...read more.

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