Angelica P. Cano August 17, 2015PHYS 193 H-1L 2012-40545

Resistance Measurement

Step 1:

Using a standard multimeter, I measured five resistors with the following values: 20

Ω, 100 Ω, 470 Ω, 2.2 KΩ, 2.2 MΩ. The resistance of each resistor was measured 50 times.

The mean, standard deviation and variance was obtained and summarized in the table

below.

Resistor Mean Standard deviation Variance20 Ω 20.0978 0.02894682 0.0008379

100 Ω 99.7600 0.440778532 0.194286

470 Ω 468.564 1.532073425 2.347249

2.2 KΩ 2.19208 0.006533555 0.00004269

2.2 MΩ 2.25854 0.044146884 0.001948947

The resistances of the five resistors were then measured using different scales of the

multimeter. Ideally, the measurements should not vary in value. But because of the

limitations of the device, the obtained values are slightly different. Resistance

measurements in the ohm scale are more precise and accurate than measurements in the

kiloohm and megaohm scale. Measurements in larger scales (kilo, mega etc.) are estimated

values and tend to be less precise when measuring low resistance components. It is advised

to use appropriate scales that are suitable to the component of interest. When measuring

low resistance components, the ohms scale will give more accurate readings; with high

resistance components it is suggested to use larger scales.

Step 2:

Using a digital DC power supply and two multimeters – one used as an ammeter and

one used as a voltmeter- the IV readings of the resistors are obtained. For each IV reading,

the Resistance values were obtained and the relevant parameters were summarized in the

table below.

Resistor Mean value of Standard deviation Variance

computed R20 Ω 19.61224 0.46696 0.218051

100 Ω 104.638 2.874659 8.263667

470 Ω 468.00 3.87113 14.98565

2.2 KΩ 2.245 0.00349 0.0000122

2.2 MΩ 1.92 0.70280781 0.493939

Step 3:

The IV readings was repeated 50 times for each resistor value. The graphs below

show the linear relationship of voltage and current. This is also described as the ohmic

behavior of common commercial resistors.

0 1 2 3 4 5 6 7 8 9 100

0.0010.0020.0030.0040.0050.0060.0070.0080.009

0.01

20 ohms

Voltage (V)

Curr

ent (

A)

0 2 4 6 8 10 120

0.002

0.004

0.006

0.008

0.01

0.012

100 ohms

Voltage (V)

Curr

ent (

A)

0 2 4 6 8 10 120.00E+00

5.00E-03

1.00E-02

1.50E-02

2.00E-02

2.50E-02

470 ohms

Voltage (V)

Curr

ent (

A)

0 2 4 6 8 10 12 140.00E+001.00E-062.00E-063.00E-064.00E-065.00E-066.00E-067.00E-06

2.2 megaohms

Voltage (V)

Curr

ent (

A)

0 1 2 3 4 5 6 7 8 90

0.00050.001

0.00150.002

0.00250.003

0.00350.004

2.2 kiloohms

Voltage (V)

Curr

ent (

A)

Step 4:

Why should an ideal voltmeter have infinite resistance?

Every measuring device impacts or interferes with the system it is measuring. The

effects, however, can be minimized by good device design and connections. A voltmeter is a

device to measure the applied voltage in an electronic circuit. It is always connected in

parallel with the circuit components under test. An ideal voltmeter should have infinite

resistance. Because it is connected in parallel, the current passing through it will still be

accounted for in the measurement of total circuit current. A voltmeter with infinite

resistance will not draw current away from the circuit [1].

Why should an ideal ammeter have zero resistance?

An ammeter is a current measuring device. Ideally, it should have zero resistance

because it should have zero potential difference between its terminals. Meters are also

circuit elements, meaning they should have the corresponding electrical properties suitable

to their functions. Ammeters are connected in series with the component under test. It

should have zero or at least negligible resistance so that it would not greatly affect the total

current of the circuit. Real ammeters, however, have a small finite resistance [1].

Explain the principle of Four point Kelvin probe resistance measurements.

The Four point Kelvin probing method is a resistance measuring technique that uses

separate pairs of current-carrying and voltage-sensing electrodes to give more accurate

readings than the common two terminal sensing method. It is named after William Thomson,

Lord Kelvin who invented the Kelvin bridge in 1861. This method is usually used in

measuring sheet resistance of thin films and measuring low resistance values [2].

Resitor Slope (1/R) Intercept R2

20 Ω 0.053483 0.00796 0.999305

100 Ω 0.001 8.67362E-19 1

470 Ω 0.002153 5.59218E-05 0.999842429

2.2 KΩ 0.000451 1.29223E-05 0.99860989

2.2 MΩ 5.4338E-07 9.67E-08 0.99945862

There are two pairs of two-wire connections – the current leads and voltage leads.

The current is supplied using the current leads, generating a voltage drop across the

resistance of the component under test. The voltage leads are then made to be adjacent to

the component under test. The current leads are usually connected as the outside pair,

while the voltage leads are the inside pair [2].

References

[1] Chapter 8 - DC Metering Circuits: Voltmeter Impact on Measured Circuit. All About

Circuits. www.allaboutcircuits.com August 14, 2015

[2] Measurement Accuracy and Kelvin Probing. Pdf file downloaded from accuprobe,

accessed using google search. August 14, 2015ss