Chapter 8

Lab #8 - ORR, MM, AI: Thickness ofgraphite pencil line

Aim

In this experiment you will:

• investigate how the resistance R of a wide pencil line varies with the length l of the

line, and

• use your results to calculate a value for the thickness, t, of this pencil line and the

number of atoms in the thickness of the pencil line.

Background

Consider a very thin strip of a conducting material. Its thickness, t, is much less than a

micron (micrometer, 10-6 m). It is not possible to measure its thickness, even if we try to

use a micrometer. Can you guess why?

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18CHAPTER 8. LAB #8 - ORR, MM, AI: THICKNESS OF GRAPHITE PENCIL LINE

Figure 8.1: Measurement of resistance of a thin metal sheet

Measurement of thickness of such a thin sample has generally been made by a use of

an indirect method. One of these methods is outlined below.

The resistance, R, of a conducting rod is given by

R = ρlA

(8.1)

where ρ is the resistivity, l is the length and A is the area of cross-section of the rod. If

we have a conductor in the shape of a strip, as shown in Figure 8.1, then its resistance, R,

measured along the length is given by

R = ρlA= ρ

lWt

(8.2)

where ρ is the resistivity, l, W and t are shown in Figure 8.1.

The thickness, t, of the strip can be determined if we measure R, l and W , and use the

known value of the resistivity, ρ , of the strip material.

Apparatus

microammeter, voltmeter, connecting wires, 2 knife-edged probes (jockeys), half-metre

rule, 3B graphite pencil, sheet of plain paper, power supply, 2 D-type dry cells and holders.

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Method

(a) On a sheet of graph paper, draw a rectangular box of length 200 mm and width 4.0 mm

with a 10 mm square at one end. Use the 3B pencil provided to shade the box heavily

(a dense black). You should try to ensure that the shading is as uniform as possible.

Figure 8.2: Measurement of resistance at different distances (measured from x=0) alongthe pencil line.

The square (Figure 8.2) is to act as an electrical contact at the end of the zero end of the

line.

(b) Construct the circuit as shown in figure 8.3. When the probes are in use in the circuit,

they must be held by the insulated sections and not the exposed metal parts.

20CHAPTER 8. LAB #8 - ORR, MM, AI: THICKNESS OF GRAPHITE PENCIL LINE

Figure 8.3:

(c) Check the uniformity of the shading by placing the probes at different positions on the

pencil line at a separation of 40 mm each time. Note the reading of the microammeter

in each case. If any of the readings are more than about 10% below the maximum

reading, continue shading the parts of the box which give low readings.

(d)(i) Place the probes on the pencil line so that their separation l is 40 mm.

(i) Measure and record the current I, potential difference V and separation l.

(iii) Change the value of l and repeat (dii) until you have six sets of values for I, V and l.

Include in your table of results all the values of R, where R =V/I.

(iv) Justify the number of significant figures which you have given for R.

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(e) The formula which relates R and l is

R =ρlA

(8.3)

where ρ is the resistivity of pencil lead and A is the cross-sectional area (normal to thecurrent) of the pencil line.

(i) Plot a graph of R as ordinates (y-axis) against l as abscissae (x-axis).

(ii) Determine the gradient of the graph.

(iii) Use your answer from (eii) and the value of ρ (= 7.837× 10−6Ωm) to determine a

value for the cross-sectional area of the pencil line. Hence, calculate t, the thickness

of the line.

(f) Assuming the size of an atom of carbon in pencil lead to be 2× 10−10m, use your

answer in (e iii) to estimate how many atoms could be placed on top of each other to

make up the thickness of the pencil line.

(g) Discuss the sources of errors in this experiment.

(h) If you were to continue to draw this pencil line beyond the 200 cm limit using a new

pencil how long (in km) would this line get before you run out of pencil lead?

Assume you have large enough paper(!) and you don’t get tired. Take density of

graphite to be 2g/cm3. Show all your steps and reasoning.