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Modern analogue of Ohm’s historical experiment

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2014 Phys. Educ. 49 689

(http://iopscience.iop.org/0031-9120/49/6/689)

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Physics Education 49 (6) 689

Modern versions of historical experiments are very valuable. They help students to master the method of scientific cognition accepted in phys-ics. Therefore, if a natural experiment is costly, computer-based simulators are used for teaching [1]. Ohm’s law is a key empirical relation, and it is often verified in educational laboratories [2], but the educational experiments usually do not reveal the essence of investigation during which Ohm established his well-known law [3]. Not only the result, but also the conceptual structure of Ohm’s experimental work, is interesting [4]. Therefore, reproduction of Ohm’s investigation in an educational laboratory favours deep under-standing of the experimental method in physics.

1. Ohm’s experimental unitFigure 1 shows the electric circuit and the appear-ance of the experimental unit created by Ohm [5]. The thermoelectric current source included a bis-muthic branch (1) and two copper branches (2) tightly screwed to its ends. One of the resulting thermocouples was dipped into a vessel (3) con-taining melting ice, the other into a vessel (4) con-taining boiling water. Over the copper branch of

the first thermocouple, suspended on a wire under a bell jar, a magnetic needle (5) was placed. The top end of the suspension was attached to a rotating indicating head. This device represented a mag-netic torsion balance like Coulomb’s electrostatic torsion balance. The mercury contacts (6) con-nected the leading-out wires of the thermoelectric current source with metal wire pieces (7) having equal diameters, but different lengths. When elec-tric current flowed in the circuit, the magnetic nee-dle deflected; Ohm returned it to the initial state, rotating a torsion balance head, and he determined the electric current according to the turning angle of the head.

2. The educational device for Ohm’s law verificationFigure 2 presents a simple device for the experi-mental substantiation of Ohm’s law. The rectangu-lar coil (1) is made of a thick copper wire having a diameter of 1.4 mm and a length of 1 m. The coil size is 12 × 40 × 40 mm3, and it contains five turns. The ends of this wire are cleaned of insula-tion. To them the bunch ends of six pieces of con-stantan wire (2) with a diameter of 1.0 mm and

V V Mayer and E I Varaksina

Modern analogue of Ohm’s historical experiment

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P a P e r s

Modern analogue of Ohm’s historical experimentV V Mayer and E I Varaksina

The Glazov Korolenko State Pedagogical Institute, Russia

E-mail: varaksina_ei@list.ru

AbstractStudents receive a more complete conception of scientific cognition methods if they reproduce fundamentally important historical investigations on their own. Ohm’s investigation realized in 1826 is one of these. This paper presents a simple and accessible experimental unit, in which Ohm’s ideas are implemented with the help of modern means. The unit includes a differential copper/constantan thermocouple, a solenoid, a compass and a spirit lamp. Doing the experiment, students investigate the dependence of current on the electromotive force of the source, source resistance and load resistance.

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V V Mayer and E I Varaksina

690 Physics Education November 2014

a length of 20 cm each are tightly screwed with thin copper wire, which is wound with the turns touching. The connection points are soldered with tin. The thick copper wire is cut apart and insulat-ing tubes are pulled onto its ends. The parts of this wire in the insulating tubes are twisted. The wire ends (3), which jut out of the tubes, are carefully cleaned of insulation. They are poles of a thermo-electric current source. The electric conductors under test (4) of various lengths are connected to the poles by twisting. Instead of twisting it is pos-sible to use alligator clips. The coil (1) is well fixed on the base (5) of an insulator with a few loops of insulating tape. The compass (6) is placed into the coil. The electric conductors under test are pieces of insulated copper wire with diameters of 0.3–0.5 mm and lengths, for example, of 25, 50, 75 and 100 nm. These wires are curled into rings (7).

3. Experimental investigationThe device shown in figure 2 is placed so that the coil axis is perpendicular to the compass needle. The compass case is turned so that one of the nee-dle ends indicates the origin. Next, we make sure that ferromagnetic objects are not near enough to have an effect on the magnetic needle. The discon-nected poles of the source are short-circuited with uninsulated copper wire. We heat one of the ther-mocouples in the flame of a spirit lamp and observe the deflection of the magnetic needle. Initially the

increase of the angle is fast, then it becomes slower. At last the heat equilibrium ensues. If the magnetic needle deflects to an angle of 80° and it is persis-tently in that position, then the unit is ready to work.

It is easy to show that the tangent of the deflection angle α of the magnetic needle from the magnetic meridian is directly proportional to the current I in the coil:

α ∼ Itg  . (1)

This fact makes it possible to measure the electric current in the wire, which is connected in series with the coil and the source current.

Without removing the spirit lamp flame, we disconnect the poles of the thermoelectric current source and connect one of the prepared wires to them. The deflection angle is written down, and the second wire is connected instead of the first, etc.

For example, we have used a copper wire having a diameter of 0.425 mm and our results are shown in the first and second rows of table 1. In the third row, the respective values of the tangent of the deflection of the compass needle angle α are given. According to formula (1) these values are proportional to the electric current in the circuit.

4. Analysis of experimental resultsNext, a graph is plotted. It shows the dependence of the current I (in units of tg α) on the wire length x. The curve turns out like the one presented in

Figure 1. George Ohm’s experimental unit (see text for explanation of numbers).

Modern analogue of Ohm’s historical experiment

691Physics EducationNovember 2014

figure 3(a). This curve is plotted according to the experimental data (table 1). The curve looks very much like a hyperbola, the equation  of which is given in a mathematics course in the following way:

=+

ya

x b, (2)

where a is the coefficient of vertical stretch of a hyperbola (y = 1/x) and b is the amount of hori-zontal shift.

If the current I depends on the wire length x in accordance with equation  (2), then the

inversely proportional value 1/I linearly depends on the wire length x:

= + = +I

x b

a ax

b

a

1 1. (3)

In table  1 row 4, the values of the quantity 1/I are given in units of ctgα. We plot a graph of the dependence of the value 1/I on the wire length x and then make sure that it is a straight line (figure 3(b)). Thus, the experiment shows that the electric current in a circuit is inversely propor-tional to the wire length. It only remains to find out the physical meaning of the constants a and b that are part of equation (2).

It is clear that quantity b has the same essence as x, as the sum of these amounts is in the denominator of equation  (2). The experi-ment shows that the greater the wire length, the smaller current I in the circuit (figure 3(a)). Therefore, the wire length determines the elec-trical resistance of the circuit connected to a cur-rent source. However, in every experiment value

Table 1. The measured angles of the deflection of the magnetic needle at the various lengths of the copper wire in which the current flows; the calculated values of the tangents and the cotangents of these angles.

x, cm 0 25 50 75 100α, ° 78 71 60 55 48tg α 4.70 2.90 1.73 1.43 1.11ctg α 0.21 0.34 0.58 0.70 0.90

Figure 2. The device for experimental substantiation of Ohm’s law (see text for explanation of numbers).

V V Mayer and E I Varaksina

692 Physics Education November 2014

b remains the same, otherwise the graph in fig-ure 3(b) would not be straight. Consequently, b is the electrical resistance of that part of the circuit which is not changed during the experiments.

Therefore, it is possible to consider that b is the source resistance and x is the external resist-ance, so they can be denoted with the familiar let-ters b = r and x = R.

In the experiment, during the increasing tem-perature of one of the thermocouples, an increase in the current is observed. Consequently, in value a in equation (2) characterizes the source’s ability to create electric current in a circuit. Therefore, we can give the name electromotive force to value a, and we can denote it with the familiar letter E=a .

As a result, Ohm’s law for a complete circuit acquires the modern look:

E=+

IR r

. (4)

The point of intersection of the graph shown in figure 3(b) with the ordinate axis gives a value directly proportional to Er / . The point of intersec-tion of this graph with the abscissa axis gives a value directly proportional to the source resistance r.

5. ConclusionDuring the study of basic electrodynamics, imple-mentation of the introduced experiment gives the

following results. First, students understand how Ohm and his contemporaries could introduce fun-damental concepts relating to an electric circuit, without having electrical measuring instruments. Second, students make sure that they have proved the truth of Ohm’s law with a first-hand experi-ment in their educational investigation, not from more or less probable speculative reasoning that should be taken on trust. Third, students master a scientific method, with the help of which a physi-cal law is determined.

References[1] Michel G 2012 Millikan’s oil-drop experiment:

a centennial setup revisited in virtual world Phys. Teach. 50 98

[2] Madsen M J 2009 Ohm’s law for a wire in contact with a thermal reservoir Am. J. Phys. 77 516

[3] Mario G 1965 Storia Della Fisica (Torino: Bollati Boringhieri)

[4] Schagrin M L 1963 Resistance to Ohm’s law Am. J. Phys. 31 536

[5] Lipson H 1968 The Great Experiments in Physics (Edinburgh: Oliver)

Figure 3. Graphical representation of Ohm’s law: (a)—the dependence of current I on wire length x looks like a hyperbolic branch; (b)—the dependence of 1/I on wire length x is linear.

Received 2 May 2014, accepted for publication 4 June 2014doi:10.1088/0031-9120/49/6/689

Mayer Valery Vilgelmovich (left) is a professor and Varaksina Ekaterina Ivanovna (right) an associate professor at the Glazov Korolenko State Pedagogical Institute in Russia. They

work in the field of educational experiments for students in various areas of physics.