Experiment 3-6. Ohm s Law

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1 Physics Laboratory Last update: Experiment 3-6. Ohm s Law Purpose of experiment By measuring voltage on a circuit consisted of resistances, electromotive forces and current flowing the circuit by means of a voltmeter and an ammeter, confirm Ohm s law and Kirchihoff s law, and obtain the values of resistances. Outline of experiment Have full knowledge of principles of an ammeter and a voltmeter. Measure resistances by use of a voltmeter and an ammeter. Guess values of resistances obtained from parallel circuits and series circuits Experimental method These equipments are prepared in the laboratory. (Parentheses mean the number of them.) DC power supply (0-10V) (1)

2 Voltmeter (1), Ammeter (1) Resistance connecting box(1) Cables (6) If you need more equipments, inquire to your teaching assistant or the experiment preparation room (19-114), or prepare them for yourself. And also you need to know the static current(voltage) sources.

3 Bellows are the recommended and standard experimental methods 1) There is a switch in the middle of the Resistance connecting box and you can get various kinds of arrangement of resistances by using it. There are three modes on the switch ;parellel, series, and parellel series. Try them and learn how it can be operated. (Hint : Use the concept of Open and Short in circuit.) 2) Connect each of +, terminals of the DC power supply with that of the resistance connecting box. Be sure that the voltmeter is connected in parrellel and ammeter in series. When you are not using an ammeter, connect a wire between the ammeter terminals of the resistance connecting box not to open the circuit. Then turn the DC power supply on and apply adequate voltage and current. Measure the voltage and the current to obtain the value of the resistance. There are 11 unknown resistances, try a variety of cirucits and guess these values of resistances using experimental data. (These videos are old ones, but they can be helpful.) [video] 3) Connect two or more resistances that you know by performing 2) with the box in series, measure the voltage and current to obtain the total resistance value of the series resistances. [video] Make a parallel circuit with resistances, do the same experiment for a parallel circuit. [video] 4) Connect resistances that you know by performing 2) with the box; in a way some of them are in series and others in parallel. Obtain the total resistance value by using the measured voltage and the current. [video] Below is a recommended format for the laboratory report.

4 Voltage applied to resistance 1 = V, Current flowing resistance 1 = A Value of resistance 1 (V/I) = ohm Voltage applied to resistance 2 = V, Current flowing resistance 2 = A Value of resistance 2 (V/I) = ohm Voltage applied to resistance 3 = V, Current flowing resistance 3 = A Value of resistance 3 (V/I) = ohm Voltage applied to resistance 4 = V, Current flowing resistance 4 = A Value of resistance 4 (V/I) = ohm Total resistance of resistance 1,2 in series = (V/I)ohm Total resistance of resistance 3,4 in parallel = (V/I)ohm Total resistance of resistance 1,2 in series and resistance 3,4 in parallel = (V/I)ohm Background theory (1) Ohm s Law The equation below holds for a voltage V for some resistant object and for a current I flowing through the object. Ie, the current I is proportional to the applied voltage V V = RI (1) with R is the resistance of the resistant object. There are two ways to construct a circuit; a sires circuit, and a parallel circuit. For a series circuit,

5 For a parallel circuit RS = R1 + R2 + R3 + (2) 1/RS = 1/R1 + 1/R2 + 1/R3 + (3) Here, because I = q / t, the unit of I is [coul/sec] = [ampere], because V = W/q, the unit of V is [joule/coul] = [volt], and because R = V/I, the unit of R is [volt/ampere] = [ohm]. (2) Kirchihoff s Law 1) 1 st Law At any node(junction) of electrical circuit, the sum of currents flowing into the node is equal to the sum of currents flowing out of the node. Ie; ΣIt = 0 (4) 2) 2 nd Law The algebraic sum of all electromotive force E in a closed circuit is equal to the algebraic sum of all voltage drops by all resistances in the same closed circuit. Ie; ΣE= ΣRI (5) According to the ohm s law, the voltage drops across the resistant object is proportional to the current that flows through the resistant object. In other words, ohm s law holds. Therefore if the resistance is constant in the range of all supplied voltages, the voltagecurrent graph would be straight. Devices having this property are called linear devices. Since many devices are heated as the current is increasing, their resistance value changes, these devices are called non-linear devices. More thinking

6 Heat emission from a filament In a static state, because the temperature of the filament don t change, all applied power is emitted. The aspect of emitting energy is different depending on the emitting mechanism. In other words, in the case of emission of heat by conduction, according to the Newton s law of cooling, the energy emitted per unit time is, by the formula P = k(a/l)(t-t0) (A1), proportional to the temperature difference between the filament and the surroundings, inversely proportional to the distance with respect to the direction of heat flow, and proportional to the cross-sectional area. The constant K is called thermal conductivity. In the case of energy transfer by radiation, the energy emitted per unit time is, according to the Stefan-Boltzmann law of radiation, P = εσa(t 4 - To 4 ) (A2), proportional to the difference of T 4, with T is the temperature of the object, A the surface area of the object, and ε is called emissivity, σ is called Stefan-Boltzmann constant(σ = 5.67x10-8 W/m 2 K 4 ). For the perfect radiating object, like a black body, ε is 1, for most objects 0<ε<1. Intensity of light emitted from black body reference E.Hecht general physics book.

7 Lights emitted from 3000 K filaments are almost infra red rays rather than visible rays. In the visible region, because the intensity of light is almost the same regardless of the wavelength, white lights, red rays are slightly stronger, are made. The intensity of light radiated by a filament reference E.Hecht general physics book As the temperature of the filament increases(picture on your right), the intensity is increases and the color becomes to be white. When you see the upper two equations(equation A1, and A2), you may notice that, depending on the way of heat transfer, the aspect of the temperature dependence of heat transfer power is different. In other words, when the temperature of the filament is not quite different from the room temperature, heat transfer mainly occurs by conduction(equation (A1)), however, as the temperature increases, radiation(equation (A2)) is expected to be the main mechanism of heat transfer. Therefore, from the power P applied to the filament and the temperature T of the filament in a static state, drawing log-log graph of P versus (T-T0) or P versus(t 4 -T0 4 ) gives you the information whether the energy transfer from the filament to the surroundings is mainly occurs by conduction or radiation and the temperature ranges where each transfer machnism is important. Reference Static current(voltage) power supply Analysis of measurement data

8 Aanlysis method based on the graph James Joule the importance of precise measurement Georg Ohm Ohm s law given a cold reception Joseph Stefan the creator of kinetic gas theory Ludwig Boltzmann the theoretical physicist laid the foundation of statistical mechanics

PHYSICS FORM 5 ELECTRICAL QUANTITES

PHYSICS FORM 5 ELECTRICAL QUANTITES QUANTITY SYMBOL UNIT SYMBOL Current I Amperes A Voltage (P.D.) V Volts V Resistance R Ohm Ω Charge (electric) Q Coulomb C Power P Watt W Energy E Joule J Time T seconds s Quantity of a Charge, Q Q = It