Съдържание

IPhO 2013, Експеримент — Задача 2.1. The dependence of the solar cell current on the distance to the light source

Оригинал на условието (PDF)Съобщи за грешка

Всички материали от IPhO 2013

Solar cells — E2 · 7 юли 2013 г.

Warnings and notices

WARNING: Do not use the multimeter as an ohmmeter on the solar cells since the measuring current can damage them. When changing the measuring range on the multimeters, please turn the dial with caution. It can be unstable and may break. Check whether there is a number under the decimal point when measuring – if the dial is not fully in place, the multimeter will not measure, even if there are digits in the display.

Notice: Do not change the voltage on the power supply. It must be 12 V throughout the experiment. (The power supply for the light source should be connected to the outlet (230 V ~) at your table.)

Notice: Uncertainty considerations are only expected when explicitly mentioned.

Notice: All measured and calculated values must be given in SI units.

Notice: For all measurements of currents and voltages in this experiment, the LED-light source is supposed to be on.

Условие

2.0 Introduction

Equipment used for this experiment is displayed in Fig. 2.1.

Photograph of the equipment laid out on a table, each item marked with a red letter: solar cells A and B, black box C with LED light source D, power supply E, variable resistor F, holders G and I, aperture plate H, shielding plate J, multimeters K and L, wires with crocodile clips M, optical vessel N, measuring tape O, scissors P, tape Q, water bottle R and paper napkin S. — Figure 2.1 Equipment used for experiment E2.

List of equipment (see Fig. 2.1):

A: Solar cell

B: Solar cell

C: Box with slots for the mounting of light source, solar cells, etc.

D: LED-light source in holder

E: Power supply for light source D

F: Variable resistor

G: Holder for mounting single solar cell in the box C

H: Circular aperture for use in the box C

I: Holder for mounting two solar cells in the box C

J: Shielding plate for use in the box C

K: Digital multimeter

L: Digital multimeter

M: Wires with mini crocodile clips

N: Optical vessel (large cuvette)

O: Measuring tape

P: Scissors

Q: Tape

R: Water for filling the optical vessel N

S: Paper napkin for drying off excess water

T: Plastic cup for water from the optical vessel N (not shown in Fig. 2.1)

U: Plastic pipette (not shown in Fig. 2.1)

V: Lid for the box C (not shown in Fig. 2.1)

Data sheet: table of fundamental constants

Speed of light in vacuum	$c = 2.998\times 10^{8}\ \mathrm{m\ s^{-1}}$
Elementary charge	$e = 1.602\times 10^{-19}\ \mathrm{C}$
Boltzmann’s constant	$k_{\mathrm{B}} = 1.381\times 10^{-23}\ \mathrm{J\ K^{-1}}$

A solar cell transforms part of the electromagnetic energy in the incident light to electric energy by separating charges inside the solar cell. In this way an electric current can be generated. Experiment E2 intents to examine solar cells with the use of the supplied equipment. This equipment consists of a box with holders for light source and solar cells along with various plates and a lid. The variable resistor should be mounted in the box, see Fig. 2.2. One of the three terminals on the resistor has been removed, since only the two remaining terminals are to be used. Also supplied are wires with mini crocodile clips and two solar cells (labeled with a serial number and the letter A or B) with terminals on the back. The two solar cells are similar but can be slightly different. The two multimeters have been equipped with terminals for designated use as ammeter and voltmeter, respectively, see Fig. 2.3. Finally, the experiment will make use of an optical vessel together with some drinking water from the bottle.

Two photographs side by side: (a) the open black box with the LED light source mounted inside and the variable resistor lying beside it; (b) the box with the resistor mounted through its wall, the shaft protruding. — Figure 2.2 (a) Box with light source and resistor for mounting. (b) The resistor mounted in the box. Notice that the small pin on the resistor fits in the hole to the right of the shaft.

2.1 The dependence of the solar cell current on the distance to the light source

For this question you will measure the current, $I$ , generated by the solar cell when in a circuit with the ammeter, and determine how it depends on the distance, $r$ , to the light source. The light is produced inside the individual light diodes and $r$ is therefore to be measured as shown in Fig. 2.4.

Top-view sketch: the LED light source (a cone with a row of diodes) on the left, the aperture a and solar cell A with + and − terminals on the right; the distance r is marked from inside the diodes to the surface of the solar cell. — Figure 2.4 Top view of setup for question 2.1. Note the aperture a immediately in front of the solar cell A. The distance is measured from inside the light diode to the surface of the solar cell.

Do not change the measuring range on the ammeter in this experiment: the internal resistance of the ammeter depends on the measuring range and affects the current that can be drawn from the solar cell. State the serial numbers of the light source and of solar cell A on your answer sheet. Mount the light source in the U-shaped holder (the light source has a tight fit in the holder, so be patient when mounting it. Mount solar cell A in the single holder and place it together with the circular aperture immediately in front of the solar cell. The current $I$ as a function of the distance $r$ to the light source can, when $r$ is not too small, be approximated by

I(r) = \frac{I_a}{1+\frac{r^2}{a^2}}

where $I_a$ and $a$ are constants.

Photograph of two yellow 2286 digital multimeters side by side, with range dials and terminals 20A, A, COM and VΩ; the left one is set up as ammeter, the right one as voltmeter. — Figure 2.3 Multimeters equipped with terminals for use as ammeter (left) and voltmeter (right), respectively. The instrument is turned on by pressing “POWER” in the top left corner. The instrument turns off automatically after a certain idle time. It can measure direct current and voltage (=) as well as alternating current and voltage (∼). The internal resistance in the voltmeter is 10 MΩ regardless of the measuring range. The potential difference over the ammeter is 200 mV at full reading, regardless of the measuring range. In case of overflow the display will show “l”, and you need to select a higher measuring range. The “HOLD” button (top right corner) should not be pushed, except if you want to freeze a measurement.

2.1a Measure $I$ as a function of $r$ , and set up a table of your measurements. [1 т.]

2.1b Determine the values of $I_a$ and $a$ by the use of a suitable graphical method. [1 т.]

Отговори

Решение

I(r) = \frac{I_a}{1+\frac{r^2}{a^2}}

slot #	r	I	1/I	r^2
	mm	mA	1/mA	mm^2
3	9.0	5.440	0.184	81
4	14.5	5.290	0.189	210
5	20.0	5.010	0.200	400
6	25.5	4.540	0.220	650
7	31.0	3.840	0.260	961
8	36.5	3.230	0.310	1332
9	42.0	2.730	0.366	1764
10	47.5	2.305	0.434	2256
11	53.0	1.985	0.504	2809
12	58.5	1.730	0.578	3422
13	64.0	1.485	0.673	4096
14	69.5	1.305	0.766	4830
15	75.0	1.140	0.877	5625
16	80.5	1.045	0.957	6480
17	86.0	0.930	1.075	7396
18	91.5	0.840	1.190	8372
19	97.0	0.755	1.325	9409
20	102.5	0.690	1.449	10506

I\left(1+\frac{r^2}{a^2}\right) = I_a

r^2 = I_a a^2\cdot\frac{1}{I} - a^2

a^2 = 1200\ \mathrm{mm}^2 \pm 100\ \mathrm{mm}^2,

a = 35\ \mathrm{mm} \pm \pm 2\ \mathrm{mm}

I_a a^2 = \frac{10870-0}{1.50-0.15}\cdot\frac{\mathrm{mm}^2}{\mathrm{mA}^{-1}} = 8051.85\ldots\ \mathrm{mm}^2\mathrm{mA}

I_a = \frac{8051.85\,\frac{\mathrm{mm}^2}{\mathrm{mA}^{-1}}}{1200\ \mathrm{mm}^2} = 6.7\ \mathrm{mA} \pm 0.5\ \mathrm{mA}

(I_a a^2)_{\min} = \frac{10700-0}{1.50-0.14}\cdot\frac{\mathrm{mm}^2}{\mathrm{mA}^{-1}} = 7867.6\ldots\mathrm{mm}^2\mathrm{mA}

\rightarrow I_{a,\max} = \frac{(I_a a^2)_{\min}}{{a^2}_{\min}} = \frac{7867.6\ \mathrm{mm}^2\mathrm{mA}}{1100\ \mathrm{mm}^2} = 7.2\ \mathrm{mA}

Hand-drawn graph on millimetre paper of r² (mm², ticks 1000, 5000, 10000) against 1/I (mA⁻¹, ticks 0.1, 0.5, 1.0, 1.5) with the measured points lying on a straight line.

Оригинал в Архива: exp2.pdf · официални решения: exp2_sol.pdf