Physics: Values for Carbon Resistor and Light Bulb Essay

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Table of Contents

Introduction
Procedure
Experimental data
Results
Discussions and Analysis
Conclusion

Introduction

The main objective of the experiment is to investigate how the voltage varies at different current values for carbon resistor and light bulb. The effects of changing the length of the graphite with constant cross sectional area on the voltage and current readings will also be investigated. The law investigated for carbon resistor and light bulb is the ohms law while for graphite is testing resistivity.

Procedure

The resistance value for carbon was calculated based on the colour codes in the order, orange, blue, brown and gold. The value of the carbon resistor was also measured using DMM. A circuit was established that enabled the voltage to be varied and the corresponding current read. The current values at the following voltage values: 0 3 5 7 9 10 and 15. The resistance of the light bulb was measured using DMM and the corresponding values of current read for the following voltages: 0.104, 0.208, 0.401, 0.501, 0.595, 2.00, 4.00, 5.00, 6.00, and 6.46. A graphite of uniform cross sectional area was used and the voltages and currents read at various lengths (L) of the graphite:

Experimental data

Part 1: Based the colour codes, the resistance of carbon is 360 ±5% ohms and the reading on DMM was 354 ohms. Table 1 shows the corresponding current values at different voltages while graph 1 in the appendix is a plot of current against voltage for carbon for a Carbon resistor

Part 2: The resistance of the light bulb from the DMM reading is 02.2 ohms. Table 2 shows the voltage and current reading for light bulb while table 3 shows current and voltage readings at different lengths of graphite

Table 1: voltage and current readings for carbon resistor

Voltage(V) Volts	Current(I) A
0	0
3	0.008
5	0.013
7	0.019
9	0.025
10	0.028
15	0.042

Table 2: Voltages and Current readings for light bulb

VOLTAGE(Volts) (VOLTS)	CURRENT(Amperes) (AMPERES)
0.104	0.003
0.208	0.047
0.401	0.059
0.501	0.065
0.595	0.070
2.000	0.132
4.000	0.194
5.000	0.220
6.000	0.243
6.460	0.253

Table3: Voltage (Volts) and Current (Amperes) readings at different lengths of graphite

Length1(11mm)		Length2(16mm)		Length3(25mm)		Length4 (36mm)		Length5 (51mm)
Voltage	current	Voltage	Current	Voltage	Current	Voltage	Current	Voltage	current
0.526	0.171	0.604	0.170	0.74	0.170	0.985	0.169	1.403	0.170
0.538	0.175	0.621	0.175	0.765	0.175	1.007	0.176	1.443	0.175
0.551	0.180	0.640	0.180	0.791	0.180	1.050	0.180	1.478	0.180
0.580	0.189	0.699	0.191	0.833	0.190	1.108	0.190	1.509	0.190
0.661	0.200	0.728	0.200	0.877	0.200	1.16	0.200	1.585	0.200

Results

Part 1

From the data obtained above the carbon resistor obeys ohms law. Therefore it is ohmic. Based on colour coding the resistance is 360 + or – 5%. From the DMM the resistance is 354 ohms.

From the graph the gradient is change in current/change in voltage

Slope =change in current (A)/change in voltage (V);

Taking two points from the graph,

Gradient= (0.028-0)/ (10-0) which gives 0.0028 A/V

Therefore resistance =1/gradient; which is 1/0.0028;

=357.14 V/A

Part 2

From the DMM meter the reading is 9.2 ohms.

For the voltages of 0 to 0.6 V the slope is change in current/change in voltage

Gradient = (0.059-0.03)/ (0.401-0.104)

=0.0976431 A/V

Resistance =1/gradient; that is 1/0.0976431

=10.24 V/A

Part 3

The diameter of the rod is 2mm = 0.002m

Area of the rod =pie/4 x d^2; that is Area = 3.14/4 x 0.002²

Area =0.00000314m²

But since Resistance = Resistivity X Length/Area;

It follows that;

At a length of 11 mm (0.011m)

Resistance =change in voltage / change in current

= (0.661-0.526)/ (0.2-0.171); which=4.655 V/A

Resistivity = resistance x area/length

Resistivity=4.655 x 0.00000314/0.011=0.001329 Vm/A

At a length of 16 mm (0.016m)

Resistance = (0.640-0.604)/ (0.180-0.170); which=3.6 V/A

Resistivity = (3.6 x 0.00000314)/0.016; which =0.0007065 Vm/A

At a length of 25 mm (0.025m)

Resistance = (0.791-0.74)/ (0.180-0.170); which=5.1 V/A

Resistivity = 5.1 x 0.00000314/0.025; we get = 0.00064056 Vm/A

At a length of 36 mm (0.036m)

Resistance = (1.16-1.007)/ (0.2-0.176); which =6.375 V/A

Resistivity = (6.375 x 0.00000314)/0.036

=0.000556 Vm/A

At a length of 51 mm (0.051mm);

Resistance = (1.509-1.403)/ (0.190-0.170) which=0.106/0.02;=5.3 V/A;

Resistivity = (5.3 x 0.00000314)/0.051

=0.000326313 Vm/A

Discussions and Analysis

When we compare the calculated values from the experiment with values from colour codes they are almost the same, i.e. (360, 354 and 357.14). It implies that when a graph of current verses voltage is drawn, a straight line which passes through the origin is obtained whose slope is the inverse of resistance. The sources of variations in the measured value with DMM may be due to: incorrect calibrations and mechanical vibrations. The variations in the experimental values may also be due to poor reading techniques of current and voltage values and parallax errors. Therefore, the carbon resistor obeys ohms law.

For light bulb, the measured value from DMM is 09.2 ohms. The graph of current against voltage provides a straight line from 0 to 0.6 volts whose gradient is 0.097±7.15 x 10^-3. The resistance is the inverse of the gradient which gives 10.24 V/A. This is not far from the measured value of 9.2 ohms. The other part of the graph is a curve. The curve rates at three different points are; A; -0.002266±0.0002966 B; 0.04672 ± 2.16 x 10^-3 and C; 0.0445± 3.16 x 10^-3.This shows that the light bulb is ohmic for some voltages beyond which it becomes non- ohmic. The variations of the two values are attributed to errors due to reasons in part one above.

For graphite, the resistance at various lengths were obtained and the resistivity. The area of the graphite rod was calculated from the diameter measured and then used together with length and resistance. The resistance were obtained by getting the change in voltages divided by the corresponding changes in the currents. The values of the resistivity are almost constant implying that the resistivity of a material is constant. When given to one significant figure the values are constant. The errors may be due to incorrect readings of values at different lengths, mechanical vibrations of instrument, and changes in physical environment. These errors cause small variations in the obtained values.

Conclusion

The lab objectives were met since the resistance obtained from the experiment are almost the same as those from instruments for part one and two. For instance in part one the measured values are 360 and 354 while the experiment value is 357.14. This implies that the objectives of the experiment were achieved. For part two the objective were also achieved in that the light bulb is ohmic for 0 to o.6 volts with resistance of 10.24 ohms close to the measured value of 09.2 ohms. For voltages above 0.6 the light bulb is non ohmic. Finally for part three, the resistivity which is almost constant is obtained (0.001Vm/A). This implies that the objectives of the experiment were achieved.

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