Design
How Resistance of Light Dependent Resistor (LDR) varies with Light Intensity
Introduction
My aim of this experiment is to investigate how effective is the Resistance of LDR with the
intensity of light. To practically work the experiment a series circuit will be built with the use of
an LDR, Ammeter, Resistor, batteries and etc. The idea popped up when I was walking down the
streets of China with my friends on a foggy day, back in 2018. What caught my eye were the
street lights turning on automatically. This got stuck in my mind, and when I got to my hotel, I
searched on the internet that how does this process happen. Then I came to know that LDR is
used in a circuit of street lights to make it work. Basically what happened is that in that foggy
evening it got dark, the resistance in the circuit of street light got increased which caused the
current flow to stop. The relay also got deactivated hence automatically turned the street lights
on. So this research got me to ask myself how the resistance of LDR varies with the light
intensity.
In order to answer the question I built a series circuit consisting of a 12V battery (PD), 1kΩ
resistor for R, Ammeter to measure Current (I), a Voltmeter to measure Voltage(V) LDR (Ω)
and Intensity Meter to measure intensity in lux. The design of the circuit is shown in figure 1.
To check the Resistance (R) variations, a torch was shed on LDR. It was decided to approach the
experiment in different ways. In the first situation, ‘Height (cm)’ from touch shed was an
independent and ‘LDR type’ was a dependent variable. In the second situation, the height (cm)
was kept constant with different types of LDR. To differ between types of LDR, it was wrapped
with two different types of paper, Aluminum and Black-colored Paper. The paper types were
holed with a constant rate and then resistance values were calculated with the increase of the
number of holes in each type of LDR wrapped.
A
LDR
1kΩ
V
The
diagram above is made
through
Microsoft Word Shapes.
Hypothesis
LDR is also known as Photoresistor is a resistor which has resistance depending on an amount of
light falling on LDR (Bhattacharya). Basically, it is a photocell that works with the rule of
photoconductivity. The resistor in LDR is a passive component whose resistance value decreases
when light intensity decreases (.K et al.). In this process of photoconductivity when photons fall
(light falls) on the device, the valance band of semiconductor material are excited to the
conduction band. These photons have more energy than the bandgap of semiconductor in order
to jump to a higher level of the conduction band (Electrical4U). And with enough energy hitting
the device, increasing number of electrons are excited to the conduction band resulting in a
bigger number of charge carriers. This causes more current flow which decreases the resistance
of the device (Electrical4U).
Regarding the experiment, there are two scenarios. In one, the light will be an independent
variable and LDR will be dependent. After researching online, I hypothesize that as we increase
the height of light from the LDR, the intensity of light should decrease which will cause
Resistance to increase. With the increasing height, the current flow in the circuit also decreases.
In the second scenario, the height of the light source is kept constant. And the LDR type is
changed. The LDR will be wrapped with two different types of materials, Type A, Black glace
paper (reflective) and Type B, Aluminum (absorbing material). Then resistance will be noted by
increasing the number of holes in the wrapped LDR. In this scenario, the Resistance will keep
decreasing with the number of holes but LDR with black paper-wrapped should have greater
resistance comparatively to aluminium wrapper LDR because Temperature is directly
proportional to resistance. As the black paper is an absorbing material and aluminium is
reflective material, the resistance must be greater in Type A of LDR.
Mathematical model
Ohms Law
V=IR
The formula represents the potential difference (E/V) between two points or Voltage of a current.
In this formula, Voltage is current (in Ampere) per unit resistance (in ohms). From the formula it
can be deduced that;
Voltage (V) is also proportional to Current (I) as long as resistance is constant. In the figure
below, the gradient represents constant Resistance (R/Ω), x-axis represent voltage (V/V), and the
y-axis represents current (I/A) (Chew et al).
Voltage (V) is directly proportional to resistance when the current is constant.
When we make current (I) subject we will get formula:
I=
V
R
From the formula, it can be deduced that current (I) is inversely proportional to Resistance.
When Current flow increases, the resistance decreases and vice versa. So it can be said that “I”
proportional to
1
(Chew et al).
R
Light Intensity and its relationship with distance
The relationship of Intensity of light and distance from its source is inversely squared. The
relationship can be understood by the diagram below. When distance increases the beam angle
increases, it spread widely in surface hence decreases the intensity of light. So the light intensity
at L0 is higher than at L0/25 (NASA).
(NASA)
Design
Variables
Variable Name
Variable Type
Situation 1
How measured
Uncertainty of
Why controlled
instrument
Height of the Independent
Meter Rule
±0.01m
Bulb
LDR Type
-
-
Dependent
LDR type has to be same, in
order to calculate variations in
resistance by changing the
height of light source falling on
Voltage (V/V)
Independent
± 0.1 V
Voltmeter
LDR
P.D in circuit must be constant
so the variations in Resistance
Current(I/A)
Dependent
Ammeter
±0.01 A
is calculated
Current in the circuit must also
be constant so that different
values of Resistance is
calculated. V=IR
Dependent
Intensity meter
±500 lux
Situation 2
Number of
Independent
-
-
Correspondin
Dependent
Resistance meter
±0.001 mΩ
g Resistance
Height
Independent
Meter rule
±0.1 cm
(Constant)
Battery 12V
Dependent
-
-
(Constant)
Voltage (V/V)
Independent
Voltmeter
± 0.1 V
(Constant)
Current(I/A)
Dependent
Ammeter
±0.01 A
Intensity lux
±500 lux
Holes
(Constant)
Intensity
of Dependent
Light
meter
Table 1
Materials

LDR

Battery (12V)

Aluminum Foil

Paper-black

1kΩ Resistor

Ammeter

Voltmeter
Photos
-
Raw data
SITUATION-1
The Data in the below table shows the experiment 1 in resistance of circuit was analyzed by
increasing the height of the light source in the circuit. In order to get the resistance, Voltage and
Current readings were taken out.
Height/cm
Intensity/lux
Readings for
Trail 1
Trail 2
Trail 3
Average
Voltage (V/V)
1.07
1.09
1.10
1.09
Max−Min
¿
2
0.02
Current
10.91
10.87
10.93
10.90
0.03
(I/mA)
Voltage (V/V)
2.06
2.05
2.09
2.07
0.02
Current
9.95
9.94
9.93
9.94
0.01
(I/mA)
Voltage (V/V)
2.61
2.63
2.64
2.63
0.02
Current
9.39
9.41
9.38
9.39
0.02
(I/mA)
Voltage (V/V)
2.72
2.71
2.74
2.73
0.02
Current
9.28
9.27
9.29
9.28
0.01
V&I
10 cm
20500±500
20cm
5131±500
30cm
40cm
1900±500
1208±500
Uncertainty
(
(I/mA)
Table 2
With the help of ohm’s Law, we will calculate the resistance of the circuit when the light
was shed with the height of 10, 20 and 30 cm.
Ohms Law
V=IR
V=Voltage or PD (V)
I= Current in Ampere (A)
R= Resistance (Ω)
Before we calculate it should be noted the values of reading of Current are noted are in mill
ampere (mA). Before starting calculations the values should be converted into Amperes
1mA= 1/1000 A
Height/cm±2
Average
10cm
Average A±
Resistance
Intensity/Lux
V ± Uncertainty Uncertainty
1.09±0.02
0.01009±0.00003
108±2
20500±500
20cm
2.07±0.02
0.00994± 0.00001
272±3
5131±500
30cm
2.58±0.02
0.00939±0.00002
40cm
2.73±0.02
0.00928±0.00001
1900±500
294±3
1308±500
Table 3
SITUATION-2
Type A- Black Glace paper
N#
Readings
Holes
1 Voltage(V/V)
Trail Trail Trail Average Uncertainty
1
2
3
7.01
7.04
7.03
7.03
0.02
Current
(I/mA)
4.49
4.50
4.48
4.49
0.01
6.56
6.52
6.54
6.54
0.02
5.44
5.44
5.43
5.44
0.01
5.71
5.70
5.72
5.71
0.01
6.99
7.00
6.98
6.99
0.01
4.41
4.45
4.44
4.43
0.02
7.59
7.60
7.61
7.60
0.01
3.85
3.88
3.87
3.87
0.01
8.15
8.16
8.13
8.15
0.01
2.77
2.78
2.76
2.77
0.01
9.23
9.24
9.21
9.23
0.01
2.74
2.73
2.72
2.73
0.01
9.26
9.25
9.24
9.25
0.01
2.71
2.70
2.69
2.70
0.01
9.30
9.29
9.31
9.30
0.01
2.67
2.65
2.64
2.65
0.01
Current
(I/mA)
9.33
9.35
9.34
9.34
0.01
10 Voltage(V/V)
2.59
2.58
2.57
2.58
0.01
Current
(I/mA)
9.41
9.43
9.44
9.43
0.01
2 Voltage(V/V)
Current
(I/mA)
3 Voltage(V/V)
Current
(I/mA)
4 Voltage(V/V)
Current
(I/mA)
5 Voltage(V/V)
Current
(I/mA)
6 Voltage(V/V)
Current
(I/mA)
7 Voltage(V/V)
Current
(I/mA)
8 Voltage(V/V)
Current
(I/mA)
9 Voltage(V/V)
Table 4
Type B- Aluminum
N#
Readings
Holes
1 Voltage(V/V)
Current
(I/mA)
2 Voltage(V/V)
Current
(I/mA)
3 Voltage(V/V)
Current
(I/mA)
4 Voltage(V/V)
Current
(I/mA)
5 Voltage(V/V)
Current
(I/mA)
6 Voltage(V/V)
Current
(I/mA)
7 Voltage(V/V)
Current
(I/mA)
8 Voltage(V/V)
Current
(I/mA)
9 Voltage(V/V)
Trail
1
Trail Trail
2
3
Averag
e
Uncertainty
7.20
7.21
7.22
7.21
0.01
4.80
4.79
4.77
4.79
0.02
6.93
6.92
6.91
6.92
0.01
5.07
5.06
5.08
5.07
0.01
6.60
6.59
6.58
6.59
0.01
5.40
5.39
5.41
5.40
0.01
6.21
6.22
6.20
6.21
0.01
5.79
5.80
5.77
5.79
0.02
5.81
5.82
5.80
5.81
0.01
6.19
6.18
6.20
6.19
0.01
5.31
5.30
5.32
5.31
0.01
6.69
6.70
6.71
6.70
0.01
4.77
4.78
4.79
4.78
0.01
7.23
7.21
7.24
7.23
0.02
4.07
4.06
4.08
4.07
0.01
7.93
7.92
7.91
7.92
0.01
3.30
3.29
3.31
3.30
0.01
Current
(I/mA)
8.70
8.71
8.69
8.70
0.01
10 Voltage(V/V)
2.76
2.74
2.77
2.76
0.01
Current
(I/mA)
9.23
9.21
9.24
9.23
0.01
Table 5
Data process, Graphs and Analysis
Now
V
=R will be used to calculate Resistance (R/Ω).
I
Working for 10 cm± 2 cm
1.09± 0.02
=R
0.01009± 0.00003
(0.02/1.09)+ (0.00003/0.01009)
Fractional uncertainty of the Resistance
0.01834862385+0.002973240833=0.02132186468
Answer= 0.02
Resistance=
1.09
=108.03
0.01009
Absolute Uncertainty
R×(Fractional uncertainty)
108.03×0.02=2.16
R=108±2 Ω
Working for 20 cm ±2 cm
2.07 ±0.02
=R
0.00994 ± 0.00001
Fractional uncertainty of the Resistance
(0.02/2.07)+ (0.00001/0.00994)
Answer =0.01
Resistance=
2.07
=271.63
0.00994
Absolute Uncertainty
R×(Fractional uncertainty)
271.63×0.01
Answer=2.72
R=272±3 Ω
Working for 30 cm± 2 cm
2.63 ±0.02
=R =273.3050847±0.02002
0.00934 ± 0.00002
Fractional uncertainty of the Resistance
(0.02/2.63)+ (0.00001/0.00939)
Answer =0.00973
Resistance=
2.63
=281.5845
0.00939
Absolute Uncertainty
R×(Fractional uncertainty)
281.5845×0.00973=2.7410
R=282±3Ω
Working for 40 cm± 2cm
2.73± 0.02
=R =273.3050847±0.02002
0.00928± 0.00001
Fractional uncertainty of the Resistance
(0.02/2.73)+ (0.00001/0.00928)
Answer =0.0084
Resistance=
2.73
=294.1810
0.00928
Absolute Uncertainty
R×(Fractional uncertainty)
294.1810×0.0084=002.4711
R=294±3Ω
In order to know how Light Dependent Resistor produces variations with the light intensity, the
graph will be drawn of Height (cm) vs. Resistance (Ω) and Intensity vs. Resistance will be
drawn
Height/cm±2
Resistance/ Ω
Absolute
10cm
108
Uncertainty/±
2
20cm
272
3
30cm
282
3
40cm
294
3
Table 6
Height vs Resistance graph
350
300
250
200
150
100
50
0
5
10
15
20
25
30
35
40
45
Figure 1
The x-axis on the graph represents the height of the light that was shed on the LDR and y-axis
represents the Resistance of the circuit. It can be analyzed from this graph that the relationship
between the two components is not linear. However, it can be deduced that with an increase in
height, as the source of light increases its distance from the LDR, the resistance of the circuit
increases but eventually, then there is a curve in the graph after 20 cm, which shows us that
resistance eventually is got decreased. When the source is brought near to the photo-resistor, the
light intensity shed on LDR increases. To prove that light intensity vs. Resistance graph will be
plotted.
Intensity/Lux
Resistance
±500
20500
5131
2225
1308
108
272
282
294
Table 7
Intensity vs Resistane Graph
350
300
250
200
150
100
50
0
0
5000
10000
15000
20000
25000
Figure 2
The graph above drawn is a practical proof that Light intensity is inversely proportional to the
Resistance, because when light intensity is injected into the LDR, it adds photons into the circuit,
increasing the current flow and reducing the Potential difference in the circuit. This causes the
Resistance to decrease.
Situation 2 Calculations
Similar steps will be followed to calculate R=V/I
First fractional uncertainty will be calculated to find the absolute uncertainty
TYPE-A-Black Paper
For 1 hole;
Fractional Uncertainty
0.01
+(
=0.00507
( 0.02
)
7.03
4.49 )
Absolute uncertainty
R×(0.00507)
R=
7.03
= 1565.7015
0.00449
1565.7015×0.00449=7.938
R=1566±8
N# of
Holes
Resistance /Ω
Percentage Uncertainty/ %
Absolute
uncertainty/±
1
1566
8
0.5
2
1202
6
0.5
3
817
3
0.4
4
583
3
0.5
5
472
2
0.4
6
300
1
0.3
7
295
1
0.3
8
290
1
0.3
9
284
1
0.4
10
274
1
0.4
Table 8
# of Holes VS Resistance graph
1800
1600
1400
1200
1000
800
600
400
200
0
Figure 3
0
2
4
6
8
10
12
Figure 3 above shows the data of table 8. The relationship between the numbers of the hole
produced in wrapped paper versus the Resistance in the circuit can be deduced from plotted data
on the graph. It can be noted that when as the number of holes are increased than the value of
Voltage decreases and current in circuit increases, the Resistance in the circuit decreases. Before
holes, no light was shed on the LDR that means no photons were injected in the circuit through
LDR. As the holes were created in the wrapper, the light had access to the photo-resistor,
allowing the photons to be added into the circuit. It has been observed that when the holes
increase, the light striking on photo-resistor increases and the resistance in circuit reduces.
TYPE-B Aluminum
For 1 hole;
Fractional Uncertainty
0.02
+
=0.0048
( 0.01
7.21 ) ( 5.79 )
Absolute uncertainty
R×(0.0048)
R=
7.21
= 1245.25
0.00579
1245.25×0.0048=
R=1245±6
Same steps will be continued for further calculations
First fractional uncertainty will be calculated to find the absolute uncertainty
N# of
Holes
Percentage Uncertainty/%
Absolute
uncertainty/± %
Resistance /Ω
1
2
3
4
5
6
7
8
9
10
1505
1241
1220
1072
939
793
661
514
379
299
Table 9
The graph of the above table is drawn in the next page
8
4
5
5
3
3
3
2
2
1
0.5
0.3
0.4
0.5
0.3
0.4
0.5
0.4
0.5
0.3
Chart Title
1600
1400
1200
1000
800
600
400
200
0
0
Figure 4
2
4
6
8
10
12
Figure 2 shows data of type B experiment. The situation here is similar to the Type A, as with
increasing number of holes, the potential difference across the LDR decreases and the current
increases. This caused the Resistance across the circuit to decrease. For example, when 2 holes
were plotted, the resistance was 1241Ω, and at with the 10 holes the, resistance decreases to
299Ω with a difference of 942Ω. The Resistance, when compared to the Type-A data (Type A,
No. of Holes=1, R= 1566Ω), is lower (Type B, No. of Holes=1, R=1505Ω). That is because in
the case of black paper when light goes through the holes, it gets absorbed by the black paper,
but in Aluminum the light reflects the edges of the holes, of the shininess, and the photons
injection reduces as less light hitting LDR, causing less effect on Voltage to decrease and
Current to increase, hence reduction of resistance in circuit decreases.
Conclusion
The circuit was built with the help of wire, power supply, 1k ohm resistor, and Multimeter. After
that, the source of light attached on the stand, with measured distance from LDR and the source
of light. Two situations were tested in the experiment. In the first one, light’s distance was varied
from the LDR. And the relationship of LDR and light distance vs Resistance was shown. In the
second situation, height was kept constant and the LDR type was changed (Aluminum and Black
paper). Holes in wrapped LDR were created and the relationship between Number of holes and
resistance was shown. In the first experiment, the results showed that Height is inversely
proportional to the Resistance of the circuit. Similarly, when the number of holes was created,
the light shed on LDR was increasing, and the resistance was affected as it was decreasing. The
black wrapped LDR circuit had more Resistance than Aluminum wrapped LDR circuit because
when the light was shed inside the holes, the black paper on the edges of the holes absorbed the
light and hence decreasing the reduction of Resistance in the circuit.
Evaluation
Strengths
Firstly, I was able to conduct multiple trials easily in my experiment. This increased the accuracy
and of my data. With this, the uncertainty of the data was also improved. The experiment was
faster to conduct as few changes were implemented as the different scenarios were created. The
resistor (1KΩ), and Power Supply of 12V was kept constant in the circuit. In addition, the light
of 1200 lumens was shed in the whole experiment. Lastly, the height from which the source of
light shed on LDR was kept the same. The whole experiment was conducted in a cupboard so
that no extra light strikes other than the source of light implanted.
Limitations
The graphs in the second scenario Type B graph was not trendy, this happened because the holes
created may be wide or short, which could be a reason for the graph to be not uniform. The
uncertainty found in Intensity lux meter was also large. Moreover, regardless of an attempt to
darken the surrounding so that no light should reach LDR except the LED light, there was some
incoming light that shed on LDR.
Recommendations
The experiment can be improved by the following methods. Firstly, the number of trials can be
increased to increase the precision, accuracy and uncertainty. Secondly, the size of the hole could
have been created with a constant material like a pin whose diameter could have been measured
through the micro-screw gauge. This method can have an improvisation on graphs with more
promising results.
Work Cited
Bhattacharya, Dr. Bishakh. Introduction to Photo Sensors,
https://nptel.ac.in/courses/112104158/lecture39.pdf. PowerPoint Presentation.
Chew, Dr Charles, and Chow Siew Foong. “Electricity and Magnetism .” Physics Matters, edited
by DR Ho Boon Tiong, 4th ed., Marshall Cavendish Education, 2013, pp. 332–337.
Electrical4U. “Light Dependent Resistor | LDR And Working Principle Of LDR |
Electrical4U”. Electrical4U, 25 Jan. 2019, https://www.electrical4u.com/light-dependentresistor-ldr-working-principle-of-ldr/.
.K, A., Â R. Bute, and A. Ranjan. “Light Dependent Resistors (LDR) ”. CircuitsToday , 1 Nov.
2018, http://www.circuitstoday.com/ldr-light-dependent-resistors.
NASA. Imagine the Universe!. NASA,
https://imagine.gsfc.nasa.gov/features/yba/M31_velocity/lightcurve/images/one_over_r_s
q.gif. Accessed 6 Oct. 2019.
Appendix