To Study the Effect of Light Intensity on an LDR
A detailed experimental worksheet exploring the resistance variation in a Light Dependent Resistor
Aim of the Experiment
To investigate and analyze how the resistance of a Light Dependent Resistor (LDR) varies with the intensity of incident light, where intensity is varied by changing the distance between the light source and the LDR.
Theory
A Light Dependent Resistor (LDR) or photoresistor is a light-controlled variable resistor. Its resistance decreases with increasing incident light intensity. This property makes LDRs useful in light-sensing applications.
The resistance of an LDR varies inversely with light intensity due to the photoelectric effect. When photons strike the semiconductor material of the LDR, they may excite electrons from the valence band to the conduction band, decreasing resistance.
The relationship between resistance and light intensity can be approximately described by:
$$R = R_0 \cdot I^{-\alpha}$$
Where:
- $R$ is the resistance of the LDR
- $R_0$ is a constant (resistance at unit intensity)
- $I$ is the intensity of incident light
- $\alpha$ is a constant depending on the semiconductor material (typically between 0.5 and 0.7)
Light intensity from a point source (like a small bulb) follows the inverse square law with distance:
$$I \propto \frac{1}{d^2}$$
Where $d$ is the distance from the light source to the LDR.
Combining these relationships, we can predict that:
$$R \propto d^{2\alpha}$$
This means that plotting $\log(R)$ against $\log(d)$ should give a straight line with slope approximately $2\alpha$.
Materials Required
- Light Dependent Resistor (LDR)
- Digital multimeter with resistance measurement capability
- Light source (preferably a small filament bulb or LED)
- DC power supply for the light source
- Meter scale or measuring tape
- Optical bench or a straight platform for alignment
- Dark room or light-proof enclosure
- Graph paper or plotting software
- Calculator
Experimental Setup
- Set up the optical bench or a straight platform in a dark room or enclosure.
- Mount the light source at one end of the bench.
- Connect the light source to a stable DC power supply.
- Mount the LDR on a movable holder that can slide along the optical bench.
- Connect the multimeter to the LDR to measure its resistance.
- Mark the distance scale along the bench starting from the light source.
- Ensure that the LDR faces directly toward the light source at all positions.
Procedure
- Turn on the light source and ensure a stable illumination.
- Place the LDR at a specific distance (start with 10 cm) from the light source.
- Record the resistance of the LDR using the multimeter.
- Repeat the resistance measurement 3 times at the same distance to ensure consistency.
- Increase the distance by suitable intervals (e.g., 5 cm) and repeat the measurements.
- Continue measurements until a distance of approximately 100 cm is reached.
- Record all readings in the observation table.
Observations
| Serial No. | Distance, d (cm) | Resistance Reading 1 (kΩ) | Resistance Reading 2 (kΩ) | Resistance Reading 3 (kΩ) | Average Resistance, R (kΩ) | log(d) | log(R) |
|---|---|---|---|---|---|---|---|
| 1 | 10 | ||||||
| 2 | 15 | ||||||
| 3 | 20 | ||||||
| 4 | 25 | ||||||
| 5 | 30 | ||||||
| 6 | 40 | ||||||
| 7 | 50 | ||||||
| 8 | 60 | ||||||
| 9 | 80 | ||||||
| 10 | 100 |
Observation Notes:
Record any specific observations or anomalies during the experiment:
- Note changes in ambient light conditions
- Record any fluctuations in power supply
- Observe response time of LDR when distance changes
Calculations
- Calculate the average resistance for each distance:
$$R_{avg} = \frac{R_1 + R_2 + R_3}{3}$$
- Calculate the logarithm (base 10) of each distance:
$$\log(d)$$
- Calculate the logarithm (base 10) of each average resistance:
$$\log(R_{avg})$$
- Plot a graph of $\log(R_{avg})$ vs $\log(d)$
- Calculate the slope of the best-fit line:
$$\text{Slope} = \frac{\Delta \log(R_{avg})}{\Delta \log(d)}$$
- The slope should be approximately equal to $2\alpha$, where $\alpha$ is the characteristic constant of the LDR material.
- Calculate $\alpha$ by dividing the slope by 2:
$$\alpha = \frac{\text{Slope}}{2}$$
Results
The relation between resistance (R) and distance (d) follows:
$$R \propto d^{2\alpha}$$
Where $\alpha =$ _________ (calculated from the slope)
Analysis and Interpretation:
- The graph should show a linear relationship between $\log(R)$ and $\log(d)$, confirming the power-law relationship between resistance and distance.
- The slope of this line gives $2\alpha$, where $\alpha$ is the characteristic constant of the LDR material.
- A typical value for $\alpha$ ranges from 0.5 to 0.7 for common CdS photoresistors.
- If the experimental value of $\alpha$ falls within this range, it confirms the theoretical model.
- If there are deviations from linearity at very short or very long distances, discuss possible reasons:
- At short distances: Saturation effects in the LDR or non-point source characteristics
- At long distances: Influence of ambient light or limitations of the multimeter sensitivity
Physical Significance:
The parameter $\alpha$ represents how strongly the resistance changes with light intensity. A higher value of $\alpha$ indicates a more sensitive LDR. This parameter depends on:
- The semiconductor material used in the LDR
- The manufacturing process
- The spectral distribution of the incident light
Sources of Error
- Ambient light interference
- Non-point source characteristics of the light source
- Temperature variations affecting the LDR's resistance
- Measurement errors in distance
- Multimeter precision limitations
- Alignment errors between light source and LDR
Precautions
- Ensure the experiment is conducted in a dark room or with minimal ambient light.
- Keep the power supply to the light source stable throughout the experiment.
- Maintain proper alignment between the light source and the LDR.
- Allow sufficient time for the LDR to stabilize after each distance change.
- Handle the LDR carefully to prevent damage or contamination of its surface.
- Ensure the multimeter is calibrated and set to the appropriate range.
- Keep the experimental setup at a constant temperature.
Applications of LDR
- Automatic Street Lights: LDRs are used to detect ambient light levels and automatically switch street lights on and off.
- Camera Exposure Control: Used in cameras to measure light intensity for automatic exposure control.
- Security Alarms: Light-activated security systems use LDRs to detect changes in light levels caused by intruders.
- Light Meters: Professional photographers use light meters with LDRs to measure scene illumination.
- Day/Night Switching Circuits: Used in various electronic devices to detect day/night conditions.
- Automatic Brightness Control: In displays and monitors to adjust brightness based on ambient light.
Conclusion
This experiment demonstrates that the resistance of an LDR varies inversely with light intensity, following a power-law relationship. By varying the distance between the light source and the LDR, we observed that:
$$R \propto d^{2\alpha}$$
The value of $\alpha$ determined from the experiment characterizes the sensitivity of the particular LDR used. This understanding of how LDRs respond to light intensity is fundamental to their application in various light-sensing circuits and devices.