# Investigating Potential Divider Circuits ## Calibrating an LDR-Based Light Meter ### Purpose of the Investigation - The goal is to build a **calibration curve** that relates light intensity to output voltage in a potential divider circuit containing an LDR - Once calibrated, the circuit can function as a light meter to measure unknown light intensities by reading the voltage and using the curve to determine the corresponding light level - This demonstrates a practical application of potential dividers in sensor technology

A calibration curve is a graph relating a sensor's output (voltage) to the physical quantity being measured (light intensity), allowing unknown values to be determined.

### Variables and Control | Variable Type | Variable | Details | |---------------|----------|---------| | **Independent** | Light intensity | Measured in lux using a digital light sensor | | **Dependent** | Output voltage $V_{\text{out}}$ | Measured in volts (V) across the fixed resistor | | **Control** | Power supply e.m.f | Keep constant throughout to ensure valid comparisons | ### Required Equipment | Component | Function in Experiment | |-----------|------------------------| | Cell or battery | Provides constant e.m.f to the potential divider | | LDR (light-dependent resistor) | Resistance decreases as light intensity increases | | Fixed resistor $R$ | Forms the other half of the potential divider; voltage measured across this component | | Voltmeter | Records potential difference across the fixed resistor (resolution: 1 mV) | | Adjustable lamp with dimmer | Provides variable light intensity for the LDR | | Digital light sensor | Measures actual light intensity in lux (resolution: 0.1 lux) | ### Experimental Procedure 1. **Circuit assembly**: Connect the LDR and fixed resistor $R$ in series with the power supply, forming a simple potential divider - Place the voltmeter across the fixed resistor to measure $V_{\text{out}}$ 2. **Initial reading**: Start in complete darkness - Record the light intensity reading from the digital sensor (should be near zero) - Record the corresponding voltage from the voltmeter 3. **Incremental light changes**: Gradually increase the brightness of the lamp using the dimmer switch - After each adjustment, allow time for the circuit to stabilize - Record both the new light intensity and the new voltage reading 4. **Range coverage**: Continue increasing brightness until the lamp reaches maximum intensity - Aim for at least 8-10 data points spread across the full range 5. **Data logging**: Tabulate all light intensity values alongside their corresponding voltages ### Analysis and Application - **Graph construction**: Plot potential difference $V$ (y-axis) against light intensity in lux (x-axis) - **Line of best fit**: Draw a smooth curve through the data points - The relationship is typically non-linear due to the LDR's resistance characteristics

The voltage across the fixed resistor increases as light intensity increases because the LDR's resistance decreases, giving the resistor a larger share of the total p.d.

**Example calibration curve for an LDR circuit:**

- **Using the calibration**: To measure an unknown light level: - Place the circuit in the test environment - Read the voltage from the voltmeter - Use the calibration curve to find the corresponding light intensity on the x-axis ### Understanding the Physics - As light intensity on the LDR **increases**, its resistance **decreases** - From Ohm's law $V = IR$, with current $I$ constant in series: - Lower LDR resistance → lower voltage across LDR - By Kirchhoff's second law, the fixed resistor receives a higher share of the total voltage - Therefore $V_{\text{out}}$ across the fixed resistor **increases** - The LDR is a **non-ohmic** component (doesn't obey Ohm's law linearly) - The total p.d is shared between the LDR and resistor according to their resistance ratio - As one component's resistance changes, the voltage distribution shifts to maintain conservation of energy ## Calibrating a Thermistor-Based Temperature Sensor ### Purpose of the Investigation - Create a calibration curve relating temperature to output voltage for a potential divider circuit containing a thermistor - Use this circuit as a temperature sensor to determine unknown temperatures from voltage readings - Demonstrates how potential dividers can be adapted for thermal sensing applications (e.g., thermostats, digital thermometers) ### Variables and Control | Variable Type | Variable | Details | |---------------|----------|---------| | **Independent** | Temperature $\theta$ | Measured in °C using a thermometer | | **Dependent** | Output voltage $V_{\text{out}}$ | Measured in volts (V) across the fixed resistor | | **Control** | Power supply e.m.f | Must remain constant throughout | ### Required Equipment | Component | Function in Experiment | |-----------|------------------------| | Cell or battery | Provides constant e.m.f to the circuit | | Thermistor (waterproof) | Resistance decreases as temperature increases (NTC type) | | Fixed resistor $R$ | Output voltage measured across this component | | Voltmeter | Records p.d across the fixed resistor (resolution: 1 mV) | | Thermometer | Measures water temperature (resolution: 1 °C) | | Beaker | Container for water bath in which thermistor is immersed | | Kettle | Provides initial hot water | | Ice | Allows cooling below room temperature | ### Experimental Procedure 1. **Circuit setup**: Replace the LDR from the previous experiment with a waterproof thermistor - Keep the same basic potential divider configuration - Ensure the thermistor is properly sealed to prevent water damage 2. **Starting hot**: Fill the beaker with freshly boiled water from the kettle - Immerse the thermistor completely in the water - Also place the thermometer in the water to monitor temperature 3. **Data collection while cooling**: As the water naturally cools down: - Record voltage readings at regular temperature intervals (e.g., every 5 °C decrease) - Wait for thermal equilibrium at each measurement point before recording 4. **Extending the range**: When water reaches room temperature, add ice to continue cooling - This extends measurements below ambient temperature - Stir thoroughly to maintain uniform water temperature 5. **Maximizing data points**: Take as many readings as practical across the widest possible temperature range (e.g., from 100 °C down to 0 °C or below)

Ensure water is stirred thoroughly between readings to avoid temperature gradients that would compromise the assumption that thermistor temperature equals water temperature.

### Analysis and Application - **Graph construction**: Plot potential difference $V$ (y-axis) against temperature $\theta$ in °C (x-axis) - **Curve fitting**: Draw a smooth curve through the data points - Expect a non-linear relationship due to the thermistor's exponential resistance-temperature characteristic **Example calibration curve for a thermistor circuit:**

- **Determining unknown temperatures**: - Place the thermistor circuit in the environment to be measured - Read the voltage from the voltmeter - Use the calibration curve to find the corresponding temperature ### Understanding the Physics - For an NTC (negative temperature coefficient) thermistor, resistance **decreases** as temperature **increases** - With constant current in series: - Higher temperature → lower thermistor resistance → lower voltage across thermistor - The fixed resistor receives a **larger share** of the total p.d - Therefore $V_{\text{out}}$ across the fixed resistor **increases** with temperature - The thermistor is **non-ohmic** with highly temperature-dependent resistance - Total voltage is conserved (Kirchhoff's second law): $V_{\text{in}} = V_{\text{thermistor}} + V_{\text{resistor}}$ ## Minimizing Experimental Uncertainties ### Systematic Errors - **Zero errors**: Check that both voltmeter and light sensor display zero before starting - If not, record the zero offset and correct all readings accordingly - **Calibration drift**: Use recently calibrated digital instruments - **Environmental interference**: Shield the LDR from stray light sources during measurements ### Random Errors - **Voltage fluctuations**: Take multiple voltage readings at each data point and calculate the mean - This reduces the impact of random electronic noise - **Temperature equilibrium**: Allow sufficient time for thermal equilibrium in the thermistor experiment - Stir water continuously and wait for stable readings ### Improving Accuracy - **Data density**: Collect as many data points as feasible across the full measurement range - More points → more reliable calibration curve - Better interpolation between measured values - **Wide range**: Cover the broadest possible range of the independent variable - For LDR: from complete darkness to maximum lamp brightness - For thermistor: from ice water (~0 °C) to boiling water (~100 °C)

The resolution of the voltmeter (1 mV) is typically much smaller than random variations, so repeated measurements are more important than instrument precision.

## Safety Precautions ### Electrical Safety - **Overheating**: Electrical components can become hot during prolonged use - If you detect a burning smell, immediately switch off the power supply - Allow components to cool before handling - **Water hazards**: Keep liquids well away from electrical equipment except where designed (waterproof thermistor) - Spillages on circuits can cause short circuits or electric shock ### Thermal Hazards - **Boiling water**: Handle hot water from the kettle carefully - Pour slowly to prevent splashing and scalding - Place beaker on a stable, heat-resistant surface - **Ice handling**: Avoid prolonged skin contact with ice to prevent ice burns ### Light Safety - **Bright lamps**: The dimmer lamp at high intensity can damage eyesight - Never look directly at the light source - Position the lamp to illuminate the LDR only, not observers ### General Laboratory Safety - **Trip hazards**: When working in darkness for the LDR experiment, be aware of obstacles - Keep bags and equipment stored under benches - Move slowly and carefully in low light conditions - **Work organization**: Keep the work area tidy to avoid knocking over beakers or equipment