We have several objectives in lab this week. Some of the things we will do include:

• Continue to learn how to use the laboratory equipment and how to build circuits on your breadboard
• Analyze a voltage divider to determine the best resistance value to use in a sensor configuration
• Set up and test a voltage divider and a bridge circuit using a thermistor to measure temperature

Voltage divider circuits are often used in measurement instruments to convert a physical quantity such as light intensity, temperature, or elastic strain into a voltage. An example circuit is shown below.

A material that changes its resistance in accordance with light is called a photoresistor, and a material that changes its resistance in accordance with temperature is called a thermistor. The resistor R_sensor in the above circuit represents such a device. Voltage dividers are also used for things like volume controls on radios and televisions, dimmer switches on lights, and intensity controls on computer screens. In these applications, the resistance of a potentiometer (or "pot" for short) is varied by the user to change the output voltage.

The above circuit produces an output voltage V_out that lies between the source voltage and ground. In your lab notebook, please derive the relationship between the output voltage and the source voltage, as determined by the resistance values. (You should have done this exercise before, but make sure you understand it.) Note that V_out will vary with the physical variable that we are measuring as R_sensor changes.

Please answer the following questions in your lab notebook.

1. Assuming that the sensor has a resistance that increases as the physical variable increases, does the output voltage of the circuit increase or decrease?

2. If the resistance decreases as the physical variable increases, how does the output voltage vary?

3. Devise a circuit in which the variation is the opposite of that in the above circuit.

Sometimes the sensor is exposed to only two values of the physical variable, and an instrument must distinguish between the two levels. For example, a light might shine or not shine on a photoresistor. Then we might want to design the circuit in order to obtain the largest difference between the two voltages produced. If the supply voltage V_s is 5 volts, and if we can make the output voltage close to 5 volts and 0 volts in the two conditions, then we have designed a circuit that produces levels close to the standard levels in digital logic. Determine the resistance R₀ that gives the greatest difference between the output voltages when R_sensor = R_max and R_sensor = R_min. Then determine the maximum difference, and how close you can get to 0 and 5 volts.

During the lab period, be sure that you understand how to set up this analysis and the approach used to find the best value for R₀. You may want to finish the steps in the analysis after the lab session.

Consider an application of your result. Suppose that you have a sensor for which the resistance varies between R_min = 1000 ohms and R_max = 5000 ohms for two fixed conditions. In digital logic circuits, anything above 3.5 volts is sensed as logical "1", and anything below 1.5 volts is sensed as logical "0". However, the more you exceed these limits, the more reliable the circuit will be. For the sensor described above, can you achieve reliable operation? We will check your prediction later in the lab by building the circuit.

Next we will construct some voltage divider circuits in order to test the results from previous sections. First let V_s = 5 volts and replace R_sensor by a resistance value of 1000 ohms. Next replace R_sensor by resistance value of 5000 ohms. Choose R₀ to achieve maximum voltage difference for the two values of R_sensor. Measure the actual voltage levels for the two cases, and compare with your earlier predictions.

Second, we will use a thermistor as R_sensor. Measure the resistance of the thermistor at room temperature, and when you heat it by squeezing between your fingers. Choose a value for R₀, and set up the voltage divider circuit. What values of V_out correspond to room temperature and body temperature? What would happen to your measurements if the source V_s deviated from 5 volts?

Let us consider a bridge circuit, which is shown below. The bridge circuit is really just two voltage dividers, and it has some practical advantages over a simple voltage divider.

In this bridge, the output voltage V_out is now a difference between the two sides of the bridge. If the circuit components are chosen properly, the voltage difference will be zero. Show the conditions for a "balanced bridge,"

Please do the following exercises with the bridge circuit.

1. Build the bridge with the thermistor as R_sensor and R₀ (R₀ is the value you chose in testing the voltage divider), R_A, and R_B chosen for balanced operation at room temperature. Note that in practice, the bridge can be "calibrated" by making R_A = R₀ and using a variable R_B that is adjusted until V_out = 0.
   (A bridge circuit is often connected to the calibration knob on devices that you use!)

2. Now measure the output voltage at room temperature and at body temperature. How do the measurements compare with the voltage divider?

3. Will your circuit measure a temperature below room temperature? Explain what you expect.

4. What advantage does the bridge provide over a single voltage divider? (You might consider what happens in the bridge if V_s changes, perhaps due to a weakening battery. How does V_out change if the bridge is nearly balanced?)

A number of interesting E-Lessons are available on voltage dividers and bridge circuits. Feel free to browse them whenever you would like. The path to the E-Lessons is described in Lab 2, and the voltage divider lessons are under "Elements -> Resistors -> Voltage Dividers".