Experiment 3 Report

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Apr 3, 2024

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ECE 110L Winter 24’ Instructor: Mesghali, Farid Exp. 3: Simple Resistive Networks Om Patel, 605518179 Experiment Introduction and Theory The set of labs in this experiment aims to verify the principle of superposition and a Wheatstone bridge. The principle of superposition states that circuits with only resistors, capacitors, and inductors are linear circuits which means that the voltage at any node or current through any branch is a linear combination of separate circuits with singular source values. In the circuit, if there exists more than one source (voltage or current), the circuit can be broken down into multiple circuits with each source acting alone. To accomplish this, one at a time, isolate each source by removing the other sources (short the voltage sources and open the current sources) and keep the other circuit elements the same. By analyzing these circuits alone and then taking the sum of the voltages and currents, the same solution can be reached as if all the sources were on all the time. Superposition allows a complex circuit with multiple sources and elements to be broken down into more digestible simple circuits. A Wheatstone bridge(figure 5), which looks like two voltage dividers in parallel, shares a unique property that is helpful in multiple cases which states that the voltage is 0 when R1/R2=R2/R4. By replacing one of the four resistors with a resistive sensor, such as a thermistor (temperature-sensitive sensor), the circuit can read a higher voltage when the sensor's resistance increases. The Wheatstone bridge amplies the change in output voltage of the sensor which helps with smaller and more precise data analysis. Usually, the three remaining resistors are selected to be equal to the sensor's nominal resistance, which sets the nominal output voltage to zero. To find a specific resistance value that would set the voltage to zero for a thermistor, a potentiometer is used because it can change its resistance by turning a simple knob. Lab1: Superposition Introduction: In this part of the experiment, we build a circuit that involves 2 voltage sources, 680, 470, and 1000 ohm resistors. The voltage and current across the middle 470-ohm resistor are measured with both voltage supplies on. For the next parts, one by one, turn the source off and measure the voltage and current across the 470-ohm resistor. Repeat for the next source. Compare these values to the theoretical values that were calculated in the prelab. Figure 1: Wire diagram for Lab 1 Figure 2: Constructed Circuit for Lab 1 (both sources)

Figure 3: Constructed Circuit for Lab 1 (+5V Only) Figure 4: Constructed Circuit for Lab 1 (-5V Only) Measured Data: Component Theoretical Resistance (Ω) Measured Resistance (Ω) Resistor 1 680 670 Resistor 2 1000 1065 Resistor 3 470 461 Table 1: Measured Resistor Resistance Values Sources Measured Voltage (V) Theoretical Voltage (V) Measured Current (mA) Theoretical Current (mA) +5V Only 1.62 1.6221 3.51 3.45 -5V Only -1.02 -1.0205 -2.19 -2.17 Sum 0.600 0.60160 1.32 1.28 Both sources 0.603 0.60161 1.27 1.31 Table 2: Voltage and Current values across 470-ohm resistor Discussion: 1. Measured voltage and current values agree with the theoretical values calculated across the 470-ohm resistor. The measured values are all within 2% of the theoretical values. a. For the sum of the +5V Only and -5V circuits, the measured voltage was 0.600V compared to 0.603V for circuits with both sources. b. For the sum of the +5V Only and -5V circuits, the measured current was 1.32mA compared to 1.27mA for circuits with both sources. c. For +5V Only, measured voltage 1.62V compared to theoretical 1.62V and measured current 3.51mA compared to 3.45mA d. For -5V Only, measured voltage -1.02V compared to theoretical -1.02V and measured current -2.19mA compared to -2.17mA

Lab 2: Wheatstone Bridge Introduction: In this part of the experiment, we will be designing, building, and calibrating a thermistor temperature sensor circuit. The end goal for this setup is to have the output voltage read 0V at the ambient temperature of the room and 0.5V at body temperature (finger in contact with a thermistor). After calibration of the circuit setup, the input voltage was varied by plus and minus 1 volt where the output voltage was recorded. Figure 5: Wheatstone Bridge Figure 6: Constructed Circuit for Lab 2 Measured Data: Component Theoretical Resistance (Ω) Measured Resistance (Ω) Resistor 1 47000 46600 Resistor 2 47000 46700 Resistor Thermistor N/A 50400 Resistor Potentiameter N/A 49400 Table 3: Measured Resistor Resistance Values Input Voltage (V) Output Voltage (Room Temp. in V) Output Voltage (Body Temp. in V) 2.939 0.0070 0.49 1.939 (-1) 0.0068 0.33 3.939 (+1) 0.0069 0.77 Table 4: Output Voltages (RT and BT) with corresponding Input Voltages Discussion: 1. The restriction on the design choice of the thermistor is that at room temperature its resistance has to be high. This is due to limited the amount of heat that is dissipated from the thermistor itself which may affect its reading. Since it follows the power equation which equals voltage squared over resistance, the higher the resistance the less power is dissipated resulting in a more accurate reading of ambient readings.

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2. 3. The output voltage at room temperature was 0.007V and 0.49V at body temperature. These values are accurate to the 0V and 0.5V we were aiming for. When we increased the input voltage by 1V, the room temperature output voltage stayed around the same while the body temperature increased slightly. When we decreased the input voltage by 1V, the room temperature output voltage stayed around the same while the body temperature decreased slightly. This verifies our Wheatstone bridge because it shows how insensitive the values are to input voltage. Signature of Professor: Prelab: