Circuits Async-4

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Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 1 Circuits and Ohm’s Law (Asynchronous) Introductory Video: https://youtu.be/Djp3YXqA0Sw In equilibrium, the electric field inside a conductor is zero. However, the flow of electrons through a circuit is not an equilibrium case; electrons are continuously pushed from one terminal of a battery or power supply to the other terminal. An electric field, that is directed parallel to the conductor, provides a force that pushes electrons through the circuit. The flow of charge through a circuit obeys Kirchoff’s circuit laws. Kirchoff’s junction rule is a statement of charge conservation. It states that the algebraic sum of currents into any junction is zero. In other words, whatever charge flows into a junction must also flow out. Kirchoff’s loop rule is a statement about energy conservation. It states that the algebraic sum of potential differences in any loop, including those associated with emfs and resistive elements, must equal zero. A resistor is a circuit component that opposes the passage of electrons, much more so than other parts of the circuit. Resistors can be composed of all sorts of materials and geometries. Below is a figure of a copper wire connected to a carbon resistor (gray) that just happens to be the same thickness of the wire. Carbon is a much weaker conductor than copper because electrons within carbon are much less mobile. As a result, when connected to a voltage source, charge accumulates on the copper-carbon interface until a sufficient electric field builds up to make the current through the carbon the same as that through the copper. The unit of resistance is the Ohm (Ω) with 1 Ω ≡ 1 V/A . For many materials, Δ࠵? and ࠵? are directly proportional to one another, and therefore ࠵? is constant. ∆࠵? = ࠵?࠵? This proportionality is called Ohm’s Law and materials that satisfy it are called “Ohmic” materials. A fluid analogy for a circuit is shown below. Electrical resistance ࠵? is analogous to a narrow constriction in a pipe. The voltage Δ࠵? across a power supply is analogous to the pressure difference Δ࠵? across a pump. Electrical ground is analogous to a fluid reservoir. ࠵? ! ࠵? " ࠵? # = ࠵? ! + ࠵? " Junction Current: ࠵? ࠵? Power Supply ࠵? High Pressure Low Pressure Flow Rate: ࠵? High Voltage Low Voltage Ground

Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 2 Prelab Exercise You are given a battery, a resistor, a light bulb, and all the connecting wire that you need. 1. Using all components, draw a schematic circuit diagram that will produce the brightest bulb and explain your reasoning. 2. Using all components, draw a schematic circuit diagram that will produce the dimmest bulb and explain your reasoning. Goals of this Lab 1. Understand how charge flows through a circuit 2. Learn to measure current and voltage at various points in a circuit 3. Understand the behavior of Ohmic circuit elements Lab Materials Variable Voltage Source This voltage source will act as a battery that can provide a variable (i.e. user defined) voltage. Multimeter The multimeter will be used to measure voltage differences and current throughout circuits. Differential Voltage Probe These can be interfaced to Logger Pro for automatic data collection of voltage differences in a circuit. Current Probe These can be interfaced to Logger Pro for automatic data collection of currents in a circuit. Logger Pro Logger Pro will be used to run the differential voltage and current probes and used for data analysis. Logger Pro Light Bulbs and resistors mounted on banana plug connectors Resistors and light bulbs have been connected to each terminal of a banana plug connector to facilitate connection. Battery Resistor Light Bulb

Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 3 Measure Voltage Differences and Current using a Multimeter Measuring DC voltage differences: • Voltage differences are measured between two points on a circuit. • Connect the probes of the multimeter to two points on the circuit. This is equivalent to connecting the multimeter in parallel to the element you want to measure. Measuring DC current: • Current is measured along a wire in a circuit. You can think of the ammeter replacing a wire. • Disconnect a part of your circuit and connect the multimeter in series . 8.2 COM V W 10A 400mA V V OFF ~ _ mV _ W ) ) ) ) ) mA ~ _ _ A ~ V DC 0.22 COM V W 10A 400mA V V OFF ~ _ mV _ W ) ) ) ) ) mA ~ _ _ A ~ A DC Measuring the voltage across a light bulb Measuring the current through a light bulb

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Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 4 Lab Procedure Measuring voltage differences and current through a circuit Here a simple circuit was built by using banana connector patch cord to a connect light bulb and resistor in series. The multimeter can serve as a voltmeter (to measure voltage differences) and an ammeter (to measure current). However, the way you connect this device to the circuit is different depending on which quantity you want to measure. Posted on YouTube is a video showing the voltage differences and currents being measured at various points in the circuit. The video link is https://youtu.be/cuptcyJwNr0 . 1. From the video, record the voltage differences and current throughout the circuit. Prelab Exercise 3. The figure shows two meters labeled 1 and 2. Which meter should be the voltmeter and which should be the ammeter? 4. What would happen to the meter readings if you connected the two in the wrong way? Questions 1. What is the voltage across the light bulb? What is the voltage across the resistor? The voltage across the two terminals of the voltage source? How are they related and why? 2. What is the current flowing through the light bulb? Through the resistor? 3. Is the current flowing into the bulb the same as the current flowing out of the bulb? Light Bulb

Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 5 Exploring how a light bulb works How does a light bulb work? Is charge somehow being used up or accumulating on the bulb filament? How does a light bulb use a voltage difference to create light? You will explore these questions here. Questions 4. Generally, how does an incandescent light bulb emit light? 5. You should have observed in the previous exercise that the current flowing into the bulb is the same as that flowing out of the bulb. Thus, charge is not being used up in the bulb. What is being “used” up in lighting the bulb? Is it really being used up or being converted into some other form? Create a branched circuit What happens to electrical current when it reaches a fork in the circuit? You will explore this here. Posted on YouTube is a video showing the voltage differences and currents being measured at various points in the circuit. The video link is https://youtu.be/eqjWU0GG0AM . 1. From the video, record the voltage differences and current throughout the circuit. Questions 6. What are your measured values for ࠵? $ , ࠵? ! and ࠵? " ? How are they related to each other and what implication does this have regarding conservation of electric charge? 7. What are the voltage differences across the light bulb and the resistor? How are they related? Building a Circuit Most of the time, circuits are designed to provide specific currents of voltages. With that in mind, you will build simulated circuits to produce desired effects. The link to circuit simulator is https://phet.colorado.edu/sims/html/circuit-construction-kit-dc/latest/circuit-construction-kit-dc_en.html . 1. Starting with supplied voltage of 85V, create a circuit of resistors and one lightbulb where the lightbulb has 15V across it and 1A going through it. 2. Starting with a lightbulb with a resistance of 5 Ω , create a circuit where the lightbulb has 10V across it and battery is producing 5A total. ࠵? $ ࠵? ! ࠵? "

Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 6 Questions 8. Attach screenshots of your branching circuits, including element labels and meters as needed. Measuring Voltage vs. Current To measure the resistance of an object and determine if it obeys Ohm’s Law, one can plot the voltage across the object as a function of the current flowing through it. You can do this in an automated way using voltmeters and ammeters that input to Logger Pro. Prelab Exercise 5. Given a graph of voltage vs. current , how can you extract the resistance from the equation of a line on that graph? Posted on YouTube is a video showing the voltage across and currents through a resistor and a lightbulb as the supplied voltage changes. For the lightbulb, there are additional trials where the rate at which the supplied voltage changes is varied. The video link is https://youtu.be/203jMUjBztw . 1. From the video, observe the voltage vs. current plots for each trial, noting any interesting behavior in the plot on the circuit element themselves. Questions 9. Do the resistors obey Ohm’s Law? How do you know that? 10. Does the light bulb obey Ohm’s Law? How do you know that? 11. What does the ࠵? vs. ࠵? plot look like at low voltages? At high voltages? What about intermediate voltages? How does this correlate to the lighting of the bulb? Why does the rate of change of the voltage matter for the lightbulb? Hint: Think about what is happening at a microscopic level as the bulb heats up. What are the electrons doing? 12. In a brief paragraph, summarize this lab. You should include a summation of the major themes of the lab, as well as brief descriptions of your procedures, analytical methods, all relevant quantitative results, and your conclusions. Also check that all graphs are included and your report is in the correct order. Current To computer Voltage To computer Alligator clip Alligator clip Resistor

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Department of Physics & Astronomy Undergraduate Labs, Distance Learning 1/18/2023 7 Feedback Do you have any comments, complaints, or suggestions about this lab? Feel free to email our Lab Manager directly at Pharnish@physics.upenn.edu .

Circuits Async-4

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