RC Circuits: Series Circuits Charging and Discharging ___________...

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RC Circuits: Series Circuits Charging and Discharging ____________________________________________________________________ Please study the theoretical pre-lab materials, check the recommended educational websites and YouTube videos given below, and try to follow the step-bystep instructions. If you still have any questions regarding the lab, I will be available by e-mail during our regular class time to provide all the necessary assistance and guidance. Please keep in mind that it might take some time to respond, especially if I receive too many of your messages at the same time. Question: How do voltage and current function relative to time in a series RC circuit? Purpose: This lab is designed to have students investigate the factors that affect the rate at which a capacitor discharges. Students can change the resistance and capacitance in the circuit and then monitor the discharging of the capacitor. Graphs can be made of voltage vs. time, current vs. time, charge vs. time. Graphs can also be constructed for the half-life of the capacitor vs. resistance and half-life vs. capacitance. Objectives By the end of this experiment, you will be able to: • Observe and quantitatively describe the charging and discharging (decay) of the voltage and current on a capacitor. • Graphically determine the time constant r for the decay Background Two labs ago, we learned about electric fields and how charges can move in an electric field. The previous lab, we learned about electrical circuit and Ohm’s Law. In this lab, we will further our knowledge of electrical circuits and another circuit component, capacitor. Like the name implies, “capacitors” have the physical capability of storing electrical charge. Many things can be accidental capacitors. Most electrical components have some amount of capacitance within them, but some devices are specifically manufactured to do the sole job of being capacitors. The capacitors in today’s lab will lose their charge rather quickly, but still slowly enough for humans to watch it happen. Capacitors in electrical circuits can have very different characteristic times for charging and discharging. An RC circuit has a voltage source, a resistor, a capacitor, and a switch all in a circuit. When the switch is open, there is no current flowing in the circuit because the circuit is open. The moment the switch is closed, the capacitor has no charge and the full current is flowing through the resistor. As the capacitor is charged, the current through the resistor exponentially decays (due to Ohm’s Law). Once the capacitor is fully charged, then the current through the resistor is zero. Theory Discharging a Capacitor Discharging a capacitor through a resistor proceeds in a similar fashion, as Figure 2 illustrates. Initially, the current is driven by the initial voltage V0 on the capacitor. As the voltage decreases, the current and hence the rate of discharge decreases, implying another exponential formula for V. Using calculus, the voltage V on a capacitor C being discharged through a resistor R is found to be V = V0e−t/RC(discharging). Figure 2. (a) Closing the switch discharges the capacitor C through the resistor R. Mutual repulsion of like charges on each plate drives the current. (b) A graph of voltage across the capacitor versus time, with V = V0 at t = 0. The voltage decreases exponentially, falling a fixed fraction of the way to zero in each subsequent time constant τ. The graph in Figure 2(b) is an example of this exponential decay. The time constant is τ = RC. Note that the units of RC are seconds. We define τ = RC where τ (the Greek letter tau) is called the time constant for an RC circuit. A small resistance R allows the capacitor to discharge in a small time, since the current is larger. Similarly, a small capacitance requires less time to discharge, since less charge is stored. In the first time interval τ = RC after the switch is closed, the voltage falls to 0.368 of its initial value, since V = V0 ⋅ e−1 = 0.368V0. During each successive time τ, the voltage falls to 0.368 of its preceding value. In a few multiples of τ, the voltage becomes very close to zero, as indicated by the graph in Figure 2(b). Glossary: RC circuit: a circuit that contains both a resistor and a capacitor Capacitor: an electrical component used to store energy by separating electric charge on two opposing plates Capacitance: the maximum amount of electric potential energy that can be stored (or separated) for a given electric potential 2 Useful resources Connecting RC circuits and its practicality RC circuits are commonly used for timing purposes. A mundane example of this is found in the ubiquitous intermittent wiper systems of modern cars. Adjusting the resistance in a RC circuit varies the time between wipes. Another example of a RC circuit is found in novelty jewelry, Halloween costumes, and various toys that have battery-powered flashing lights A more crucial use of RC circuits for timing purposes is in the artificial pacemaker, used to control heart rate. The heart rate is normally controlled by electrical signals generated by the sino-atrial (SA) node, which is on the wall of the right atrium chamber. This causes the muscles to contract and pump blood. Sometimes the heart rhythm is abnormal and the heartbeat is too high or too low. The artificial pacemaker is inserted near the heart to provide electrical signals to the heart when needed with the appropriate time constant. Pacemakers have sensors that detect body motion and breathing to increase the heart rate during exercise to meet the body’s increased needs for blood and oxygen. 2.2 YouTube videos http://www.youtube.com/watch?v=_6pj5gk4O0M http://www.youtube.com/watch?v=cMbK7V1M7Ew How to read the value of a resistor using the color bar codes. https://www.youtube.com/watch?v=G1mZutobxDU and many-many others available online. 3 Procedure 1. Go to the website: www.thephysicsaviary.com/Physics/singlepage.php?ID=52 Or --- Type “RC-Circuit Lab - The Physics Aviary” in Google and click the link. Part 3A: Basic Discharge Ideas Part 3B: Changing Resistance Part 3C: Changing Capacitance Part 3A: Basic Discharge Ideas Procedure – This lab will be performed using “Labs Available on the Physics Aviary” 1. For this part of the experiment you will be looking at the discharging of the capacitor as a function of time. So set up a data table that has one column for time, one for voltage, one for current, and one for charge on the capacitor. 2. Click on the capacitor to see its capacitance and write this down near your data table. 3. Also write down the value of the resistor at some place in your lab book near your data table. 4. Click on the charge capacitor button to give your capacitor an initial charge. When you charge the capacitor, the simulation will pause to give you time to measure the voltage and current in the circuit. The voltage on the resistor will be the same as voltage on the capacitor, because the resistor is getting its energy from the capacitor. 5. Calculate the charge on the capacitor based on the voltage and capacitance. 6. ‘Un-pause’ your simulation and allow some time to go by. Then pause the simulation again and record new values for voltage, current and charge. If there has not been a significant change in your voltage, don't record your data yet, but instead resume the simulation and allow more time to tick away. 7. Collect at least 10 data points over a three-minute time frame. It is not incredibly important that your times are equally spaced. 8. Open up Excel and create three different graphs (Voltage vs. time, current vs. time and charge vs. time). Make sure your curve fits the graph. Also ensure that your graph is labeled, has a title, and an equation is displayed. Data: Type your answers below. No. Of pts Time Voltage Current Charge on the Capacitor 1 2 3 4 5 6 7 8 9 10 Capacitance = Resistance = Graph – Use Excel to provide a sketch of the 4 graphs. Copy and paste below. Part 3B: Changing Resistance Procedure – This lab will be performed using “Labs Available on the Physics Aviary” 1. For this part of the experiment you will be looking at effect that resistor has on the rate of discharge. For each trial you will see how much time elapses until the capacitor drops to half of its original voltage. 2. Create a data table that contains one column for resistor value and one column for time. 3. Write down the value of your first resistor, recharge your capacitor and note the value of the voltage at time = 0. 4. ‘Un-pause’ your simulation and periodically check the voltage value. Write down the elapsed time when the voltage has reached half its original value. 5. Repeat this procedure for a total of five different resistances. 6. Plot a graph of time vs. resistance and then transfer the graph over to your lab book with all the things a good graph should contain. Data: Type your answers below. No. Of Obs. Resistance Time 1 2 3 4 5 Graph #5 Part 3C: Changing Capacitance Procedure – This lab will be performed using “Labs Available on the Physics Aviary” 1. For this part of the experiment you will be looking at effect that capacitor has on the rate of discharge. For each trial you will see how much time elapses until the capacitor drops to half of its original voltage. 2. Create a data table that contains one column for capacitor value and one column for time. 3. Write down the value of your first capacitor, recharge your capacitor and note the value of the voltage at time = 0. 4. ‘Un-pause’ your simulation and periodically check the voltage value. Write down the elapsed time when the voltage has reached half its original value. 5. Repeat this procedure for a total of five different capacitances. 6. Plot a graph of time vs. capacitance and then transfer the graph over to your lab book with all the things a good graph should contain. Data: Type your answers below Graph #6 No. Of Obs. Capacitance Time 1 2 3 4 5 Sketch the diagram of the circuit you were using for examining the discharging of a capacitor in your lab write-up. Questions: Print your answers in the space provided. 1. Graph 1 What type of Graph did you get for Voltage vs. Time as the capacitor discharged? 2. Graph 5 What type of Graph did you get for Time vs. Resistance for tracking when the capacitor reached half charge? 3. Graph 6 What type of Graph did you get for Time vs. Capacitance for tracking when the capacitor reached half charge? 4. Resistor Usage When using our simulation program, all the resistors had third bands that were orange or yellow. Why was simulated lab programmed to only allow those colors? 5. Calculation: Show your work in the space below. How much charge is stored on a 5400 µF capacitor when the voltage on it is 7 V? Convert to mC Part 4: Conclusions 21. Provide a short summary of your research regarding the relationship of voltage, current, resistance and capacitance. Also, discuss what is the relationship of the resistance and current in a series RC circuit.

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