Lab 5 RC Circuits. What You Need To Know: Physics 212 Lab

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1 Lab 5 R ircuits What You Need To Know: The Physics In the previous two labs you ve dealt strictly with resistors. In today s lab you ll be using a new circuit element called a capacitor. A capacitor consists of two small metal plates that are separated by a small distance. This is evident in a capacitor s circuit diagram symbol, see Figure 1. When a capacitor is hooked up to a circuit, charges will accumulate on the plates. Positive charge will accumulate on one plate and negative will accumulate on the other. The amount of charge that can accumulate is partially dependent upon the capacitor s capacitance,. With a charge distribution like this (i.e. plates of charge), a uniform electric field will be created between the plates. [You may remember this situation from the Equipotential Surfaces lab. In the lab, you had set-ups for two point-charges and two lines of charge. The latter set-up represents a capacitor.] A main function of a capacitor is to store energy. It stores its energy in the electric field between the plates. Battery apacitor (with charges shown) R FIGURE 1 - Battery/apacitor FIGURE 2 - R ircuit If you hook up a battery to a capacitor, like in Figure 1, positive charge will accumulate on the side that matches to the positive side of the battery and vice versa. When the capacitor is fully charged, the voltage across the capacitor will be equal to the voltage across the battery. You know this to be true because Kirchhoff s Loop Law must always be true. onvince yourself of this, it s important later. The capacitor will reach its maximum voltage almost instantaneously because there is nothing in the circuit to slow down the current flow. If we now put a resistor in series with the capacitor, see Figure 2, it will slow down the flow of current. It will now take a longer time for the capacitor to charge up. If you make a graph of the voltage across the capacitor, V c, versus time, t, as it is charging up, it would look like the graph in Figure 3. This is an exponential curve. FIGURE 3 Voltage vs. Time V c t 5-1

2 The equation that determines the exponential graph in Figure 3 is as follows V V ( 1 e MAX (harging) t R ) V is the voltage across the capacitor (in volts, V) V MAX is the maximum capacitor voltage (in volts, V) R is the resistance of the resistor (in ohms, ) is the capacitance of the capacitor (in farads, F) t is the time (in seconds, s) Due to the fact that the equation is exponential, it will take an infinite amount of time for the capacitor to charge to its maximum voltage. You can see this in the graph. This is too long to wait, so instead we talk about the time it takes the capacitor to reach half of its maximum value. This is called the half-life. The equation for the half-life is as follows t 1 R ln 2 2 t 1/2 is the half-life (in seconds, s) R is the resistance (in ohms, ) is the capacitance (in farads, F) Eventually the capacitor will be sufficiently charged, as shown after a long time in Figure 3. If we remove the battery and replace it with a wire, then the capacitor will want to discharge. This is because there is no longer anything forcing the capacitor to hold its charge. There is a different equation for V when the capacitor is discharging (you ll see this later in the lab), but the half-life equation holds for charging and discharging. In today s lab you will be measuring the half-life for the R circuit shown in Figure 4. You will be finding the half-life in three different ways: using a direct measurement, using a graph, and using the computer. Finally, there will be a fourth section in which you will have to apply what you ve learned thus far in the lab. What You Need To Do: Switch Power Supply Position to charge Position to discharge R FIGURE 4 R circuit Part 1 Half-life By Stopwatch The first way you are going to measure the halflife of your circuit (Figure 4) is by using observation and a stopwatch. A) If not already done, hook up the circuit to the power supply using OUTPUT1. 5-2

5 G) Use Graphical Analysis to make plot of y vs. time. [Make sure you erase the other data first.] You have now forced the original graph to be linear. Sketch the graph on your paper. H) Press the R= button to calculate the slope of the line. The slope will be given in a small screen. I) Use the expression you got for m and set it equal to the value for the slope. From this equation, calculate the value of R. J) Use this R value to calculate the half-life using the half-life equation and place the value in the chart. Question 3 Is this new half-life value better or worse than the value you calculated in Part 1? Explain why you think so in either case. Part 3 Half-life By omputer Now you are going to use the Logger Pro software on the computer to measure the value R directly by using both the charging case and discharging case. HARGING A) lose out of Graphical Analysis and bring up R ircuits on the desktop. If you cannot find the software then ask your TA, a certified P expert. B) Detach the voltmeter cables from the circuit. Attach the voltage probe, coming from the LabPro [blue box on top of the computer], across the capacitor. Make sure the red cable attaches to the positive side of the capacitor. ) Make sure the switch is set to Discharge. At the top of the computer screen, the potential should read zero. If not, then either wait for it to discharge or just use the extra wire to dissipate the charge. D) Push the ollect button. Wait 2 seconds and then flip the switch to harge. The computer will monitor the voltage across the capacitor and plot it out on the graph as the voltage increases. Let it charge up so that it fills the screen. E) Use the mouse to highlight the region of the graph where it is charging. Push the urve Fit button, it looks like f(x)=. F) Scroll down and choose INVERSE EXPONENT from the list in the lower left, then push TRY FIT. heck to see if it s a good fit and then click OK. If it s not, then grab your TA. G) In the little window that points to the curve, there is a value labeled. This is not the capacitance. It is equal to 1/R. Use this to calculate R and then calculate the half-life. Show your work. Place this value in the chart. DISHARGING A) Make sure the switch is set to harge and the capacitor is sufficiently charged. 5-5

6 B) Push ollect, erase the old data, wait 2 seconds and then flip the switch to Discharge. Let it fill the graph. ) Use the mouse to highlight the region of the graph where it is discharging. Push the urve Fit button again. hoose NATURAL EXPONENT from the list this time, then TRY FIT, check it, and then OK. D) Use the value and calculate the half-life like you did before. Now, average these two half-life values. Show your work. Place these values in the chart. Question 4 Notice that the three half-life values you measured in Parts 1 3 are all somewhat similar. Notice also that they are not very similar to the half-life value you calculated with the given values of R and. Explain this behavior. HINT: Both the voltmeter and the LabPro have an internal resistance. Part 4 Voltage Across the Resistor Disconnect the voltage probe from the capacitor and attach it across the resistor with the red probe on the side of the resistor closer to the switch. Push ollect, wait 2 seconds, and then flip the switch to harge. Question 5 Why does the graph for the voltage of the resistor look the way it does on the computer screen? In your explanation you must use Kirchhoff s Loop Law. Part 5 lean Up Please detach the voltage probe from the circuit, flip the switch to Discharge, and turn off your power supply and voltmeter. Thanks! What You Need To Turn In: Turn in all the data you took. Make sure you showed all the work for any half-lives and such. All questions must be answered in the sections where they are asked. Spring 2013 by Michael J. Dubuque 5-6

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Simple circuits 3 hr Identification page Instructions: Print this page and the following ones before your lab session to prepare your lab report. Staple them together with your graphs at the end. If you

Exercise 1: RC Time Constants

Exercise 1: RC EXERCISE OBJECTIVE When you have completed this exercise, you will be able to determine the time constant of an RC circuit by using calculated and measured values. You will verify your results

Physics E-1ax, Fall 2014 Experiment 3. Experiment 3: Force. 2. Find your center of mass by balancing yourself on two force plates.

Learning Goals Experiment 3: Force After you finish this lab, you will be able to: 1. Use Logger Pro to analyze video and calculate position, velocity, and acceleration. 2. Find your center of mass by

Lab 4 RC Circuits. Name. Partner s Name. I. Introduction/Theory

Lab 4 RC Circuits Name Partner s Name I. Introduction/Theory Consider a circuit such as that in Figure 1, in which a potential difference is applied to the series combination of a resistor and a capacitor.

Fundamentals of Circuits I: Current Models, Batteries & Bulbs

Name: Lab Partners: Date: Pre-Lab Assignment: Fundamentals of Circuits I: Current Models, Batteries & Bulbs (Due at the beginning of lab) 1. Explain why in Activity 1.1 the plates will be charged in several

Capacitance Measurement

Overview The goal of this two-week laboratory is to develop a procedure to accurately measure a capacitance. In the first lab session, you will explore methods to measure capacitance, and their uncertainties.