Lab Report: Discharge of a Capacitor and Time Constant Analysis, Exercises of Physics

Download Lab Report: Discharge of a Capacitor and Time Constant Analysis and more Exercises Physics in PDF only on Docsity! Physics 121 Lab 6B: The Discharge of a Capacitor Part 1: The Functional Form of the Discharge Law for a Capacitor: Make a plot of the potential difference across the discharging capacitor as a function of time and from the plot determine the functional form of the discharge of the capacitor through the resistor by creating three plots, a standard Cartesian plot, a semi-log plot and a log-log plot. Which plot makes your data look linear? If the Cartesian plot makes your data look linear fit the data with a straight line. If the semi-log plot makes your data look linear then on the Cartesian plot fit the data with an exponential curve fit. If the log-log plot makes the data look linear then on the Cartesian plot fit the data with a power law. Does the discharge of the capacitor behave according to theory? To answer this, derive an expression for discharge of a capacitor through a single resistor. Then, comparing your expression with the curve fit that you chose, what do the constants in the curve fit represent? What does the exponent of the curve fit represent? What is the expected (theoretical) time constant τ theo for the circuit? What is your experimental value for the time constant τ exp of the circuit? Calculate percent difference and explain any discrepancies. Do your calculations and answer the questions on the graph you produced. Using your equation for the discharge of the capacitor through the resistor, what physically does the time constant τ represent? Answer this question on your graph and you should not have to use any data to answer this question. Part 2: τ versus R From the data you took on τ versus R , make a plot of the experimental value of the time constant versus the resistance. On the same graph, plot the theoretical value of the time constant versus the resistance. Using the data on the experimental values of the time constant curve fit the data with a power law (why?) and from the curve fit, determine the functional form of the time constant as a function of the resistance. What do the slopes of each of the curves represent? How do the slopes compare to the value of the capacitance stamped on the capacitor? Are these as expected? Comment on your findings and do your calculations on your graph. Part 3: τ versus C Applying the loop and node rules to two capacitors wired first in series and then in parallel, derive two separate rules for how capacitors in series and parallel add. Show the derivations below.