# RC Circuits Lab Report

Topics: Capacitor, Dielectric, RC circuit Pages: 5 (1500 words) Published: November 2, 2013
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Experiment 5: RC Circuits

Abstract

The purpose of this lab is to learn and understand RC Circuits. An RC circuit is composed of at least one resistor and at least one capacitor. A capacitor is composed of two plates with either air or an insulator also known as a dielectric between the plates. We do not want the plates to be touching, because then we would only have a conductor. The insulator between the plates is also known as the dialectic, which affect how the capacitor will store charge. In an RC circuit, voltage will flow from the battery to the capacitor and through the resistor. When the capacitor is charging, the voltage across the battery is decreasing until the capacitor is fully charged. When the capacitor is fully charged, then the voltage through the battery is zero. That would also mean that the voltage of the circuit would drop until it is also zero. Now when the capacitor completely discharges, the voltage through the battery increases. We were able to measure the half-time of the charging and discharging of the capacitor by connecting the circuit to the oscilloscope with the signal generator providing the potential for the circuit. The time constant was calculated from the half-time of charging and discharging. The time constant is a measure of the length of time a capacitor took to charge and discharge. We used the average of the charging and discharging time constants to calculate the capacitance by using the equation τ = RC. Since we know the resistance and the time constant, we are able to solve for the capacitance and compared the observed and theoretical values in order to verify the capacitance. For the RC circuit with one capacitor, we compared the theoretical and observed time constant and obtained a percent difference of 9.5%. For the RC circuit with two capacitor in series and the RC circuit with two capacitors in parallel, percent differences between the observed and theoretical values were all 9.5%. So we were able to verify the capacitance for all the parts of experiment one. In part two of the experiment, we made a capacitor by placing a sheet of wax paper between two aluminum foil plates. First, we measured the thickness of the wax paper by using the micrometer. Through this method, we measured the thickness to be 35±05 micrometers. Then we found the average time constant and then calculated for the capacitance. Then from the capacitance, we were able to solve for the distance between the plates. The distance between the plates through this method was solved to be 580 micrometers. Our percent difference for the theoretical and measured thickness was 180%. The calculated thickness should be equal to the measured thickness, but this was not the case.

Sample Calculations

One capacitor
½ timecharge = ½ timedischarge  = 0.3 division x 250 μs/division = 75 μs
τchrage = τdischrage =
τaverage = = 110 μs
τtheoretical = RC = 100Ω x 1μF = 100μs
Percent Difference =
= = 9.5%
Uncertainty capacitance = 20% x 1μF = 0.2 μF
½ timeuncertainty = 0.1 division x 250 μs/division = 25 μs
½ timeaverage = = 35 μs
τuncertainty = = 36μs
τuncertainty average = 0 μs

Two Capacitors in Parallel
Ctotal = C1 + C2 = 1μF + 1μF = 2μF
C =
Percent Difference =
= = 9.5%

Two Capacitors in Series
Ctotal = = = 0.5 μF
C =
Percent Difference =
= = 9.5%

Thickness of Wax Paper
d = 65μm - 30μm = 35μm
C =
d = = m2 / C2= 580μm
Percent Difference =
= = 180%

Discussions

To find the time constant, we first need to determine the peak and trough of the graph on the oscilloscope. We then adjusted the graph by centering it and translating it along the x-axis so that the peak is align with the y-axis. Then we read the time between a peak and a trough and divided that value by 2 to obtain the half time, which is the time required for the...