Measuring capacitance
Capacitors are useful circuit elements because they can store charge. For a capacitor, there is a fundamental relationship between the applied voltage and the amount of charge stored on the capacitor. In this experiment you will measure the charge on a capacitor versus the applied voltage for several values of the applied voltage. A plot of charge vs. applied voltage should form a straight line with a slope equal to the capacitance.
(1)
You will use this relation to measure the capacitance of capacitors with different areas and distances between plates. Then you will verify the relation below using these different values.
(2)
objectives
· Determine the mathematical relationship between charge, applied voltage, and capacitance.
· Determine the capacitance of a capacitor.
· Verify the theoretical formula
MATERIALS
Computer w/ internet access
Logger Pro or Excel
PRELIMINARY Setup
Do the following by yourself to get idea how to use tools on simulation page.
1. Go to the following website.
https:
phet.colorado.edu/en/simulation/capacitor-lab-basics
2. Open the capacitor only screen.
3. Play with the controls until you are familiar with how they work. Make sure you can use the voltmeter to measure the potential difference between the plates.
4. The screen will look like this.
PROCEDURE
You will measure the capacitance for each capacitor using the following protocol. Note that the theoretical value is given to you at the top of the screen----your fit of your data should agree with this value.
1. Open the website and capacitance page. Go to capacitance page. Click “Top plate charge” on the top left on the screen. Also, make sure that the options on top right are clicked for “Plate charges”, “Bar Graph”. Record the value of capacitance (theoretical value given at the top left of the screen), Separation between plates (d), Area of the plates (A) from this page.
2. Connect voltmeter between plates of the capacitor. The voltage in battery and voltmeter will be zero at this time. The screen will look like this. Position voltmeter to measure potential difference.
3. Now start changing voltage of the battery from 0 V to 1.4 V in steps of 0.2 V and record co
esponding values of charge (Q) of the plates from the screen (shown on the screen at the top left). Look at the screen shot for the value of 0.6 V voltage (V) of battery, the charge (Q) 0.18 pC and theoretical capacitance (Cth) is 0.30 pF.
4. Record these values in Table 1 for V and Q1.
5. Now pick a different Area (A) and distance (d) between the capacitor plates by pulling a
ows outwards or inwards and change A and d.
6. You will repeat the above steps from 1-4 for this value of A and d. Fill out Table 1 with Q2 Values. Here is how screen will look with different A and d.
7. Now pick another value of A and d and then repeat steps from 1-4 and fill out Table 1 with Q3.
8. When complete table 1, use Excel or LoggerPro to plot a graph between Q (Y axis) and V (X axis) for all three columns and you will get three linear graphs for Q and V. Do linear curve fitting and determine slope. The slope is called capacitance obtained by slope as (Cs). Remember to use SI units when plotting which means Q should be in C and V should be in V! Include all plots with fits in lab report.
9. Here are unit conversion if you need help with.
1 mm = 1 *10^-3 m, 1mm^2 = 1*10^-6 m^2, 1pF = 1*10^-12 F, 1pC = 1*10^-12C
10. You will also calculate value of Capacitance using equation 2 and that capacitance will be called as Cc which means calculated capacitance.
11. When you complete this task, fill out the Data table 2 with values of three different areas (A), separation (d), theoretical capacitance (Cth), calculated capacitance (Cc) and slope capacitance (Cs).
12. Find percent e
or between three values of C as shown in the table 2.
DATA TABLEs
Data Table 1
Voltage (V)
Q1 (C)
Q2 (C)
Q3 (C)
0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
Data Table 2
capacito
A (mm2)
d (mm)
Theoretical Cth (pF)
Calculated Cc (pF)
Slope - Cs (pF)
Percent E
or 1 for Cth and Cc
Percent E
or 1 for Cth and Cs
1
2
3
ANALYSIS
1. You have already plotted the Q vs. V and determined the slopes. This is the first part of the analysis. Put these slopes in column 4 of data table 2.
2. For the second part of the analysis, use Eq. (2) and the data in columns 2 and 3 in data table 2 to calculate the capacitance for each capacitor geometry you measured. Put these values in column 6 of data table 2.
3. You will compare the results of C in columns 4 and 5, 4 and 6 in your lab report.