The Parallel Plate Capacitor

The parallel plate capacitor consists of two plates separated by a dielectric (insulator).

Our ready-made capacitor consists of a fiberglass board as the dielectric, with a thin coating of copper acting as the conductive parallel plates.

The electric field in the region between the capacitor plates is given by

(5) E=0

Experimental Approach

We wish to explore the relationships of the variables in equation 1.

(1) C=k0Ad

Equipment Tips:

We use multimeters to measure the capacitance of each capacitor, and of the capacitors we build. Make sure that each probe of the multimeter is only making contact with one side of the capacitor.

1. Capacitance vs. Area (Capacitors in Parallel)

1. Use the digital caliper to measure the length and width of the two plates. Convert these dimensions into meters and compute the area of each plate. This area should be essentially identical for each plate.

1. Make sure the probes of your multimeter connect to COM and the capacitor symbol on your multimeter.

2. Connect each probe to opposite sides of the capacitor and record the measured capacitance.

Table 1: Area and capacitance of the individual capacitors

Area of plate (m2)	Capacitance (nF) where n=10-9
A1 =	C1=
A2 =	C2=
Aaverage =	Caverage=

3. Use the conducting tape to connect the two capacitors side by side, then measure and record the new capacitance C_Parallel.

Table 2: Area and capacitance

Area of plate(s) (m2)	Capacitance (nF) where n=10-9
Aaverage =	Caverage=
A1+A2 = AParallel =	CParallel =

Is the capacitance for the doubled area, C_Parallel, consistent with the theory,C=k0Ad, for capacitance? Explain.

2. Series Capacitors

You just dealt with capacitors connected in parallel (connected side-by-side), and that will be a recurring topic which we will view in more detail later. Now, let's look at what happens when we connect capacitors in series by stacking capacitors one on top of another.

You will see these equations and relationships between parallel and series capacitors in detail in future labs! For now we just want to use the concept of parallel capacitors where we have two dielectrics side-by-side and series capacitors where they share a common middle plate (not visible) as in the second diagram.

1. Untape your two capacitors and measure their thickness d using the digital caliper, convert the value to meters, and record their thicknesses below.

2. Stack these capacitors one on top of the other. Once stacked, the only plates that matter are the two outermost plates. Measure their capacitance in series. You might need to use a piece of the conducting tape between the two to make a better connection if the multimeter does not give you a reading.

3. Use the theoretical formula for the capacitance to compute k and complete the table below, where0= 8.854 x10^-12F/m.

Table 3: Thickness and capacitance

	d (m)	Capacitance (nF) where n=10-9	k (unitless dielectric constant)
Capacitor 1	d1 =	C1 =
Capacitor 2	d2 =	C2 =
Series Capacitor	d1+d2 =	CSeries =

What happens to the capacitance when you double the distance? Is this consistent with the theory,C=k0Ad, for capacitance?

Charge Q Stored in a Capacitor

Purpose: By collecting and graphing data for the charge, Q, and the potential difference across a capacitor,VCap,the capacitance of a store-bought capacitor will be experimentally determined.

Equipment

Each station should have: A variable power supply, a store-bought capacitor, a chargemeter, a voltmeter, and a capacitance meter.

Procedure

1. DO NOT EXCEED 2.0 VOLTS on the variable power supply throughout this experiment. Set this power supply to 0 volts.

2. Build the circuit by connecting your capacitor, C, the variable power supply ("-" connection and the "+" connection), and the voltmeter, to the chargemeter as shown in the diagram below:

Figure 1.1 Diagram showing the setup for the experiment

3. Apply about 0.1 volts to the system (this value should be read using the voltmeter) and record the precise value of thisVCapin your data table.

4. Follow your instructor's demonstration in how to use the charge meter to measure the charge, Q, on the capacitor. Record this Q in nC=10^-9 Coulombs.

5. Increase the voltage by about another 0.15 volts, and repeat steps 3. and 5. Collecting at least six sets of data.

VCap (volts)[x-axis]
Q (nC) [y-axis]

6. Graph your data. If youUse Google Sheets select and copy paste your completed data table into a google sheet. If you haven't used Google Sheets before here is what to do: Click on the link. Paste your data table into a new blank spreadsheet. Highlight the data (including row headings), then from the menuInsertChart.

7. Use the theoretical relationshipQ=CVCapto interpret your data. The experimental value for the capacitance, C, of your capacitor will be given by the slope of a linear graph through your data set.

8. If you are working in Google Sheets you can curve fit your data following this procedure:

To curve fit your data in Sheets, double click your graph Customize Series scroll down check Trendline,and select Linear. Also, under Label select Use Equation. Check the R² box. When R² is close to 1 your data fits the curve very well.

9. Paste a copy of your graph in the box below. If you used Google Sheets you will see in the equation Q(nC)=C*x+b, where hopefully R²=something close to 1. The experimental value of the capacitance C, found from this graph, will be in nF.

10. Remove the capacitor from the circuit, then use a capacitance meter to measure the actual capacitance of your capacitor.

11. Show the calculation for the percent error below. Remember to have both values for the capacitance in nF=10^-9F.

% Error=Actual Value-Experimental ValueActual Valuex 100