Parallel Plate Capacitor

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1 Parallel Plate Capacitor Theory A capacitor is able to store charge. The amount of charge Q it stores is proportional to the potential difference V across it. This ratio C of charge to potential C = Q V (1) is constant and is known as the capacitance of the capacitor. The unit of capacitance is the farad (F). The simplest capacitor is two parallel plates separated by some distance d, possibly with some material in the space between the plates. Its capacitance is given by C = κɛ oa d where A is the area of either plate, ɛ o is the permittivity of free space, and κ the dielectric constant of the material between the plates (vacuum/air = 1.000). In this experiment, you will use two small aluminum plates in order to confirm the relationships shown above between C, A, and d. (2) Apparatus Two free-standing aluminum plates, Rule, Wires, Digital capacitance meter, Dielectric plate, Non-conducting clip, Micrometer. Procedure You do not need to worry about charge or potential in this experiment. The capacitance meter is connected to the aluminum plates and will automatically display the capacitance offered in each configuration directly. The arrangement is shown in Figure 1. This is a very simple experiment, but you should take the time to obtain good data. In each procedure, make sure that the variable under question is the only one which changes. The capacitances are very small, so the meter will respond to any objects in the vicinity of the plates (including you) move away as the meter measures the capacitance and allow the values to stabilize. Before beginning each procedure ensure that the capacitance meter is zeroed; connect the wires to the meter (only), turn it on (200pF setting), and zero if necessary. the plates are discharged; touch the (unconnected) plates together. 1

Figure 1: The Capacitor Capacitance and Plate Separation 1. Measure the width and height of one of the plates and calculate the plate area. Record this value in Table 1. 2.

2 Figure 1: The Capacitor Capacitance and Plate Separation 1. Measure the width and height of one of the plates and calculate the plate area. Record this value in Table Connect the capacitance meter to the plates and place them 0.5cm apart. Record the capacitance shown on the meter at this distance. 3. Increase the distance between the plates in 0.5cm increments until the distance between the plates is 2.5cm. At each distance, record the capacitance shown on the meter. 4. Graph capacitance vs. inverse distance between the plates. Plot the straight line of best fit over the data points and determine its slope. 2

3 Table 1: Capacitance and Plate Separation Plate area (m 2 ) Distance Inverse Capacitance Distance (m) (m 1 ) (F) Capacitance and Plate Area Obviously, you cannot physically alter the plate area. However, the effective area for a parallel plate capacitor is that which is common to both plates; i.e., those portions which overlap. As you slide one of the plates left or right relative to the other, the effective area changes, as shown in Figure 2. Figure 2: Area Determination 1. Measure the thickness of the plastic dielectric plate with the micrometer. Record this value in Table 2. Note that this is also the plate separation. 2. Assemble the capacitor such that the dielectric is between the two aluminum plates (you can hold everything together with the non-conducting plastic clip). Record the capacitance. 3. Slide one of the plates to the side relative to the other in 1.0cm increments until you have moved a total of 5.0cm. After area move, record the effective area and capacitance. 4. Graph capacitance vs. effective area. Plot the straight line of best fit over the data points and determine its slope. 3

4 Table 2: Capacitance and Plate Area Thickness of dielectric (m) Area Capacitance (m 2 ) (F) Analysis Capacitance and Plate Separation 1. According to Equation 2, what is the relationship between C and d? Does your graph confirm the relationship? Why or why not? [If not, explain why this might be the case.] 2. Use the slope of the line you determined to calculate κ for the air in the physics lab. Show all work. 4

5 Capacitance and Plate Area 1. According to Equation 2, what is the relationship between C and A? Does your graph confirm the relationship? Why or why not? [If not, explain why this might be the case.] 2. Use the slope of the line you determined to calculate κ for the plate you used in this procedure. Show all work. 5

6 Pre-Lab: Parallel Plate Capacitor Name Section Answer the questions at the bottom of this sheet, below the line - continue on the back if you need more room. Any calculations should be shown in full. 1. What is the formula for the capacitance C of a parallel plate capacitor with plate area A, plate separation d, and with a material of dielectric constant κ between the plates? 2. According to your equation from Question 1, what is the relationship between C and d? 3. According to your equation from Question 1, what is the relationship between C and A? 4. A 25pF capacitor has plate dimensions 5.00cm by 5.00cm and these plates are separated by a distance of 5.0mm. What is the dielectric constant of the material between the plates? 6

Measurement of Capacitance

Measurement of Capacitance Pre-Lab Questions Page Name: Class: Roster Number: Instructor:. A capacitor is used to store. 2. What is the SI unit for capacitance? 3. A capacitor basically consists of two