Physics-report-1.docx

PHYSICS FOR ENGINEERING

Capacitor AND CAPACITANCE

APRIL 2019 PHYSICS FOR ENGINEERING LECTURE Instructor: Engr. Claudio Cajes

REPUBLIC OF THE PHILIPPINES CEBU TECHNOLOGICAL UNIVERSITY - MAIN CAMPUS MJ. CUENCO AVE., COR. R. PALMA ST., CEBU CITY BACHELOR OF SCIENCE IN MECHANICAL ENGINEERING CAPACITOR & CAPACITANCE 88

March 2019

PHYSICS FOR ENGINEERING

Faughn, J.S., Serway, R.A., Vuille, C., & Bennet, C.A.(2006). Capacitance. Serway’s College Physics (Thompson Asian Edition). pp-545-546 Pacific Grove, United States of America: Brooks/Cole. CAPACITANCE Capacitor is a device used in a variety of electric circuits – for example, to tune the frequency of radio receivers, eliminate sparking in automobile ignition systems, or store short-term energy for rapid release in electronic flash units. Used in electric circuit, the plates are connected to the positive and negative terminals of a battery or some other voltage source. When this connection is made, electrons are pulled off one of the plates, leaving it with a charge of +Q, and are transferred through the battery to the other plate, leaving it with a charge of –Q, as shown in the figure. The transfer of charge stops when the potential difference across the plates equals the potential difference of the battery. A charged capacitor is a device that stores energy that can be reclaimed when needed for a specification application.

Figure 1. A parallel-plate capacitor consists of two parallel plates, each area A, separated by a distance d. The plates carry equal and opposite charges.

The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates): 𝑄

𝐶 = ∆𝑉 , Equation 1.0 𝐶

SI units: farad (F) = coulomb per volt (𝑉) The quantities Q and ∆V are always taken to be positive when used in Equation 1.0. For example, if a 3.0 µF capacitor is connected to a 12-V battery, the magnitude of the charge on eaach plate of capacitor is 𝑄 = 𝐶∆𝑉 = (3.0 × 10−6 𝐹)(12 𝑉) = 36𝜇𝐹

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From the Equation 1.0, we see that a large capacitance is needed to store large amount of charge for given applied voltage. The farad is a very large unit of capacitance. In practice, most typical capacitors have capacitances ranging from microfarads ((1𝜇𝐹 = 1 × 10−6 𝐹) to picofarads (1𝑝𝐹 = 1 × 10−12 𝐹). THE PARALLEL-PLATE CAPACITOR The capacitance of a device depends on the geometric arrangement of the conductors. The capacitance of a parallel-plate capacitor with plates separated by air (see firgure 1.0). can be easily calculated from three facts. First, recall that 𝜎 the magnitude of the elctric field between two plates is given by 𝐸 = 𝜖 , where σ 0

is the magnitude of the charge per unit area on each plate. Second, we found earlier in this chapter that the potential difference between two plates is ∆𝑉 = 𝐸𝑑, where d is the distance between the plates. Third, the charge on one plate is given by 𝑞 = 𝜎𝐴, where A is the area of the plate. Substituting these three facts into the definition of capacitance gives the desired result: 𝑞 𝜎𝐴 𝜎𝐴 𝐶= = = 𝜎 ∆𝑉 𝐸𝑑 ( ) 𝑑 𝜖0 𝐴

Canceling the charge per unit area, σ, yields: 𝐶 = 𝜖0 𝑑 , where A is the area of one plates, d is the distance between the plates, and 𝜖0 is the permittivity of the free space. 𝐴 From the equation 𝐶 = 𝜖0 𝑑 , we see that plates with larger area can store more charge. The same is true for a small plate separation d, because then the positive charges on one plate exert a stronger force on the negative charges on the other plate, allowing more chrage to be held on the plates.

Figure 2. (a) The electric field between the plates of parallel-plate capacitor is uniform near the center, but non-uniform near the edges. (b) Electric field pattern of two oppositely charged conducting parallel plates. Small pieces of thread on an oil surface align with electric field.

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Figure 2 show the electric field lines of a more realistic parallel-plate capacitor. The electric field is very nearly constant in the center between the p[lates, but becomes less so when approaching the edges. For most purposes, however, the field may be taken as constant throughout the region between the plates. One practical device that uses a capacitor is the flash attachment on a camera. A battery is used to charge the capacitor, and stored charge is then released when the shutter-release button is pressed to take a picture. The stored charge delivered to a flash tube very quickly, illuminating the subject at the instant more light is needed. Computers make use of capacitors in many ways. For example, one type of computer keyboard has capacitors at the bases of its keys, as in Figure 3. Each key is connected to a movable plate, hich represents one side of the capacitor; the fixed plate on the bottom of the keyboard represents the other side of the capoacitor. When a key is pressed, the capacitor spacing decreases, causing an increase in capacitance. External electronic circuits recognize each key by the change in its capacitance when it is pressed.

Capacitors are useful for storing a large amount of charge that needs to be delivered quickly. A good example on the forefront of fusion research is electrostatic confinement. In this role, capacitors discharge their electrons through a grid. The negatively charged electrons in the grid draw prositively charfged particales to them and therefore to each other, causing some particles to fuse and release energy in the process. Figure 3. When the key of one type of keyboard is pressed, the capacitance of a parallel-plate capacitor increases as the plate spacing decreases. The substance labeled “dielectric” is an insulating material.

APPLICATION Camera flash attachment Computer keyboard Electrostatic Confinement

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A PARALLEL-PLATE CAPACITOR Objective: To calculate fundamental physical properties of a parallel-plate capacitor. Problem: A paralell-plate capacitor has an area 𝐴 = 2.00 × 10−4 𝑚2 and a plate separation 𝑑 = 1.00 × 10−3 𝑚 . (a) Find its capacitance. (b) How much charge is on the positive plate if the capacitor is connected to a 3.00 − 𝑉 battery? (c) Calculate the charge density on the positive plate, assuming the density is uniform, and (d) the magnitude of the electric field between the plates. Stategy: Parts (a) and (b) can be solved by substituting into the basic equations for capacitance. In Part (c), use the fact that the voltage difference equals the electric field times the distance. Solution: (a) Find the capacitance. 𝐶2

A

2.00 ×10−4 𝑚2

C = 𝜀0 𝑑 = (8.85 × 10−12 N∙𝑚2 ) ( 1.00×10−3 𝑚 ) C = 1.77 × 10−12 𝐹 = 1.77 𝑝𝐹 (b) Find the charge on the positive plate after the capacitor is connected to a 3.00-V battery. 𝑄

𝐶 = ∆𝑉 → 𝑄 = 𝐶∆𝑉 = (1.77 × 10−12 𝐹) × (3.00 𝑉) = 5.31 × 10−12 𝐶 (c) Calculate the charge density on the positive plate. Charged density is divoded by the area: 𝑄

5.31×10−12 𝐶

𝐶

𝜎 = 𝐴 = 2.00 ×10−4 𝑚2 = 2.66 × 10−8 𝑚2 (d) Calculate the magnitude of the electric field between the plates. 𝜎

𝐸=𝜀 = 0

𝐶

2.66×10−8 2 𝑚

𝐶2 8.85×10−12 N∙𝑚2

𝑁

= 3.01 × 103 𝐶

Remarks: The answer to part (d) could also have been obtained from the lectric potential, which is ∆𝑉 = 𝐸𝑑 for a parallel-plate capacitor. ------------------------------------------------------------------------------------------------Exercise Problem: Two plates, each of area 3.00 × 10−4 𝑚2 , are used to construct a parallel-plate capacitor with capacitance 1.00 𝑝𝐹, (a) Find the necessary separation distance. (b) If the positive plate is to hold a charge of 5.00 × 10−12 𝐶, find the charge density.

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(c) Find the electric field between the plates. (d) what voltage battery should be attached to the plate to obtain the preceeding results? 𝐶

𝑁

Answers: (a) 2.66 × 10−3 𝑚 (b) 1.67 × 10−8 𝑚2 (c) 1.89 × 103 𝐶

(d) 5.00 𝑉

------------------------------------------------------------------------------------------------Symbols for Circuit Elements and Circuits The symbol that is commonly used to represent a capacitor in a circuit is, or sometimes

. Don’t confuse either of these symbols with the circuit

symbol, which is used to designate a battery (or any other source of direct current). The positive terminal of the battery is the higher potential and is represented by the longer vertical line in the battery symbol. ------------------------------------------------------------------------------------------------CAPACITORS WITH DIELECTRICS A dielectric is an insulating material, such as rubber, plastic, or waxed paper. When a dielectric is inserted between the plates of a capacitor, the capacitance increases. If the dielectric completely fills the space between the plates, the capacitance is multiplied by the factor k, called the dielectric constant. The following experiment illustrates the effect of dielectric in a capacitor. Consider a parallerl-plate capacitor of charge 𝑄0 and capacitance 𝐶0 in the absence of a dielectric. The potential difference across the capacitor plates can be measured, and is given by ∆𝑉0 =

𝑄0 𝐶0

. Because the capacitor is not connected

to an external circuit, there is no pathway for charge to leave or be added to the plates. If a dielectric is now inserted between the plates as in Figure 4, the voltage across the plates is reduced by the factor k to the value, ∆𝑉 =

∆𝑉0 𝐾

Because k>1, ∆𝑉 is less than ∆𝑉0. Because the charge 𝑄0 on the capacitor doesn’t change, we conclude that the capacitance in the presence of the dielectric must change to the value, 𝑄

𝐶 = ∆𝑉0 =

𝑄0 ∆𝑉0 𝐾

=

𝑘𝑄0 ∆𝑉0

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Figure 4. (a) With air between the plates, the voltage across the capacitor is ∆𝑉0 , the capacitance is 𝐶0 , and the charges is 𝑄0 . (b) With a dielectric between the plates, the charges remains at 𝑄0 , but the voltage and capacitance change. According to this result, the capacitance is multiplied by the factor k when the dielectric fills the region between the plates. For a parallelplate capacitor, where tha capacitance in the absnece of a dielectric is 𝐶0 =

𝜀0 𝐴 𝑑

, we can express the capacitance is the presence of a

dielectric as, 𝐶0 =

𝜀0 𝐴 𝑑

REFERENCES

CAPACITOR & CAPACITANCE March 2019

PHYSICS FOR ENGINEERING

Mechanical Engineering (2010). Safety Precautions and measurements [Blogspot]. Retrieved from https://engineeringhut.blogspot.com/2010/11/safety-precautions.html

Babu, S. (2014, September 24). Machine Shop Notes [PowerPoint Slides]. Retrieved from https://www.slideshare.net/sureshbabuem/machine-shop-notespdf

Seyferth, N. (2017, November 16). 7 Essential Metrology Tools for Modern CNC Machine Shops [blog Post]. Retrieved from https://blog.eaglegroupmanufacturers.com/precision-machined-parts-measuring-toolsevery-cnc-shop-should-have

Little Machine Shops. (2009). Retrieved From https://littlemachineshop.com/images/gallery/instructions/steelrules.pdf

Dial Test Indicator. (2014). Retrieved from http://www.disenoart.com/products/tools/dial_test_indicator.html

El-Sherbeeny, A. (2015). 2 - Machining Fundamentals – Measurement. Retrieved from https://fac.ksu.edu.sa/sites/default/files/2__machining_measurement_ams_sep09_13.pdf

Carbide Processor Inc. (2018). Types of Machine Coolant. Retrieved from http://www.carbideprocessors.com/pages/machine-coolant/types-of-machinecoolant.html

Engineering 360. (2018). Functions of Lubricants. Retrieved from https://www.globalspec.com/reference/38788/203279/functions-of-lubricants

Anonymous. (2012, September 5). Functions of Lubricants. Retrieved from http://www.thegreenbook.com/functions-of-lubricants.htm

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