Lecture 5 n n n Potential Difference Capacitance
![Lecture 5 n n n Potential Difference Capacitance Combinations of Capacitors Energy stored in Lecture 5 n n n Potential Difference Capacitance Combinations of Capacitors Energy stored in](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-1.jpg)
![Electric Field and Electric Potential Depend on Distance n n The electric field is Electric Field and Electric Potential Depend on Distance n n The electric field is](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-2.jpg)
![Electric Potential of Multiple Point Charges n n Superposition principle applies The total electric Electric Potential of Multiple Point Charges n n Superposition principle applies The total electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-3.jpg)
![Fig. 16 -6, p. 539 Fig. 16 -6, p. 539](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-4.jpg)
![Electrical Potential Energy of Two Charges n n n V 1 is the electric Electrical Potential Energy of Two Charges n n n V 1 is the electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-5.jpg)
![Notes About Electric Potential Energy of Two Charges n If the charges have the Notes About Electric Potential Energy of Two Charges n If the charges have the](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-6.jpg)
![Problem Solving with Electric Potential (Point Charges) n Draw a diagram of all charges Problem Solving with Electric Potential (Point Charges) n Draw a diagram of all charges](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-7.jpg)
![Problem Solving with Electric Potential, cont n Use the superposition principle when you have Problem Solving with Electric Potential, cont n Use the superposition principle when you have](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-8.jpg)
![Potentials and Charged Conductors n Since W = -q(VB – VA), no work is Potentials and Charged Conductors n Since W = -q(VB – VA), no work is](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-9.jpg)
![Conductors in Equilibrium n n n The conductor has an excess of positive charge Conductors in Equilibrium n n n The conductor has an excess of positive charge](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-10.jpg)
![The Electron Volt n The electron volt (e. V) is defined as the energy The Electron Volt n The electron volt (e. V) is defined as the energy](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-11.jpg)
![Equipotential Surfaces n An equipotential surface is a surface on which all points are Equipotential Surfaces n An equipotential surface is a surface on which all points are](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-12.jpg)
![Equipotentials and Electric Fields Lines – Positive Charge n n The equipotentials for a Equipotentials and Electric Fields Lines – Positive Charge n n The equipotentials for a](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-13.jpg)
![Equipotentials and Electric Fields Lines – Dipole n n n Equipotential lines are shown Equipotentials and Electric Fields Lines – Dipole n n n Equipotential lines are shown](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-14.jpg)
![Application – Electrostatic Precipitator n n n It is used to remove particulate matter Application – Electrostatic Precipitator n n n It is used to remove particulate matter](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-15.jpg)
![Fig. 16 -11 c, p. 543 Fig. 16 -11 c, p. 543](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-16.jpg)
![Fig. 16 -11 b, p. 543 Fig. 16 -11 b, p. 543](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-17.jpg)
![Application – Electrostatic Air Cleaner n n Used in homes to relieve the discomfort Application – Electrostatic Air Cleaner n n Used in homes to relieve the discomfort](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-18.jpg)
![Application – Xerographic Copiers n n The process of xerography is used for making Application – Xerographic Copiers n n The process of xerography is used for making](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-19.jpg)
![The Xerographic Process The Xerographic Process](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-20.jpg)
![Application – Laser Printer n The steps for producing a document on a laser Application – Laser Printer n The steps for producing a document on a laser](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-21.jpg)
![Capacitance n n A capacitor is a device used in a variety of electric Capacitance n n A capacitor is a device used in a variety of electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-22.jpg)
![Capacitance, cont n n Units: Farad (F) n n 1 F=1 C/V A Farad Capacitance, cont n n Units: Farad (F) n n 1 F=1 C/V A Farad](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-23.jpg)
![Parallel-Plate Capacitor n n The capacitance of a device depends on the geometric arrangement Parallel-Plate Capacitor n n The capacitance of a device depends on the geometric arrangement](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-24.jpg)
![Parallel-Plate Capacitor, Example n n n n The capacitor consists of two parallel plates Parallel-Plate Capacitor, Example n n n n The capacitor consists of two parallel plates](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-25.jpg)
![Electric Field in a Parallel. Plate Capacitor n The electric field between the plates Electric Field in a Parallel. Plate Capacitor n The electric field between the plates](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-26.jpg)
![Applications of Capacitors – Camera Flash n The flash attachment on a camera uses Applications of Capacitors – Camera Flash n The flash attachment on a camera uses](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-27.jpg)
![Applications of Capacitors – Computers n Computers use capacitors in many ways n n Applications of Capacitors – Computers n Computers use capacitors in many ways n n](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-28.jpg)
![Capacitors in Circuits n n A circuit is a collection of objects usually containing Capacitors in Circuits n n A circuit is a collection of objects usually containing](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-29.jpg)
![Capacitors in Parallel n n n When capacitors are first connected in the circuit, Capacitors in Parallel n n n When capacitors are first connected in the circuit,](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-30.jpg)
![Capacitors in Parallel n The total charge is equal to the sum of the Capacitors in Parallel n The total charge is equal to the sum of the](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-31.jpg)
![Fig. 16 -16 a, p. 548 Fig. 16 -16 a, p. 548](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-32.jpg)
![Fig. 16 -17, p. 549 Fig. 16 -17, p. 549](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-33.jpg)
![More About Capacitors in Parallel n The capacitors can be replaced with one capacitor More About Capacitors in Parallel n The capacitors can be replaced with one capacitor](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-34.jpg)
![Capacitors in Parallel, final n n Ceq = C 1 + C 2 + Capacitors in Parallel, final n n Ceq = C 1 + C 2 +](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-35.jpg)
![Fig. 16 -18, p. 550 Fig. 16 -18, p. 550](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-36.jpg)
- Slides: 36
![Lecture 5 n n n Potential Difference Capacitance Combinations of Capacitors Energy stored in Lecture 5 n n n Potential Difference Capacitance Combinations of Capacitors Energy stored in](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-1.jpg)
Lecture 5 n n n Potential Difference Capacitance Combinations of Capacitors Energy stored in Capacitor Dielectrics
![Electric Field and Electric Potential Depend on Distance n n The electric field is Electric Field and Electric Potential Depend on Distance n n The electric field is](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-2.jpg)
Electric Field and Electric Potential Depend on Distance n n The electric field is proportional to 1/r 2 The electric potential is proportional to 1/r
![Electric Potential of Multiple Point Charges n n Superposition principle applies The total electric Electric Potential of Multiple Point Charges n n Superposition principle applies The total electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-3.jpg)
Electric Potential of Multiple Point Charges n n Superposition principle applies The total electric potential at some point P due to several point charges is the algebraic sum of the electric potentials due to the individual charges n The algebraic sum is used because potentials are scalar quantities
![Fig 16 6 p 539 Fig. 16 -6, p. 539](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-4.jpg)
Fig. 16 -6, p. 539
![Electrical Potential Energy of Two Charges n n n V 1 is the electric Electrical Potential Energy of Two Charges n n n V 1 is the electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-5.jpg)
Electrical Potential Energy of Two Charges n n n V 1 is the electric potential due to q 1 at some point P The work required to bring q 2 from infinity to P without acceleration is q 2 V 1 This work is equal to the potential energy of the two particle system
![Notes About Electric Potential Energy of Two Charges n If the charges have the Notes About Electric Potential Energy of Two Charges n If the charges have the](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-6.jpg)
Notes About Electric Potential Energy of Two Charges n If the charges have the same sign, PE is positive n n n Positive work must be done to force the two charges near one another The like charges would repel If the charges have opposite signs, PE is negative n n The force would be attractive Work must be done to hold back the unlike charges from accelerating as they are brought close together
![Problem Solving with Electric Potential Point Charges n Draw a diagram of all charges Problem Solving with Electric Potential (Point Charges) n Draw a diagram of all charges](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-7.jpg)
Problem Solving with Electric Potential (Point Charges) n Draw a diagram of all charges n n n Note the point of interest Calculate the distance from each charge to the point of interest Use the basic equation V = keq/r n n Include the sign The potential is positive if the charge is positive and negative if the charge is negative
![Problem Solving with Electric Potential cont n Use the superposition principle when you have Problem Solving with Electric Potential, cont n Use the superposition principle when you have](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-8.jpg)
Problem Solving with Electric Potential, cont n Use the superposition principle when you have multiple charges n n Take the algebraic sum Remember that potential is a scalar quantity n So no components to worry about
![Potentials and Charged Conductors n Since W qVB VA no work is Potentials and Charged Conductors n Since W = -q(VB – VA), no work is](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-9.jpg)
Potentials and Charged Conductors n Since W = -q(VB – VA), no work is required to move a charge between two points that are at the same electric potential n n n W = 0 when VA = VB All points on the surface of a charged conductor in electrostatic equilibrium are at the same potential Therefore, the electric potential is a constant everywhere on the surface of a charged conductor in equilibrium
![Conductors in Equilibrium n n n The conductor has an excess of positive charge Conductors in Equilibrium n n n The conductor has an excess of positive charge](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-10.jpg)
Conductors in Equilibrium n n n The conductor has an excess of positive charge All of the charge resides at the surface E = 0 inside the conductor The electric field just outside the conductor is perpendicular to the surface The potential is a constant everywhere on the surface of the conductor The potential everywhere inside the conductor is constant and equal to its value at the surface
![The Electron Volt n The electron volt e V is defined as the energy The Electron Volt n The electron volt (e. V) is defined as the energy](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-11.jpg)
The Electron Volt n The electron volt (e. V) is defined as the energy that an electron gains when accelerated through a potential difference of 1 V n n Electrons in normal atoms have energies of 10’s of e. V Excited electrons have energies of 1000’s of e. V High energy gamma rays have energies of millions of e. V 1 e. V = 1. 6 x 10 -19 J
![Equipotential Surfaces n An equipotential surface is a surface on which all points are Equipotential Surfaces n An equipotential surface is a surface on which all points are](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-12.jpg)
Equipotential Surfaces n An equipotential surface is a surface on which all points are at the same potential n n No work is required to move a charge at a constant speed on an equipotential surface The electric field at every point on an equipotential surface is perpendicular to the surface
![Equipotentials and Electric Fields Lines Positive Charge n n The equipotentials for a Equipotentials and Electric Fields Lines – Positive Charge n n The equipotentials for a](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-13.jpg)
Equipotentials and Electric Fields Lines – Positive Charge n n The equipotentials for a point charge are a family of spheres centered on the point charge The field lines are perpendicular to the electric potential at all points
![Equipotentials and Electric Fields Lines Dipole n n n Equipotential lines are shown Equipotentials and Electric Fields Lines – Dipole n n n Equipotential lines are shown](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-14.jpg)
Equipotentials and Electric Fields Lines – Dipole n n n Equipotential lines are shown in blue Electric field lines are shown in red The field lines are perpendicular to the equipotential lines at all points
![Application Electrostatic Precipitator n n n It is used to remove particulate matter Application – Electrostatic Precipitator n n n It is used to remove particulate matter](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-15.jpg)
Application – Electrostatic Precipitator n n n It is used to remove particulate matter from combustion gases Reduces air pollution Can eliminate approximately 90% by mass of the ash and dust from smoke
![Fig 16 11 c p 543 Fig. 16 -11 c, p. 543](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-16.jpg)
Fig. 16 -11 c, p. 543
![Fig 16 11 b p 543 Fig. 16 -11 b, p. 543](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-17.jpg)
Fig. 16 -11 b, p. 543
![Application Electrostatic Air Cleaner n n Used in homes to relieve the discomfort Application – Electrostatic Air Cleaner n n Used in homes to relieve the discomfort](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-18.jpg)
Application – Electrostatic Air Cleaner n n Used in homes to relieve the discomfort of allergy sufferers It uses many of the same principles as the electrostatic precipitator
![Application Xerographic Copiers n n The process of xerography is used for making Application – Xerographic Copiers n n The process of xerography is used for making](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-19.jpg)
Application – Xerographic Copiers n n The process of xerography is used for making photocopies Uses photoconductive materials n A photoconductive material is a poor conductor of electricity in the dark but becomes a good electric conductor when exposed to light
![The Xerographic Process The Xerographic Process](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-20.jpg)
The Xerographic Process
![Application Laser Printer n The steps for producing a document on a laser Application – Laser Printer n The steps for producing a document on a laser](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-21.jpg)
Application – Laser Printer n The steps for producing a document on a laser printer is similar to the steps in the xerographic process n n Steps a, c, and d are the same The major difference is the way the image forms on the selenium-coated drum n n n A rotating mirror inside the printer causes the beam of the laser to sweep across the seleniumcoated drum The electrical signals form the desired letter in positive charges on the selenium-coated drum Toner is applied and the process continues as in the xerographic process
![Capacitance n n A capacitor is a device used in a variety of electric Capacitance n n A capacitor is a device used in a variety of electric](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-22.jpg)
Capacitance n n A capacitor is a device used in a variety of electric circuits The capacitance, C, of a capacitor is defined as the ratio of the magnitude of the charge on either conductor (plate) to the magnitude of the potential difference between the conductors (plates)
![Capacitance cont n n Units Farad F n n 1 F1 CV A Farad Capacitance, cont n n Units: Farad (F) n n 1 F=1 C/V A Farad](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-23.jpg)
Capacitance, cont n n Units: Farad (F) n n 1 F=1 C/V A Farad is very large n Often will see µF or p. F
![ParallelPlate Capacitor n n The capacitance of a device depends on the geometric arrangement Parallel-Plate Capacitor n n The capacitance of a device depends on the geometric arrangement](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-24.jpg)
Parallel-Plate Capacitor n n The capacitance of a device depends on the geometric arrangement of the conductors For a parallel-plate capacitor whose plates are separated by air:
![ParallelPlate Capacitor Example n n n n The capacitor consists of two parallel plates Parallel-Plate Capacitor, Example n n n n The capacitor consists of two parallel plates](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-25.jpg)
Parallel-Plate Capacitor, Example n n n n The capacitor consists of two parallel plates Each have area A They are separated by a distance d The plates carry equal and opposite charges When connected to the battery, charge is pulled off one plate and transferred to the other plate The transfer stops when DVcap = DVbattery Demo 2
![Electric Field in a Parallel Plate Capacitor n The electric field between the plates Electric Field in a Parallel. Plate Capacitor n The electric field between the plates](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-26.jpg)
Electric Field in a Parallel. Plate Capacitor n The electric field between the plates is uniform n n n Near the center Nonuniform near the edges The field may be taken as constant throughout the region between the plates
![Applications of Capacitors Camera Flash n The flash attachment on a camera uses Applications of Capacitors – Camera Flash n The flash attachment on a camera uses](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-27.jpg)
Applications of Capacitors – Camera Flash n The flash attachment on a camera uses a capacitor n n n A battery is used to charge the capacitor The energy stored in the capacitor is released when the button is pushed to take a picture The charge is delivered very quickly, illuminating the subject when more light is needed
![Applications of Capacitors Computers n Computers use capacitors in many ways n n Applications of Capacitors – Computers n Computers use capacitors in many ways n n](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-28.jpg)
Applications of Capacitors – Computers n Computers use capacitors in many ways n n n Some keyboards use capacitors at the bases of the keys When the key is pressed, the capacitor spacing decreases and the capacitance increases The key is recognized by the change in capacitance
![Capacitors in Circuits n n A circuit is a collection of objects usually containing Capacitors in Circuits n n A circuit is a collection of objects usually containing](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-29.jpg)
Capacitors in Circuits n n A circuit is a collection of objects usually containing a source of electrical energy (such as a battery) connected to elements that convert electrical energy to other forms A circuit diagram can be used to show the path of the real circuit
![Capacitors in Parallel n n n When capacitors are first connected in the circuit Capacitors in Parallel n n n When capacitors are first connected in the circuit,](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-30.jpg)
Capacitors in Parallel n n n When capacitors are first connected in the circuit, electrons are transferred from the left plates through the battery to the right plate, leaving the left plate positively charged and the right plate negatively charged The flow of charges ceases when the voltage across the capacitors equals that of the battery The capacitors reach their maximum charge when the flow of charge ceases
![Capacitors in Parallel n The total charge is equal to the sum of the Capacitors in Parallel n The total charge is equal to the sum of the](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-31.jpg)
Capacitors in Parallel n The total charge is equal to the sum of the charges on the capacitors n n Qtotal = Q 1 + Q 2 The potential difference across the capacitors is the same n And each is equal to the voltage of the battery
![Fig 16 16 a p 548 Fig. 16 -16 a, p. 548](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-32.jpg)
Fig. 16 -16 a, p. 548
![Fig 16 17 p 549 Fig. 16 -17, p. 549](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-33.jpg)
Fig. 16 -17, p. 549
![More About Capacitors in Parallel n The capacitors can be replaced with one capacitor More About Capacitors in Parallel n The capacitors can be replaced with one capacitor](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-34.jpg)
More About Capacitors in Parallel n The capacitors can be replaced with one capacitor with a capacitance of Ceq n n The equivalent capacitor must have exactly the same external effect on the circuit as the original capacitors Demo 3
![Capacitors in Parallel final n n Ceq C 1 C 2 Capacitors in Parallel, final n n Ceq = C 1 + C 2 +](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-35.jpg)
Capacitors in Parallel, final n n Ceq = C 1 + C 2 + … The equivalent capacitance of a parallel combination of capacitors is greater than any of the individual capacitors
![Fig 16 18 p 550 Fig. 16 -18, p. 550](https://slidetodoc.com/presentation_image_h/32a31582ac182197716d1e196fbd7285/image-36.jpg)
Fig. 16 -18, p. 550
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