Physics
Potential Difference
Potential difference, also known as voltage, refers to the difference in electric potential between two points in an electric circuit. It is measured in volts and represents the work done per unit charge in moving a positive test charge between the two points. Potential difference is essential for the flow of electric current and is a fundamental concept in understanding electrical circuits.
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12 Key excerpts on "Potential Difference"
eBook - PDF- William Moebs, Samuel J. Ling, Jeff Sanny(Authors)
- 2016(Publication Date)
- Openstax(Publisher)
(The default assumption in the absence of other information is that the test charge is positive.) We briefly defined a field for gravity, but gravity is always attractive, whereas the electric force can be either attractive or repulsive. Therefore, although potential energy is perfectly adequate in a gravitational system, it is convenient to define a quantity that allows us to calculate the work on a charge independent of the magnitude of the charge. Calculating the work directly may be difficult, since W = F → · d → and the direction and magnitude of F → can be complex for multiple charges, for odd-shaped objects, and along arbitrary paths. But we do know that because F → = q E → , the work, and hence ΔU, is proportional to the test charge q. To have a physical quantity that is independent of test charge, we define electric potential V (or simply potential, since electric is understood) to be the potential energy per unit charge: Electric Potential The electric potential energy per unit charge is (7.4) V = U q . Since U is proportional to q, the dependence on q cancels. Thus, V does not depend on q. The change in potential energy ΔU is crucial, so we are concerned with the difference in potential or Potential Difference ΔV between two points, where Chapter 7 | Electric Potential 293 ΔV = V B − V A = ΔU q . Electric Potential Difference The electric Potential Difference between points A and B, V B − V A , is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of Potential Difference are joules per coulomb, given the name volt (V) after Alessandro Volta. 1 V = 1 J/C The familiar term voltage is the common name for electric Potential Difference. Keep in mind that whenever a voltage is quoted, it is understood to be the Potential Difference between two points. For example, every battery has two terminals, and its voltage is the Potential Difference between them.
eBook - PDF- SA Chuturgoon(Author)
- 2021(Publication Date)
- Troupant(Publisher)
Simply put, Potential Difference is an electrical pressure that produces current flow in a closed electric circuit . It is also known as terminal voltage . Potential Difference is represented by the symbol V or PD and is measured in joules per coulomb or volts. elementary charge: charge carried by a single electron electricity (current flow): flow of charge (electrons) in a specific direction conventional current flow: flow of current from the positive terminal of a battery to the negative terminal of the battery electron flow: the flow of current from the negative terminal of a battery to the positive terminal of the battery circuit: a movement that starts and finishes at the same point closed electric circuit: a complete electrical connection around which current flows terminal voltage: Potential Difference between the terminals of a cell when current flows 44 Module 4 TVET FIRST 4.1.3 Electromotive force Electromotive force is an electrical potential produced by any source of electrical energy. Its function is to initiate and maintain a Potential Difference. Electromotive force (emf) is represented by the symbol E and is also measured in volts (V). Definition of electromotive force (emf) Electromotive force is the voltage measured across the ends of an energy source of an open circuit . (Remember that no current is flowing in an open circuit.) Sources of electromotive force The following are sources of electromotive force or sources of electrical energy: • Cells or batteries. • Generators . • Solar energy . • Heat. • Friction . Electromotive force versus Potential Difference Did you notice that Potential Difference and electromotive force are both measured in volts? Over the years people have started to refer to both Potential Difference and electromotive force as voltage (which also means electrical potential). So, let us talk about the differences between the two in order to avoid confusion.
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2022(Publication Date)
- CRC Press(Publisher)
Electric Potential Difference is electric potential energy difference per unit charge, and therefore, like its vector counterpart E , does not depend on the charge q + moved. Like electric field rather than electric force, electric Potential Difference is more useful than electric potential energy difference. This is because, once ΔV is known, ΔU e can then be determined for any charge q moved. To illustrate this, let’s calculate the electric Potential Difference associated with the uniform field (magnitude E) between two parallel plates: Δ = Δ = = + + + V U q q Ed q Ed e Potential Difference (for parallel plates) (16.2) Notice that the charge moved, q + , cancels out. Thus the Potential Difference ΔV depends on only the plates – their field (E) and separation ( d). This result can be described in electric potential language as follows: For a pair of oppositely charged parallel plates, the positively charged plate is at a higher electric potential than the negatively charged plate by an amount equal to ΔV . Notice that electric Potential Difference is defined with- out defining electric potential (V) itself. Although this may seem strange, there is good reason for it. Of the two, electric + + + + + – – – – – h d B A E = F e q + q + (a) F g m + + (b) m B A g = ▲ FIGURE 16.1 Changes in potential energy in uniform electric and gravitational fields (a) Moving a positive charge q + against the electric field requires positive work and involves an increase in electric potential energy. (b) Moving a mass m against the gravitational field requires posi- tive work and involves an increase in gravitational potential energy. 419 Electric Potential, Energy, and Capacitance Potential Difference (or voltage) is the only physically mean- ingful quantity – the quantity actually measured. The electric potential V , in contrast, isn’t definable in an absolute way – it depends entirely on the choice of a reference point.
eBook - ePub- Adrian Waygood(Author)
- 2018(Publication Date)
- Routledge(Publisher)
V – depending on context (more on this later).We shall be examining the differences between potential and Potential Difference in more detail later in this chapter.The volt
We are now in a position to define the SI unit of both potential and Potential Difference, which is the volt , named in honour of the Italian physicist, Count Alessandro Volta (1745–1827).The volt (symbol: V ) is defined as ‘the Potential Difference between two points such that the energy used in conveying a charge of one coulomb from one point to the other is one joule’ .Again, you do not have to memorise this definition, however we will need to refer back to it when we discuss energy, work and power, in a later chapter.In practice, Potential Differences can vary enormously. For example, a simple AA disposable battery (or, more accurately, ‘cell’) will provide a Potential Difference of just 1.5 V, whereas electricity transmission voltages (in the UK) can be as high as 400 kV.The preceding definition may be expressed in the form of an equation:where:E =W Q- E = Potential Difference, in volts (symbol: V)
- W = work, in joules (symbol: J)
- Q = electric charge, in coulombs (symbol: C)
Worked example 1 The work done by a gener-ator in separating a charge of 20 C is 50 kJ.What is the resulting Potential Difference across its terminals?Solution Important ! Don’t forget, we must first convert the kilojoules to joules.E =W Q== 2.5 × 1( 5 0 × 10 3)2 00 3= 2500 V (Answer)Creating a Potential Difference through charge separation
So we now know what we mean by a Potential Difference and how it is measured. But how
eBook - ePubElectrical Engineering
Fundamentals
- Viktor Hacker, Christof Sumereder(Authors)
- 2020(Publication Date)
- De Gruyter Oldenbourg(Publisher)
φ of the field at that point.Defining equation:φ =W pQ +1.9 Voltage V
Voltage is the difference in electric potential between two points. In a static electric field, voltage is defined as the work needed to move a unit charge between two points.The necessary charge to transport a chargeQ +from object 1 to object 2 equals the difference of the potential energiesof the charges on the two objects.W=1 , 2W−p , 2Wp , 1The Potential Difference equals the work for the unit charge:Q += 1 A sφ 2−φ 1=WQ1 , 2It is called voltage V (14 ).Defining equation:V =W1 , 2Q +V = V15 SI unit:V o l tV =JA sThe voltage between two objects therefore is the work that is necessary to transport the unit chargefrom the negatively charged object to the positively charged object. If this voltage is expended, the charges are separated.Q += 1A sVoltage can cause electric current: If there is a voltage between two particles and these two particles are connected through a conductor, current flows. (More specifically: There is an electric field between the two particles. This field exerts force on the free charge carriers, which causes them to move.)Voltage is connected to force:
eBook - PDF- Paul Peter Urone, Roger Hinrichs(Authors)
- 2012(Publication Date)
- Openstax(Publisher)
Electric Potential This is the electric potential energy per unit charge. (19.2) V = PE q Since PE is proportional to q , the dependence on q cancels. Thus V does not depend on q . The change in potential energy ΔPE is crucial, and so we are concerned with the difference in potential or Potential Difference ΔV between two points, where (19.3) ΔV = V B − V A = ΔPE q . The Potential Difference between points A and B, V B – V A , is thus defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of Potential Difference are joules per coulomb, given the name volt (V) after Alessandro Volta. (19.4) 1 V = 1 J C Potential Difference The Potential Difference between points A and B, V B - V A , is defined to be the change in potential energy of a charge q moved from A to B, divided by the charge. Units of Potential Difference are joules per coulomb, given the name volt (V) after Alessandro Volta. (19.5) 1 V = 1 J C The familiar term voltage is the common name for Potential Difference. Keep in mind that whenever a voltage is quoted, it is understood to be the Potential Difference between two points. For example, every battery has two terminals, and its voltage is the Potential Difference between them. More fundamentally, the point you choose to be zero volts is arbitrary. This is analogous to the fact that gravitational potential energy has an arbitrary zero, such as sea level or perhaps a lecture hall floor. In summary, the relationship between Potential Difference (or voltage) and electrical potential energy is given by (19.6) ΔV = ΔPE q and ΔPE = qΔV . Potential Difference and Electrical Potential Energy The relationship between Potential Difference (or voltage) and electrical potential energy is given by (19.7) ΔV = ΔPE q and ΔPE = qΔV . The second equation is equivalent to the first. Voltage is not the same as energy.
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2015(Publication Date)
- Wiley(Publisher)
19.2 The Electric Potential Difference The electric potential V at a given point is the electric potential energy of a small test charge q 0 situated at that point divided by the charge itself, as shown in Equation 19.3. The SI unit of electric potential is the joule per coulomb (J/C), or volt (V). The electric Potential Difference between two points A and B is given by Equation 19.4. The Potential Difference between two points (or between two equipotential surfaces) is often called the “voltage.” W AB 5 EPE A 2 EPE B (19.1) V 5 EPE q 0 (19.3) V B 2 V A 5 EPE B q 0 2 EPE A q 0 5 2W AB q 0 (19.4) Focus on Concepts 535 FOCUS ON CONCEPTS Note to Instructors: The numbering of the questions shown here reflects the fact that they are only a representative subset of the total number that are available online. However, all of the questions are available for assignment via an online homework management program such as WileyPLUS or WebAssign. Section 19.2 The Electric Potential Difference 2. Two different charges, q 1 and q 2 , are placed at two different locations, one charge at each location. The locations have the same electric poten- tial V. Do the charges have the same electric potential energy? (a) Yes. If the electric potentials at the two locations are the same, the electric potential energies are also the same, regardless of the type (1 or 2) and magnitude of the charges placed at these locations. (b) Yes, because elec- tric potential and electric potential energy are just different names for the same concept. (c) No, because the electric potential V at a given location depends on the charge placed at that location, whereas the electric poten- tial energy EPE does not. (d) No, because the electric potential energy EPE at a given location depends on the charge placed at that location as well as the electric potential V. 4. A proton is released from rest at point A in a constant electric field and accelerates to point B (see part a of the drawing).
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2021(Publication Date)
- Wiley(Publisher)
The SI unit of electric potential is the joule per coulomb (J/C), or volt (V). The electric Potential Difference between two points A and B is given by Equation 19.4. The Potential Difference between two points (or between two equipotential surfaces) is often called the “voltage.” V = EPE ____ q 0 (19.3) V B − V A = EPE B _____ q 0 − EPE A _____ q 0 = − W AB _____ q 0 (19.4) A positive charge accelerates from a region of higher potential toward a region of lower potential. Conversely, a negative charge accelerates from a region of lower potential toward a region of higher potential. An electron volt (eV) is a unit of energy. The relationship between electron volts and joules is 1 eV = 1.60 × 10 −19 J. The total energy E of a system is the sum of its translational ( 1 _ 2 mυ 2 ) and rotational ( 1 _ 2 Iω 2 ) kinetic energies, gravitational potential energy (mgh), elastic potential energy ( 1 _ 2 kx 2 ) , and electric potential energy (EPE), as indicated by Equation 1. If external nonconservative forces like friction do no net work, the total energy of the system is conserved. That is, the final total energy E f is equal to the initial total energy E 0 ; E f = E 0 . E = 1 _ 2 m υ 2 + 1 _ 2 I ω 2 + mgh + 1 _ 2 kx 2 + EPE (1) 19.3 The Electric Potential Difference Created by Point Charges The electric potential V at a distance r from a point charge q is given by Equation 19.6, where k = 8.99 × 10 9 N · m 2 /C 2 . This expression for V assumes that the electric potential is zero at an infinite distance away from the charge. The total electric potential at a given location due to two or more charges is the algebraic sum of the potentials due to each charge. V = kq ___ r (19.6) The total potential energy of a group of charges is the amount by which the electric potential energy of the group differs from its initial value when the charges are infinitely far apart and far away.
eBook - PDF- Michael Tammaro(Author)
- 2019(Publication Date)
- Wiley(Publisher)
524 | Chapter 19 This example illustrates the power and utility of the concept of potential energy. Without knowing anything about the paths taken when the charges were assembled, or in what order they were assembled, we calculated the exact amount of work required to complete the task. 19.3 Solve problems dealing with the electric potential created by point charges. According to Equation 19.1.3, the electric Potential Difference is the change in elec- tric potential energy per unit charge—that is, ∆ = ∆ V U q 0 / . The Potential Difference ∆V , however, was not created by q 0 —it was created by other charges. Here in Section 19.3, we will develop an expression for the electric potential created by point charges and use it to calculate the electric potential. Consider the situation in Figure 19.3.1, where a point charge q is at a fixed position. A second charge q 0 is moved from very far away to point P, which is a distance r from charge q. 19.3 ELECTRIC POTENTIAL OF POINT CHARGES Learning Objective Figure 19.3.1 When q 0 moves from very far away to point P, the change in potential energy is given by ∆U = kqq 0 /r. r P q q 0 The initial potential energy is zero, so the change in potential energy is equal to the final potential energy—that is, ∆ = U kqq r 0 / (according to Equation 19.2.1). The electric poten- tial difference, therefore, is ∆ = ∆ = V U q kq r 0 / / . It is customary to choose the zero of elec- tric potential to be infinitely far from the charge q, in which case the change in electric potential is simply equal to its final value: The Electric Potential Created by a Point Charge The electric potential V created by a point charge q is given by = V k q r (19.3.1) where r is the distance from q to where the potential is being evaluated. Positive charges create positive potential, while negative charges create negative poten- tial.
eBook - ePubCollege Physics Essentials, Eighth Edition
Electricity and Magnetism, Optics, Modern Physics (Volume Two)
- Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
- 2019(Publication Date)
- CRC Press(Publisher)
points. Δ V = Δ U e q + (16.1) • The electric Potential Difference between two parallel plates is Δ V = E d (parallel plates) (16.2) • Equipotential surfaces (also equipotentials) are of constant electric potential. These surfaces are everywhere perpendicular to the electric field. • The electric Potential Difference between two locations near a point charge is Δ V = k q r B − k q r A (16.3) • The electric potential near a point charge (choosing zero reference at infinite distance) is V = k q r (16.4) • The electric potential energy of two point charges (choosing U = 0 at r = ∞) is U 12 = k q 1 q 2 r 12 (16.5) • The electric potential energy of more than two point charges is the sum of point charge pair terms from Equation. 16.5: U = U 12 + U 23 + U 13 + U 14 ⋯ (16.6) • The electric field (E →) is in the direction of the most rapid decrease in electric potential (V). The field magnitude (E) is the maximum rate of change of the potential with distance, or E = | Δ V Δ x | max (16.8) • The electron-volt (eV) is the kinetic energy gained by an electron or a proton accelerated through a Potential Difference of 1 V. The conversion factor to SI units is 1 eV = 1.60 × 10 − 19 J. • A capacitor is any arrangement of two metallic plates that can store charge and energy. Its capacitance is a measure of how effective it is in storing charge and is defined as the magnitude of the charge stored on either plate per volt: C = Q Δ V (16.9) • The expression for the capacitance of a parallel plate capacitor (in air) is C = ε o A d (16.12) where ε o = 8.85 × 10 − 12 C 2 /(N · m 2) is the permittivity of free space. • The energy stored in a capacitor depends on its capacitance and the charge the capacitor stores (or, equivalently, the voltage across its plates). There are three equivalent expressions for this energy: U C = 1 2 Q ⋅ Δ V = Q 2 2 C = 1 2 C (Δ V) 2 (16.13) • A dielectric is a non-conducting material that increases capacitance
eBook - PDF- John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
- 2018(Publication Date)
- Wiley(Publisher)
(b) The definition of capacitance (Equation 19.8) can be used to find the charge on each plate. Solution (a) Applying Equation 19.11b with the data given in the problem, we have Energy = 1 2 CV 2 = 1 2 (22.5 × 10 −6 F)(1250 V) 2 = 17.6 J (b) The charge on the capacitor is given by Q = CV = (22.5 × 10 −6 F)(1250 V) = 0.028 C 544 CHAPTER 19 Electric Potential Energy and the Electric Potential Concept Summary 19.1 Potential Energy When a positive test charge +q 0 moves from point A to point B in the presence of an electric field, work W AB is done by the elec- tric force. The work equals the electric potential energy (EPE) at A minus that at B, as given by Equation 19.1. The electric force is a conservative force, so the path along which the test charge moves from A to B is of no consequence, for the work W AB is the same for all paths. W AB = EPE A − EPE B (19.1) 19.2 The Electric Potential Difference The electric potential V at a given point is the electric potential energy of a small test charge q 0 situated at that point divided by the charge itself, as shown in Equation 19.3. The SI unit of electric potential is the joule per coulomb (J/C), or volt (V). The electric Potential Difference between two points A and B is given by Equation 19.4. The Potential Difference between two points (or between two equipotential surfaces) is often called the “voltage.” V = EPE q 0 (19.3) V B − V A = EPE B q 0 − EPE A q 0 = −W AB q 0 (19.4) A positive charge accelerates from a region of higher potential toward a region of lower potential. Conversely, a negative charge accelerates from a region of lower potential toward a region of higher potential. An electron volt (eV) is a unit of energy. The relationship between elec- tron volts and joules is 1 eV = 1.60 × 10 −19 J.
No longer available |Learn morePhysics for Scientists and Engineers
Foundations and Connections, Extended Version with Modern Physics
- Debora Katz(Author)
- 2016(Publication Date)
- Cengage Learning EMEA(Publisher)
Electric potential energy U E is a scalar that depends on both the source’s charge and the subject’s charge. Only changes in U E are physically important. 2. Electric potential V E is a scalar that depends only on the source’s charge. Find V E by dividing the electric potential energy U E by the charge q of a test subject: V E 5 U E q (26.6) Only differences in V E are physically important. Electric Potential Differences depend only on the endpoints, not on the particular path between them. 3. Finding the electric potential from the electric field. The electric Potential Difference DV between two points can be found by taking the path integral of the electric field E u between those points: DV 5 2 3 r f r i E u ? d r u (26.15) 4. Finding the electric field from the electric potential. The electric field is found by taking the partial derivative of V. In Cartesian coordinates, E x 5 2 'V 'x , E y 5 2 'V 'y , E z 5 2 'V 'z (26.21) In polar coordinates, E r 5 2 'V 'r (26.22) Each point on an E-versus-position graph is the negative of the slope of the tangent on the corre- sponding V-versus-position graph. ▲ Special Cases 1. Electric potential energy U E in systems with a spheri- cally symmetrical source (a particle, outside a sphere or spherical shell where r is greater than the radius of the sphere or spherical shell): U E 1r 2 5 kQq r (26.3) By the usual convention, U E 5 0 when the source and subject are infinitely far apart. If a system has more than two charged particles, the system’s electric potential energy is found by applying Equation 26.3 to each pair and then adding the results. 2. Electric potential V due to: a. A source with spherical symmetry. For a particle source with excess charge Q, V 5 k Q r (26.8) The electric potential due to a collection of n charged particles is V 5 k a n i 51 q i r i (26.9) where q i is the charge of the ith particle and r i is its distance to the point at which the electric po- tential is calculated.
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