College Physics for AP® Courses

Section Summary

19.1Electric Potential Energy: Potential Difference

• Electric potential is potential energy per unit charge.
• The potential difference between points A and B, $VB–VAVB–VA size 12{V rSub { size 8{B} } -V rSub { size 8{A} } } {}$, defined to be the change in potential energy of a charge $qq size 12{q} {}$ moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol $ΔVΔV size 12{V= { {"PE"} over {q} } "." } {}$.
$Δ V = ΔPE q and ΔPE = qΔV . Δ V = ΔPE q and ΔPE = qΔV . size 12{?V= { {?"PE"} over {q} } " and "D"PE="q?V "." } {}$
• An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
$1 eV = 1.60 × 10 –19 C 1 V = 1.60 × 10 –19 C 1 J/C = 1.60 × 10 –19 J. 1 eV = 1.60 × 10 –19 C 1 V = 1.60 × 10 –19 C 1 J/C = 1.60 × 10 –19 J.$
• Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, $KE+PE.KE+PE. size 12{"KE"+"PE"} {}$ This sum is a constant.

19.2Electric Potential in a Uniform Electric Field

• The voltage between points A and B is
$V AB = Ed E = V AB d (uniform E - field only), V AB = Ed E = V AB d (uniform E - field only),$
where $dd size 12{d} {}$ is the distance from A to B, or the distance between the plates.
• In equation form, the general relationship between voltage and electric field is
$E=–ΔVΔs,E=–ΔVΔs, size 12{E= - { {ΔV} over {Δs} } } {}$
where $ΔsΔs size 12{Δs} {}$ is the distance over which the change in potential, $ΔVΔV size 12{Δ`V} {}$, takes place. The minus sign tells us that $EE size 12{E} {}$ points in the direction of decreasing potential.) The electric field is said to be the gradient (as in grade or slope) of the electric potential.

19.3Electrical Potential Due to a Point Charge

• Electric potential of a point charge is $V=kQ/rV=kQ/r size 12{V= ital "kQ"/r} {}$.
• Electric potential is a scalar, and electric field is a vector. Addition of voltages as numbers gives the voltage due to a combination of point charges, whereas addition of individual fields as vectors gives the total electric field.

19.4Equipotential Lines

• An equipotential line is a line along which the electric potential is constant.
• An equipotential surface is a three-dimensional version of equipotential lines.
• Equipotential lines are always perpendicular to electric field lines.
• The process by which a conductor can be fixed at zero volts by connecting it to the earth with a good conductor is called grounding.

19.5Capacitors and Dielectrics

• A capacitor is a device used to store charge.
• The amount of charge $QQ size 12{Q} {}$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
• The capacitance $CC size 12{C} {}$ is the amount of charge stored per volt, or
$C=QV.C=QV. size 12{C=Q/V} {}$
• The capacitance of a parallel plate capacitor is $C=ε0AdC=ε0Ad size 12{C=e rSub { size 8{0} } A/d} {}$, when the plates are separated by air or free space. $ε 0 ε 0$ is called the permittivity of free space.
• A parallel plate capacitor with a dielectric between its plates has a capacitance given by
$C=κε0Ad,C=κε0Ad, size 12{C=e rSub { size 8{0} } A/d} {}$
where $κ κ$ is the dielectric constant of the material.
• The maximum electric field strength above which an insulating material begins to break down and conduct is called dielectric strength.

19.6Capacitors in Series and Parallel

• Total capacitance in series $1CS=1C1+1C2+1C3+...1CS=1C1+1C2+1C3+... size 12{ { {1} over { {C} rSub { size 8{S} } } } = { {1} over { {C} rSub { size 8{1} } } } + { {1} over { {C} rSub { size 8{2} } } } + { {1} over { {C} rSub { size 8{3} } } } + "." "." "." } {}$
• Total capacitance in parallel $Cp=C1+C2+C3+...Cp=C1+C2+C3+... size 12{ {C} rSub { size 8{p} } = {C} rSub { size 8{1} } + {C} rSub { size 8{2} } + {C} rSub { size 8{3} } + "." "." "." } {}$
• If a circuit contains a combination of capacitors in series and parallel, identify series and parallel parts, compute their capacitances, and then find the total.

19.7Energy Stored in Capacitors

• Capacitors are used in a variety of devices, including defibrillators, microelectronics such as calculators, and flash lamps, to supply energy.
• The energy stored in a capacitor can be expressed in three ways:
$Ecap=QV2=CV22=Q22C,Ecap=QV2=CV22=Q22C, size 12{E rSub { size 8{"cap"} } = { { ital "QV"} over {2} } = { { ital "CV" rSup { size 8{2} } } over {2} } = { {Q rSup { size 8{2} } } over {2C} } } {}$
where $QQ size 12{Q} {}$ is the charge, $VV size 12{V} {}$ is the voltage, and $CC size 12{C} {}$ is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.
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