College Physics

# Section Summary

College PhysicsSection 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. Do you know how you learn best?
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