Contents

Section Summary

Electric potential is potential energy per unit charge.
The potential difference between points A and B, $V_{B} - V_{A} V_{B} - V_{A} size 12{V rSub { size 8{B} } -V rSub { size 8{A} } } {}$ , defined to be the change in potential energy of a charge $q q size 12{q} {}$ 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 $Δ V Δ V size 12{V= { {"PE"} over {q} } "." } {}$ .
$Δ V = \frac{ΔPE}{q} and ΔPE = q Δ V . Δ V = \frac{ΔPE}{q} size 12{?V= { {?"PE"} over {q} } " and "D"PE="q?V "." } {}$
An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
$\begin{array}{l} 1 eV & = & (1.60 \times 10^{–19} C) (1 V) = (1.60 \times 10^{–19} C) (1 J/C) \\ = & 1.60 \times 10^{–19} J. \end{array} \begin{array}{l} 1 eV & = & (1.60 \times 10^{–19}) (1 V) = (1.60 \times 10^{–19}) (1 J/C) \\ = 1.60 \times 10^{–19} \end{array}$
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.

The voltage between points A and B is
$\begin{matrix} \begin{matrix} V_{AB} = Ed \\ E = \frac{V_{AB}}{d} \end{matrix}\} (uniform E - field only), \end{matrix} \begin{matrix} \begin{matrix} V_{AB} = Ed \\ E = \frac{V_{AB}}{d} \end{matrix}\} (uniform \end{matrix}$
where $d d size 12{d} {}$ 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
$E = - \frac{Δ V}{Δ s}, E =, size 12{E= - { {ΔV} over {Δs} } } {}$
where $Δ s Δ s size 12{Δs} {}$ is the distance over which the change in potential, $Δ V Δ V size 12{Δ`V} {}$ , takes place. The minus sign tells us that $E E size 12{E} {}$ 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.

Electric potential of a point charge is $V = kQ / r V = kQ / r size 12{V= ital "kQ"/r} {}$ .
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.

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.

A capacitor is a device used to store charge.
The amount of charge $Q Q size 12{Q} {}$ a capacitor can store depends on two major factors—the voltage applied and the capacitor’s physical characteristics, such as its size.
The capacitance $C C size 12{C} {}$ is the amount of charge stored per volt, or
$C = \frac{Q}{V} . C = \frac{Q}{V} . size 12{C=Q/V} {}$
The capacitance of a parallel plate capacitor is $C = ε_{0} \frac{A}{d} C = ε_{0} size 12{C=e rSub { size 8{0} } A/d} {}$ , 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
$C = {κε}_{0} \frac{A}{d}, C = {κε}_{0}, size 12{C=e rSub { size 8{0} } A/d} {}$
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.

Total capacitance in series $\frac{1}{C_{S}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} + . . . \frac{1}{C_{S}} = \frac{1}{C_{1}} + \frac{1}{C_{2}} + \frac{1}{C_{3}} + . . . size 12{ { {1} over { {C} rSub { size 8{S} } } } = { {1} over { {C} rSub { size 8{1} } } } + { {1} over { {C} rSub { size 8{2} } } } + { {1} over { {C} rSub { size 8{3} } } } + "." "." "." } {}$
Total capacitance in parallel $C_{p} = C_{1} + C_{2} + C_{3} + . . . C_{p} = C_{1} + C_{2} + C_{3} + . . . size 12{ {C} rSub { size 8{p} } = {C} rSub { size 8{1} } + {C} rSub { size 8{2} } + {C} rSub { size 8{3} } + "." "." "." } {}$
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.

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:
$E_{cap} = \frac{QV}{2} = \frac{{CV}^{2}}{2} = \frac{Q^{2}}{2 C}, E_{cap} = \frac{QV}{2} = \frac{{CV}^{2}}{2} = \frac{Q^{2}}{2 C}, size 12{E rSub { size 8{"cap"} } = { { ital "QV"} over {2} } = { { ital "CV" rSup { size 8{2} } } over {2} } = { {Q rSup { size 8{2} } } over {2C} } } {}$
where $Q Q size 12{Q} {}$ is the charge, $V V size 12{V} {}$ is the voltage, and $C C size 12{C} {}$ 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.