0195136047.pdf

1.1 ELECTRICAL QUANTITIES 11

v(x)=

dw(x)

dq

(1.1.13)

wherew(x)is the potential energy that a particle with chargeqhas when it is located at the
positionx. The zero point of potential energy can be chosen arbitrarily since only differences in
energy have practical meaning. The point where electric potential is zero is known as thereference
pointorground point, with respect to which potentials at other points are then described. The
potential differenceis known as thevoltageexpressed in volts (V) or joules per coulomb (J/C).
If the potential atBis higher than that atA,

vBA=vB−vA (1.1.14)

which is positive. Obviously voltages can be either positive or negative numbers, and it follows that

vBA=−vAB (1.1.15)

The voltage at pointA, designated asvA, is then the potential at pointAwith respect to the
ground.

Energy and Power

If a chargedqgives up energydwwhen going from pointato pointb, then the voltage across
those points is defined as

v=

dw

dq

(1.1.16)

Ifdw/dqis positive, pointais at the higher potential. The voltage between two points is the
work per unit positive charge required to move that charge between the two points. Ifdwanddq
have the same sign, then energy isdeliveredby a positive charge going fromatob(or a negative
charge going the other way). Conversely, charged particlesgainenergy inside asourcewheredw
anddqhave opposite polarities.
Theloadandsourceconventions are shown in Figure 1.1.3, in which pointais at a
higher potential than pointb. The loadreceivesorabsorbsenergy because a positive charge
goes in the direction of the current arrow from higher to lower potential. The source has
a capacity tosupplyenergy. Thevoltage sourceis sometimes known as anelectromotive
force,oremf, to convey the notation that it is a force that drives the current through the
circuit.
Theinstantaneous power pis defined as the rate of doing work or the rate of change of
energydw/dt,

p=

dw

dt

=

(

dw

dq

)(

dq

dt

)

=vi (1.1.17)

The electric power consumed or produced by a circuit element is given by its voltage–current
product, expressed in volt-amperes (VA) or watts (W). The energy over a time interval is found
by integrating power,

w=

∫T

0

pdt (1.1.18)

which is expressed in watt-seconds or joules (J), or commonly in electric utility bills in kilowatt-
hours (kWh). Note that 1 kWh equals 3. 6 × 106 J.