phy1020.DVI

• Nequal resistorsRconnected in series have an equivalent resistance ofNR.

For resistors connectedin parallel:

• The equivalent resistance will be smaller than the smallest resistance in the parallel combination.


• If one resistor in the parallel combination is much smaller than the others, the equivalent resistance will
  be approximately equal to the smallest resistance.


• Nequal resistorsRconnected in parallel have an equivalent resistance ofR=N.


• For the special case of justtworesistors in parallel, Eq. (20.9) becomes the product of the resistances
  divided by their sum:

RpD

R 1 R 2

R 1 CR 2

: (20.11)

It may sometimes be handy to use the notation

xjjy

xy

xCy

(20.12)

so that the equivalent resistance of two resistors in parallel isR 1 jjR 2 DR 1 R 2 =.R 1 CR 2 /.

20.3 Conductance

Related to the resistanceRand resistivity are the conductanceGand conductivity:

GD

1

R

I D

1

: (20.13)

Conductance is measured in units ofsiemens(S), named for German inventor Ernst Werner von Siemens. The
siemens is also sometimes called themho(Ã), which is “ohm” spelled backwards. Conductivity is measured
in units of S/m.
The relation between conductance and conductivity is found by taking the reciprocal of Eq. (20.1):

GD

A

L

: (20.14)

20.4 Wire

In computing the resistivity or conductivity of wire in Eqs. (20.1) and (20.14), you will need to know the
cross-sectional areaAof the wire. In the United States, wire is sold in standard diameters that are numbered
according to theAmerican Wire Gauge(AWG), as shown in Table 20-2. Wire used in laboratory work is
typically 20-gauge or 22-gauge copper wire.
By definition, AWG 0000 wire has a diameter of 0.46 inches, and AWG 36 wire has a diameter of 0.005
inches. This implies that AWGnwire has a diameterdof

dD0:005 92 .36n/=39 inches; (20.15)

wherenD 3 for AWG 0000,nD 2 for AWG 000, andnD 1 for AWG 00. This formula was used to
create Table 20-2. (Note that alargerAWG number corresponds to asmallerdiameter wire.)