0195136047.pdf

1.2 LUMPED-CIRCUIT ELEMENTS 19

TABLE 1.2.3Standard Available Values of Resistors

1.0 1.5 2.2 3.3 4.7 6.8
1.1 1.6 2.4 3.6 5.1 7.5
1.2 1.8 2.7 3.9 5.6 8.2
1.3 2.0 3.0 4.3 6.2 9.1

Seriesandparallelcombinations of resistors occur very often. Figure 1.2.2 illustrates these
combinations.
Figure 1.2.2(a) shows two resistorsR 1 andR 2 in series sharing the voltagevin direct
proportion to their values, while the same currentiflows through both of them,

v=vAC=vAB+vBC=iR 1 +iR 2 =i(R 1 +R 2 )=iReq

or, whenR 1 andR 2 are in series,

Req=R 1 +R 2 (1.2.6)
Figure 1.2.2(b) shows two resistors in parallel sharing the currentiin inverse proportion to
their values, while the same voltagevis applied across each of them. At nodeB,

i=i 1 +i 2 =

v

R 1

+

v

R 2

=v

(

1

R 1

+

1

R 2

)

=v/

(

R 1 R 2

R 1 +R 2

)

=

v

Req

or, whenR 1 andR 2 are in parallel,

Req=

R 1 R 2

R 1 +R 2

or

1

Req

=

1

R 1

+

1

R 2

or Geq=G 1 +G 2 (1.2.7)

Notice thevoltage divisionshown in Figure 1.2.2(a), and thecurrent divisionin Figure
1.2.2(b).

i

A

C

(a) (b)

B

+

−

v = vAC = vAB + vBC v

AD = vBC = v

vAB = iR 1

=

=

vR 1

R 1 + R 2

vBC = iR 2

R 1

R 2

A

D

B

C

+

−

i = i 1 + i 2

i 2 = v/R 2

= vG 2

i 1 = v/R 1

= vG 1

R 1 R 2

=

iG 2

G 1 + G 2

=

iG 1

G 1 + G 2

vR 2

R 1 + R 2

Figure 1.2.2Resistances in series and in parallel.(a)R 1 andR 2 in series.(b)R 1 andR 2 in parallel.

EXAMPLE 1.2.1

A no. 14 gauge copper wire, commonly used in extension cords, has a circular wire diameter of
64.1 mils, where 1 mil=0.001 inch.

(a) Determine the resistance of a 100-ft-long wire at 20°C.