phy1020.DVI

Multiplying both sides of Eq. (20.2) byL=A, we see the resistance changes with temperature by a similar
formula:

RDR 0 Œ1C ̨.TT 0 /: (20.3)

HereR 0 is the resistance at temperatureT 0 , andRis the resistance at temperatureT.
Forcopperwire, a convenient empirical equation is [7]

RDR 0

234:5CT

234:5CT 0

;.copper only/ (20.4)

whereTandT 0 are in degrees Celsius.
Eq. (20.3) suggests that it would be possible to use a resistor as a thermometer: by accurately measuring
the resistance of a resistor, one can infer the temperature. Solving Eq. (20.3) for the temperatureT,wefind

TDT 0 C

1

̨



R

R 0

 1



: (20.5)

In principle, this equation could be used to measure the temperature of a resistor by measuring its resistance.
Athermistoris a type of resistor specifically designed for this type of temperature measurement. How-
ever, Eq. (20.5) is not really adequate for accurate temperature measurement with a thermistor. Instead, one
uses a more accurate model called theSteinhart-Hart equation:

TD

1

aCblnRCc.lnR/^3

; (20.6)

wherea,b, andcare called theSteinhart-Hart parameters, and are provided by the thermistor manufacturer.

20.2 Resistors in Series and Parallel.

Several resistors connected end-to-end (in series) have an equivalent resistance equal to the sum of the indi-
vidual resistances:

RsD

X

i

Ri (20.7)

DR 1 CR 2 CR 3 C (20.8)

If they are connectedin parallel, the the equivalent resistance is the reciprocal of the sum of the reciprocals
of the individual resistances:

1

Rp

D

X

i

1

Ri

(20.9)

D

1

R 1

C

1

R 2

C

1

R 3

C (20.10)

A common error in computing parallel resistances is to compute sum of the reciprocals of the individual
resistances, then forget to take the reciprocal of the result at the end. Be careful not to do this!
Note the following points. For resistors connectedin series:

• The equivalent resistance will be bigger than the largest resistance in the series combination.


• If one resistor in the series combination is much larger than the others, the equivalent resistance will be
  approximately equal to the largest resistance.