PROPERTIES AND USES OF THERMISTORS 187 



some unavoidable small resistance, such as that of the leads, in series with 

 the thermistor and hence the parts of the curves corresponding to low re- 

 sistances may not be observable. Also at high powers the temperature may 

 attain such values that something in the thermistor structure will go to 

 pieces thus limiting the range of observation. These unobservable ranges 

 have been indicated by dashed lines in Fig. 12. The exact location of the 

 dashed portions will of course depend on how a completed thermistor is con- 

 structed. In setting these limits consideration is given to temperature limi- 

 tations beyond which aging efifects might become too great. 



The curves in Figs. 9 to 12 have been computed on the basis of the follow- 

 ing equations: 



W = C(T - To) = VI (11) 



For these curves the constants Rq , To , B, and C are specified. The values 

 of temperature, T^ , power, W^ , resistance, R^. , voltage, F„ , and current, 

 Im , that prevail at the maximum in the voltage current curve are given 

 by the following equations in which T^ is chosen as the independent param- 

 eter. By differentiating equations (10) and (11) with respect to /, putting 

 the derivatives equal to zero, one obtains 



Tl = B{Tm - To) (12) 



whose solution is 



r„ = {B/2) (1 T Vl - 4To/B). (13) 



The minus sign pertains to the maximum in Figs. 10 to 12 while the plus 

 sign pertains to the minimum. Note that Tm depends only on B and To , 

 and not on R, Ro or C. From equations (4), (10) and (11) it follows that: 



- a^ {T^ - To) = 1 (14) 



\V„. = C{T„, - To) (15) 



i?,„ = Ro r^""'^" ^ Ro t-'iX - (r„ - To)/To + 



(1/2) {(n.- To)/ToV ] (16) 



F„ = [C Ro {Tm - To) {e-'-'^')]'" 



= \\C Ro (r„. - To) €-' [1 - {Tm - To)/ To 4- 



(1/2) \{Tm- To)/ToV- WV" (17) 



Jr. = [{C/Ro) {Tm - To) e'-'^^r- 



= {{{C/Ro) {Tm - To) e[\ + {Tm - To)/To + 



(1/2)1 (r.- To)/To}'+ ■■■ ]}V'' (18) 



