188 



BELL SYSTEM TECHNICAL JOURNAL 



Thus far the presentation has been limited to steady state conditions, in 

 which the power supplied to the thermistor is equal to the power dissipated 

 by it, and the temperature remains constant. In many cases, however, it 

 is important to consider transient conditions when the temperature, and 

 any quantities which are functions of temperature, var}^ with time. A 

 simple case which will illustrate the concepts and constants involved in 

 such problems is as follows: A massive thermistor is heated to about 150 to 

 200 degrees centigrade by operating it well beyond the peak of its voltage 



150 200 



TIME IN SECONDS 

 Fig. 13.— Cooling characteristic of a massive thermistor: log of temperature above 

 ambient versus time. 



current characteristic. At time / = 0, the circuit is switched over to a con- 

 stant current having a value so small that PR is always negligibly small. 

 The voltage across the thermistor is then followed as a function of time. 

 From this, the resistance and temperature are computed. Figure 13 shows i 

 a plot of log (r - Ta) versus / for a rod thermistor of Material No. 1 about 

 1.2 centimeters long, 0.30 centimeter in diameter and weighing 0.380 gram. 

 In any time interval Al, there are C(T - To) A/ joules being dissipated. | 

 .As a result the temperature will decrease by A7" given by 



-HAT = ar - Ta) A/ or (7' - 7'„) - -{H/C) (A7'/A/) iV)) 



