Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

(^240) Aptitude Test Problems in Physics
change in the resistance to its previous value, and
the process will be repeated. Therefore, current
oscillations caused by the jumpwise dependence
of the resistance on temperature will emerge in the
circuit.
During these oscillations, the temperature of
the resistor is nearly constant (it varies between
T2 = 99 °C and T 1 = 100 °C) so that we can
assume that the heat removal is constant, and the
removed power is a (T 1 — To). Then, by introduc-
ing the time t 1 of heating (from 99 °C to 100 °C),
the time t 2 of cooling, and the oscillation period
T = t 1 ft 2 , we can write the heat balance equa-
tions:

RP

I

(Ti — To) ti +C(Ti —T 2 ),

i

p a (T 1 — To) t 2 —C (Ti T2)•

II 2

Using the value of a obtained from Eq. (1), we

find that

C (Ti — T o)

ti= 1111Ri—U?(T1—T0)1[R1(T3-7' 3)1'

C (Ti -

1.2 - (I (T 1 — T 0 )/1/7 1 (To — To)j—UVR 2 •

Substituting the numerical values of the quanti-

ties, we obtain t 1 = t 2 = 3/32 s c_s_ 0.1 s and ,

T 0.2 s.

The maximum and minimum values of the

current can easily be determined since the resi-

stance abruptly changes from R 1 = 50 52 to R2 =

100 Q in the process of oscillations. Consequently,

/max=4=1.6A, /min =-- 11 /T = 0.8 A. 2 -

It should be noted that the situation described

in the problem corresponds to a first-order phase

transition in the material of the resistor. As a

result of heating, the material goes over to a new

(2)