596 
26 
The initial conditions are that q(0) = Q(0) = Q,, the initial charge 
produced. Therefore 
1 -t/RC ' +/RC 
q(t) = Q(t) — sre Q(r) e dr 
RC J 
where 7 is the variable of integration. The relative error is 
Oe) ight) 4 AQ) ng FG 
Q(t) Chas [13] 
Thus far the expression for the charge produced by the crystal has 
been an arbitrary function. Now two special forms for Q(t) will be considered. 
Case 1 Q(t) = Opielwitt (14) 
Case 2 Q(t) = Q,(1 = =) [15] 
where t, = RC is the time constant of the discharge. 
For what time ought the 
relative error to be calculated? 
It is seen that the error increases Relative brror 42 as a Function of ue 
with time. As a practical choice for Case 1 and Case 2 ¥ 
the comparison may be made for the 
time at which 
TABLE 3 
= 1 in Case-1 
and 
Rte 
t 3 in Case 2 
In both cases Q(t) is reduced to ap- 
proximately 1/3 of its original 
value. 
Table 3 is based on Equa- 
tion [13]. It gives the relative 
error 4Q/Q as a function of RC/t). 
The conclusion to be drawn 
in each of the two cases is substan- 
tially the same. If the error is not 
to exceed 10 per cent, the time con- 
stant should be 10 to 15 times as 
NO OW FWN — 
SO ONO ONO TO 1 
Sy 
ile 
0. 
0. 
0. 
0. 
0. 
0. 
0. 
0. 
0. 
