High resistances above 10
10 Ohms are measured by various methods, such as
1) by observing, the rate of discharge of a sensitive electoroscope through the lesulater in .question.
2) by observing the deflection of a sensitive galvanometer caused by, the leakage current, and
3) by the method in which the insulator and a standard high resistance are potentiometrically combined and the potential difference at both ends of the insulator is amplified and measured by a valve voltmeter.
But the measurement becomes repidly uncertain with decreasing leakage. It is quite natural that a good insulator reveals an apparent, capacity caused by absorption or adhering of electric charge at a high potential, even if it has a very simple geometrical form as a cylindrical rod or a plate.
Therefore in the leakage measurement of a good insulator, it is essential to investigate the complex behavior of capacity and leakage of a good insulator at a high potential.
In the present work, a method of integration of the leakage current is employed considering
Cz and
Zc. (Cf. Fig. 1 (a))
2 Fortunately the network, with a restriction of initial conditions
(
i1)
0=
V/
Z and (
VC)
0=0, is transformed into an equivalent circuit (Cf. Fig. 1 (b)) and is simply analysed as
Vc=
V'{1-exp(-
t/
Z'
C')}.
where
V'=
ZcV/
Z+
Zc Z'=
ZZc/
Z+
Zc'
C'=
C+
Czand by expanding
Vc in a power series of
t we get
Z=
t/
p(
C+
Cz)
where
p is a parameter taken as the ratio of potentials
Vc/
V and
t the time of integration. Thus
Zc is elliminated.
Accordingly a new method of integration can easily be developed and
Z=10
14 Ohms is easily detected if we take
p=10
-3,
C=10
-9F and
t=10
2 sec. The limit of possibility of the measurement is estimated as 10
15 or 10
16 Ohms by inserting a galvanometer in place of μ A-meter in a self-recording valve voltmeter. (Cf. Fig. 8)
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