Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Элементы теории образования электрического тока в грунтовых и водных средах (проводниках второго рода). Монография
.pdf
ɫɤɢɯ ɱɚɫɬɢɰ ɡɚ ɨɛɭɫɥɨɜɥɟɧɧɭɸ ɜɟɤɬɨɪɨɦ ɉɨɣɧɬɢɧɝɚ (ɷɧɟɪɝɟɬɢɱɟɫɤɢɦ ɛɚɥɚɧɫɨɦ
Z
[6; 9].
)
ȼɵɹɜɥɟɧɧɚɹ, ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɢɡɦɟɧɹɸ
ɳɢɣɫɹ ɩɚɪɚɦɟɬɪ İȝ ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɭɪɨɜɧɹ ɩɪɢɥɨɠɟɧɧɨɣ ɗȾɋ ɜɵɩɪɹɦɥɟɧɧɨɝɨ
R
:
R
g
ɩɨɷɬɨɦɭ
,cos
ϕ=⋅
R
rZ
+
g
+
rZ
−+
R
ϕ==ϕ==
g
−
−
ɢɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
2
α−εμ
g
sin
εμ
Z
=
(78)
ɝɞɟ
Z –
ɥɨɦɥɟɧɢɹ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ; İȝ
ɰɚɟɦɨɫɬɢ
Ɏɚɪɚɞɟɹ
ɜɨɞɢɦɨɫɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɱɚɫɬɢɰ
2
sin
ɤɚɠɭɳɟɟɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ; Į, ij
; R –
; g –
ɨɦɢɱɟɫɤɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɜɢɠɭɳɢɯɫɹ ɩɪɨɬɢɜɨɩɨɥɹɪɧɨ ɱɚɫɬɢɰ
ɨɛɳɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ ɩɪɢ ɨɩɪɟɞɟɥɟɧɧɨɦ ɭɪɨɜɧɟ ɷɧɟɪɝɢɢ
Ʉɚɤ ɥɟɝɤɨ ɜɢɞɟɬɶ ɢɡ ɮɨɪɦɭɥɵ
Į
= 0
; g
–
–
(78),
–
ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɭɝɨɥ ɩɚɞɟɧɢɹ ɢ ɩɪɟ
–
ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɢ ɦɚɝɧɢɬɧɚɹ ɩɪɨɧɢ
; g
–
+
ɩɪɨɜɨɞɢɦɨɫɬɶ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɱɚɫɬɢɰ
ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ ɬɨɥɶɤɨ ɩɪɢ İȝ
= 1
ɩɪɨ
.
-
,cos;cos
-
-
-
ɢ
R
Z = (79)
,
g
ɩɪɢ ɷɬɨɦ ɭɫɥɨɜɢɢ ɧɚɛɥɸɞɚɟɬɫɹ ɭɫɬɨɣɱɢɜɨɟ ɪɚɜɧɨɜɟɫɢɟ, ɩɪɨɜɨɞɢɦɨɫɬɶ ɫɨɫɬɚɜɥɹɟɬ
:
R
g = (80)
.
2
P
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɯɨɪɨɲɨ ɢɡɜɟɫɬɧɚɹ ɮɨɪɦɭɥɚ
ɪɨɞɚ ɨɤɚɡɵɜɚɟɬɫɹ ɚɧɚɥɨɝɢɱɧɨɣ ɮɨɪɦɭɥɟ
,
ɬɨɥɶɤɨ ɜ ɢɞɟɚɥɶɧɨɦ ɫɥɭɱɚɟ
ɤɨɬɨɪɨɝɨ ɜ ɩɪɢɪɨɞɟ ɧɟ ɫɭɳɟɫɬɜɭɟɬ
g =
(80)
ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ
2
U
ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɜɬɨɪɨɝɨ ɪɨɞɚ
.
ɉɨɷɬɨɦɭ ɞɥɹ ɭɫɥɨɜɧɨ ɩɪɢɧɹɬɨɝɨ ɪɚɜɧɨɜɟɫɢɹ ɫ ɜɵɫɨɤɨɣ ɫɬɟɩɟɧɶɸ ɬɨɱɧɨɫɬɢ
ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɢɡɦɟɧɹɸɳɢɟɫɹ ɩɚɪɚɦɟɬɪɵ ɥɸɛɨɣ ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɨɣ ɫɢɫɬɟ
ɦɵ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɭɪɨɜɧɹ ɩɨɫɬɨɹɧɧɨɣ ɢ ɜɵɩɪɹɦɥɟɧɧɨɣ ɗȾɋ ɫ
.
ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɢɦ ɬɨɤɨɩɪɢɺɦɧɢɤɨɦ
ɉɨɫɤɨɥɶɤɭ, ɤɚɤ ɦɵ ɬɨɥɶɤɨ ɱɬɨ ɞɨɤɚɡɚɥɢ
-
,
141
Z
P
Z
ϕ−ϕ
ρ
U
İ
= ɫ/
=
R
ɫ
0
,
ɚ ɷɬɨ ɞɨɫɬɢɝɚɟɬɫɹ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ İȝ
22
, ȝ /
ȝ
,
ɢɞɟɚɥɶɧɵɟ ɩɚɪɚɦɟɬɪɵ ɫɬɚɧɨɜɹɬɫɹ ɪɚɜɧɵɦɢ ɩɪɢ
0
= 1, sin
2
Į
ɏ
= 0,
= X
L
ɩɪɢ ɷɬɨɦ
,
ɚɩɚɪɚ
C
-
ɦɟɬɪZɩɪɨɹɜɥɹɟɬ ɬɨɥɶɤɨ ɮɢɡɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ
(
ɢɡ ɡɚɤɨɧɚ Ɏɚɪɚɞɟɹ
ɜɵɞɟɥɟɧɧɨɝɨ ɤɨɥɢɱɟɫɬɜɚ ɦɚɬɟɪɢɚɥɶɧɵɯ ɱɚɫɬɢɰ
R.
Ɍɨɥɶɤɨ ɜ ɷɬɨɦ ɫɥɭɱɚɟ, ɢɫɯɨɞɹ
ɭɫɫɚ (ɫɜɹɡɚɧɧɨɝɨ ɫ ɜɟɥɢɱɢɧɨɣ ɩɨɬɨɤɚ ɧɚɩɪɹɠɟɧɧɨɫɬɢ, ɚɧɟɗȾɋ
ɧɹɬɶ Ɋ
ɜɬɨɪɨɝɨ ɪɨɞɚ
ɹɧɧɨɝɨ ɢɥɢ ɜɵɩɪɹɦɥɟɧɧɨɝɨ ɬɨɤɚ
= Ic·U.
w
Ɍɨɝɞɚ ɪɚɫɱɟɬɧɚɹ ɮɨɪɦɭɥɚ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ (ɜɩɪɨɜɨɞɧɢɤɚɯ
)
ɩɪɢ ɥɸɛɨɦ ɭɪɨɜɧɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɣ ɷɧɟɪɝɢɢ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨ
–
ɡɚɤɨɧɨɦɟɪɧɨɫɬɶ ȼ.ȼ. ɉɚɥɚɲɨɜɚ ɞɥɹ ɩɪɨɜɨɞ
ɧɢɤɨɜ ɜɬɨɪɨɝɨ ɪɨɞɚ
RU
I
c
ɝɞɟ
U –
ɢɡɦɟɪɹɟɦɨɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ
ɧɨɫɬɶ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ (ɜ ɨɬɥɢɱɢɟ ɨɬ
⋅
= (81)
,
2
; P
–
ɢɡɦɟɪɹɟɦɚɹ ɜɚɬɬɦɟɬɪɨɦ ɦɨɳ
w
Ɋ
= I+·U
ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ
U
); ;
=
ɪɨɞɚ
Z I
I
+
–
ɬɨɤ, ɢɡɦɟɪɹɟɦɵɣ ɚɦɩɟɪɦɟɬɪɨɦ (ɜɨɬɥɢɱɢɟɨɬ
+
),
ɩɨɬɨɤɚ Ƚɚ
),
ɦɨɠɧɨ ɩɪɢ
I
ɞɥɹ ɩɪɨɜɨɞ
c
-
-
-
-
-
-
ɧɢɤɨɜ ɜɬɨɪɨɝɨ ɪɨɞɚ
ɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ ɪɨɞɚ
). I
I
.
ɋɪɚɜɧɢɦ ɩɨɥɭɱɟɧɧɭɸ ɮɨɪɦɭɥɭ
U
=
R
I
++
′
=
(81)
E
;; –
′
+
B
21
=
′
RrR
ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɩɪɨ
ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɤɚ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨ
ɝɨ ɪɨɞɚ ɫ ɮɨɪɦɭɥɨɣ Ɉɦɚ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɤɚ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ. Ʌɟɝɤɨ
ɜɢɞɟɬɶ
: ,,,,, PPrRzRzrRRRR
=
+
ɢɨɧɢɡɚɰɢɢ
≠
′
),( RIfP
).
′
ɢɥɢ
′
≠
.),(
= IIrRfP
′
′
≠+
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɩɟɪɜɵɟ ɜ Ɋɨɫɫɢɢ ɢ ɡɚ ɪɭɛɟɠɨɦ ɩɨɥɭɱɟɧɧɵɟ ɮɨɪɦɭɥɵ
81)
ɹɜɥɹɸɬɫɹ ɨɫɧɨɜɨɩɨɥɚɝɚɸɳɢɦɢ ɞɥɹ ɪɚɫɱɟɬɚ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ, ɤɚɤ ɢ ɮɨɪ
ɦɭɥɵ Ɉɦɚ ɢ Ⱦɠɨɭɥɹ
–
Ʌɟɧɰɚ ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ ɪɨɞɚ
′
≠
≠+
cB
ɉɪɢ ɷɬɨɦ
+
≠+
wBB
ɩɨɫɤɨɥɶɤɭ
′
,(),,,(
=
),(
fP ε=
aw
fRslfR ε=
a
(78–
.
-
-
-
142
9.2. Ɉɬɥɢɱɢɬɟɥɶɧɵɟ ɨɫɨɛɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɩɪɨɜɨɞɢɦɨɫɬɢ ɜɟɳɟɫɬɜ
ɉɨ ɷɥɟɤɬɪɨɩɪɨɜɨɞɢɦɨɫɬɢ ɪɚɡɥɢɱɚɸɬ ɩɪɨɜɨɞɧɢɤɢ ɩɟɪɜɨɝɨ ɢ ɜɬɨɪɨɝɨ ɪɨɞɚ
ɗɥɟɤɬɪɨɩɪɨɜɨɞɧɨɫɬɶ ɞɢɷɥɟɤɬɪɢɤɨɜ, ɤɚɤ ɩɪɚɜɢɥɨ, ɪɚɫɫɦɚɬɪɢɜɚɟɬɫɹ ɨɬɞɟɥɶɧɨ, ɱɬɨ
,
ɩɪɢɜɨɞɢɬ ɢɧɨɝɞɚ ɤ ɧɟɩɨɧɢɦɚɧɢɸ ɩɪɨɰɟɫɫɨɜ
ɪɨɝɨ ɪɨɞɚ (ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ
!) [4].
ɩɪɨɢɫɯɨɞɹɳɢɯ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨ
ɉɪɨɜɨɞɧɢɤɢ ɩɟɪɜɨɝɨ ɪɨɞɚ ɨɛɥɚɞɚɸɬ ɷɥɟɤɬɪɨɧɧɨɣ ɩɪɨɜɨɞɢɦɨɫɬɶɸ, ɩɪɨɜɨɞ
ɧɢɤɢ ɜɬɨɪɨɝɨ ɪɨɞɚ
ɦɟɠɞɭ ɷɥɟɤɬɪɨɧɚɦɢ ɢ ɹɞɪɨɦ ɚɬɨɦɚ ɫɥɚɛɚɹ
ɜɨɡɞɟɣɫɬɜɢɟɦ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɩɨɥɹ
ɥɟɧɧɨɟ ɞɜɢɠɟɧɢɟ
ɬɪɨɥɢɬɢɱɟɫɤɨɣ ɞɢɫɫɨɰɢɚɰɢɢ (ɢɨɧɢɡɚɰɢɢ
ɫɤɨɝɨ ɩɨɥɹ
ȿ
ɫɬ
–
ɢɨɧɧɨɣ
[16].
ɩɪɨɜɨɞɢɦɨɫɬɶɸ. ȼ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ ɫɜɹɡɶ
,
ɩɨɷɬɨɦɭ ɫɜɨɛɨɞɧɵɟ ɷɥɟɤɬɪɨɧɵ ɩɨɞ
ȿ
ɩɪɢɧɢɦɚɸɬ ɧɚɩɪɚɜ
ȼ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ ɩɪɨɢɫɯɨɞɢɬ ɩɪɨɰɟɫɫ ɷɥɟɤ
),
ɩɨɷɬɨɦɭ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɫɬɚɬɢɱɟ
ɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɨɫɬɨɹɧɧɨɝɨȿɢɨɧɵ ɩɪɢɧɢɦɚɸɬ ɩɪɨɬɢɜɨɩɨɥɹɪ
ɧɨɟ ɞɜɢɠɟɧɢɟ: ɩɨɥɨɠɢɬɟɥɶɧɵɟ ɢɨɧɵ ɞɜɢɠɭɬɫɹ ɤ ɨɬɪɢɰɚɬɟɥɶɧɨɦɭ ɷɥɟɤɬɪɨɞɭ, ɚ
–
ɨɬɪɢɰɚɬɟɥɶɧɵɟ
ɤ ɩɨɥɨɠɢɬɟɥɶɧɨɦɭ. ȼ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ ɷɥɟɤɬɪɨɫɬɚ
.
-
-
-
-
-
-
-
ɬɢɱɟɫɤɨɟ ɩɨɥɟ ɨɬɫɭɬɫɬɜɭɟɬ ɩɨ ɨɩɪɟɞɟɥɟɧɢɸ
[4, 5].
ȼ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ ɜ
ɪɟɡɭɥɶɬɚɬɟ ɪɚɡɞɟɥɟɧɢɹ ɡɚɪɹɞɨɜ ɜɧɭɬɪɢ ɷɥɟɤɬɪɨɥɢɬɚ ɫɨɡɞɚɟɬɫɹ ɫɜɨɟ ɷɥɟɤɬɪɢɱɟ
ɫɤɨɟ ɩɨɥɟ
(
ȿ
ɫɬɨɪ
),
ɧɚɩɪɚɜɥɟɧɧɨɟ ɨɬ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɡɚɪɹɞɨɜ ɤ ɨɬɪɢɰɚɬɟɥɶɧɵɦ
.
ɉɪɨɜɨɞɧɢɤɢ ɩɟɪɜɨɝɨ ɪɨɞɚ ɨɛɥɚɞɚɸɬ ɩɨɥɨɠɢɬɟɥɶɧɵɦ ɬɟɦɩɟɪɚɬɭɪɧɵɦ ɤɨɷɮ
ɮɢɰɢɟɧɬɨɦ, ɚ ɩɪɨɜɨɞɧɢɤɢ ɜɬɨɪɨɝɨ ɪɨɞɚ, ɤɚɤ ɩɪɚɜɢɥɨ, ɨɬɪɢɰɚɬɟɥɶɧɵɦ
[33]. ɉɨ-
ɷɬɨɦɭ ɫ ɪɨɫɬɨɦ ɬɟɦɩɟɪɚɬɭɪɵ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɷɥɟɤɬɪɨɥɢɬɨɜ ɭɦɟɧɶɲɚɟɬɫɹ, ɚɫɨɩɪɨ
ɬɢɜɥɟɧɢɟ ɦɟɬɚɥɥɨɜ ɭɜɟɥɢɱɢɜɚɟɬɫɹ. Ɉɫɨɛɨ ɨɬɦɟɬɢɦ, ɱɬɨ ɩɪɢ ɪɟɝɭɥɢɪɨɜɚɧɢɢ ɧɚ
ɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɪɟɡɤɨ ɢɡɦɟɧɹɟɬɫɹ ɫɤɨɪɨɫɬɶ ɩɪɨɰɟɫɫɚ ɢɨɧɢɡɚ
ɰɢɢ, ɱɬɨ ɜ ɤɨɧɟɱɧɨɦ ɫɱɟɬɟ ɩɪɢɜɨɞɢɬ ɤ ɢɡɦɟɧɟɧɢɸ ɚɛɫɨɥɸɬɧɨɣ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɫɪɟɞɵ ɷɥɟɤɬɪɨɥɢɬɚ
ɦɨɠɟɬ ɩɨɥɧɨɫɬɶɸ ɨɬɫɭɬɫɬɜɨɜɚɬɶ
ɫɭɬɫɬɜɢɹ ɬɨɤɚ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ ɩɪɢ ɞɨɫɬɢɠɟɧɢɢ ɪɚɜɟɧɫɬɜɚ
(
İ
).
ɉɪɢ ɷɬɨɦ ɜ ɷɥɟɤɬɪɨɥɢɬɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟ
ɚ
(
ɷɮɮɟɤɬ ɫɜɟɪɯɩɪɨɜɨɞɢɦɨɫɬɢ ɦɟɬɚɥɥɨɜ ɢɥɢ ɨɬ
ȿ
=
ȿ
).
ɫɬɨɪ
ɂɫɤɥɸɱɢ
ɬɟɥɶɧɭɸ ɪɨɥɶ ɜ ɷɬɨɦ ɩɪɨɰɟɫɫɟ ɢɝɪɚɟɬ ɜɟɥɢɱɢɧɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ
-
-
-
-
-
-
-
İ
,
ɪɟɡɤɨ ɢɡɦɟɧɹɸɳɚɹɫɹ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɜɟɤɬɨɪɚ Ƚɚɭɫɫɚ
ɚ
143
.
9.3. Ɋɨɥɶ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ ɢ ɩɨɬɨɤɚ ɜɟɤɬɨɪɚ Ƚɚɭɫɫɚ
ɜ ɫɬɚɧɨɜɥɟɧɢɢ ɟɞɢɧɢɰ ɢɡɦɟɪɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ
Ɉɫɧɨɜɧɵɦ ɩɨɧɹɬɢɟɦ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɹɜɥɹɟɬɫɹ ɧɚɩɪɹɠɟɧɧɨɫɬɶ
,
ɩɨɧɹɬɢɟ ɢɫɯɨɞɢɬ ɢɡ ɡɚɤɨɧɚ Ʉɭɥɨɧɚ
ɞɜɭɯ ɬɨɱɟɱɧɵɯ ɡɚɪɹɞɨɜQɢ
q (Q –
ɤɨɬɨɪɵɣ ɫɜɹɡɵɜɚɟɬ ɫɢɥɵ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɡɚɪɹɞ, ɫɨɡɞɚɸɳɢɣ ɩɨɥɟ
ȿ
.
; q –
ɗɬɨ
F
ɩɪɨɛɧɵɣ ɩɨɥɨɠɢɬɟɥɶɧɵɣ ɡɚɪɹɞ) ɫ ɪɚɫɫɬɨɹɧɢɟɦrɦɟɠɞɭ ɡɚɪɹɞɚɦɢ ɢ ɚɛɫɨɥɸɬɧɨɣ
ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ ɫɪɟɞɵ
F = Q·q/4·
Ɍɨɝɞɚ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɩɨɥɹ
ȿ
=F/q = Q/4·ʌ·r
Ⱥ
ɉɚɪɚɦɟɬɪ
Q
ɜ ɡɚɤɨɧɟ Ʉɭɥɨɧɚ ɫɜɹɡɚɧ ɜ ɬɟɨɪɟɦɟ Ƚɚɭɫɫɚ ɫ ɩɨɬɨɤɨɦ ɜɟɤɬɨɪɚ
ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ
N = Q /
İ
,
ɝɞɟ ɫɨɡɞɚɟɬɫɹ ɫɢɥɨɜɨɟ ɩɨɥɟ
ɚ
2
ʌ
·r
·
İ
.
ɚ
:
:
2
·
İ
.
ɚ
(82)
:
İɚ.
(83)
ɉɪɢɧɹɬɢɟ ɜ ɤɚɱɟɫɬɜɟ ɢɫɯɨɞɧɨɝɨ ɩɨɥɨɠɟɧɢɹ, ɱɬɨ ɩɨɬɨɤ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɫɬɚ
-
ɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɟɫɬɶ ɜɟɤɬɨɪɧɚɹ ɜɟɥɢɱɢɧɚ, ɩɨɡɜɨɥɢɥɨ ɫɨɡɞɚɬɶ ɫɢɫɬɟɦɭ ɟɞɢɧɢɰ
.
ɢɡɦɟɪɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɢ ɦɚɝɧɢɬɧɵɯ ɜɟɥɢɱɢɧ
Ɍɚɤ, ɧɚɩɪɢɦɟɪ, ɜɟɥɢɱɢɧɚ ɩɨ
ɬɟɧɰɢɚɥɚ ɜ ɤɚɠɞɨɣ ɬɨɱɤɟ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɜɵɪɚɠɟɧɢɟɦ
ij
= Q / 4·ʌ·r·
A
İ0İ
.
ɚ
Ʉɚɠɞɚɹ ɬɨɱɤɚ ɩɨɥɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɷɧɟɪɝɢɟɣ, ɚ ɩɨɬɟɧɰɢɚɥɵ ɤɚɠɞɨɣ ɬɨɱɤɢ
ɢij
–
ij
A
ɱɟɫɤɨɝɨ ɩɨɥɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬ ɧɚɩɪɹɠɟɧɢɟ
ɷɧɟɪɝɢɟɣ
ɡɚɪɹɞɚ
ɫɤɚɥɹɪɧɵɟ ɜɟɥɢɱɢɧɵ. Ɍɨɝɞɚ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɞɜɭɯ ɬɨɱɟɤ ɷɥɟɤɬɪɢ
K
W
,
ɡɚɬɪɚɱɟɧɧɨɣ ɧɚ ɩɟɪɟɦɟɳɟɧɢɟ ɟɞɢɧɢɰɵ ɩɨɥɨɠɢɬɟɥɶɧɨɝɨ ɩɪɨɛɧɨɝɨ
ȺɄ
q
ɧɚ ɪɚɫɫɬɨɹɧɢɟlɦɟɠɞɭ ɷɬɢɦɢ ɬɨɱɤɚɦɢ
U
= WȺɄ/ q =
ȺɄ
ij
–
ij
Ⱥ
= Fl / q = ȿ·l. (84)
Ʉ
(U),
ɚ ɧɚɩɪɹɠɟɧɢɟ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ
:
ȼ ɷɬɨɦ ɜɵɪɚɠɟɧɢɢ ɡɚ ɟɞɢɧɢɰɭ ɧɚɩɪɹɠɟɧɧɨɫɬɢ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɥɹ ɩɪɢɧɹ
ɬɚ ɟɞɢɧɢɰɚ ɢɡɦɟɪɟɧɢɣ ɜɨɥɶɬ ɧɚ ɦɟɬɪ, ɬ.ɟ. ȼ·ɦ, ɬ.ɤ
.
-
-
-
ȿ
= UȺɄ/ l.
144
(84)
ɉɨɫɤɨɥɶɤɭ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɜ ɨɞɧɨɣ ɬɨɱɤɟ ɩɨɥɹ, ɤɚɤ ɛɵɥɨ ɨɬɦɟɱɟɧɨ ɜ ɮɨɪ
ɦɭɥɟ
(82),
ȿ
Ⱥ
= F/q,
ɬɨ ɡɚ ɟɞɢɧɢɰɭ ɢɡɦɟɪɟɧɢɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ
-
,
ɟɫɬɟɫɬɜɟɧɧɨ, ɩɪɢɧɹɬɚ Ʉɥ/ȼ·ɦ
ɦɨɫɬɶ ɜɚɤɭɭɦɚ
İ
= 109/36
0
ʌɎ/ɦ
= Ɏ/ɦ.
= 8,25·10
Ɉɩɪɟɞɟɥɟɧɚ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟ
12
Ɏ/ɦ ɢ ɹɜɥɹɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɨɫɬɨ
ɹɧɧɨɣ. Ⱦɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɨɫɬɨɹɧɧɭɸ ɥɸɛɨɣ ɫɪɟɞɵ ɜɵɪɚɠɚɸɬ ɱɟɪɟɡ ɷɥɟɤɬɪɢɱɟ
ɫɤɭɸ ɩɨɫɬɨɹɧɧɭɸ
ɱɢɧɭ, ɤɨɬɨɪɭɸ ɧɚɡɵɜɚɸɬ ɨɬɧɨɫɢɬɟɥɶɧɨɣ, ɩɨɫɤɨɥɶɤɭ
Ɍɚɛɥɢɱɧɚɹ ɜɟɥɢɱɢɧɚ
,
ɧɚɩɪɹɠɟɧɢɟ
ɞɢɷɥɟɤɬɪɢɤɚ
ɩɪɢ ɤɨɬɨɪɨɦ ɩɪɨɢɫɯɨɞɢɬ ɩɪɨɛɨɣ ɞɢɷɥɟɤɬɪɢɤɚ, ɫɜɹɡɚɧɨ ɫ ɬɨɥɳɢɧɨɣ
:
İ
ɢ ɞɢɷɥɟɤɬɪɢɱɟɫɤɭɸ ɩɪɨɧɢɰɚɟɦɨɫɬɶ
0
İ
ɫɜɹɡɚɧɚ ɫ ɩɪɨɛɢɜɧɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɞɢɷɥɟɤɬɪɢɤɚ, ɚ
r
ȿ
= Uɩɪ/l,
ɩɪ
ɤȼ/ɦɦ
. (85)
İ
–
r
İr= İɚ / İ
ɬɚɛɥɢɱɧɭɸ ɜɟɥɢ
, ɬ.ɟ.
0
İ
= İ
·
ɚ
İ
r
0
ɋɭɳɧɨɫɬɶ ɩɪɨɛɨɹ ɡɚɤɥɸɱɚɟɬɫɹ ɜ ɨɬɪɵɜɟ ɷɥɟɤɬɪɨɧɚ ɨɬ ɚɬɨɦɚ ɜ ɞɢɷɥɟɤɬɪɢɤɟ
ɉɪɨɢɫɯɨɞɢɬ ɬɚɤ ɧɚɡɵɜɚɟɦɚɹ ɢɨɧɢɡɚɰɢɹ ɞɢɷɥɟɤɬɪɢɤɚ (ɢɨɧɫɬɚɧɨɜɢɬɫɹɩɪɨɜɨɞ
ɧɢɤɨɦ
).
ɉɪɨɰɟɫɫɵ ɩɪɟɜɪɚɳɟɧɢɹ ɞɢɷɥɟɤɬɪɢɤɚ ɜ ɩɪɨɜɨɞɧɢɤ ɪɚɡɥɢɱɧɵɯ ɫɪɟɞ
-
-
-
-
.
.
-
(
ɬɜɟɪɞɵɯ, ɠɢɞɤɢɯ) ɨɬɥɢɱɚɸɬɫɹ ɦɟɠɞɭ ɫɨɛɨɣ, ɩɨɷɬɨɦɭ ɬɚɛɥɢɱɧɚɹ ɜɟɥɢɱɢɧɚ ɞɥɹ
ɪɚɡɥɢɱɧɵɯ ɫɪɟɞ ɧɟ ɦɨɠɟɬ ɪɚɫɤɪɵɬɶ ɯɚɪɚɤɬɟɪɚ ɢɡɦɟɧɟɧɢɹ ɥɸɛɨɣ ɫɪɟɞɵ ɢ ɹɜɥɹ
ɟɬɫɹ, ɩɨ ɫɭɳɟɫɬɜɭ, ɫɪɚɜɧɢɬɟɥɶɧɵɦ ɩɨɤɚɡɚɬɟɥɟɦ, ɨɩɪɟɞɟɥɹɸɳɢɦ, ɜɨ ɫɤɨɥɶɤɨ ɪɚɡ
ɚɛɫɨɥɸɬɧɚɹ ɞɢɷɥɟɤɬɪɢɱɟɫɤɚɹ ɩɪɨɧɢɰɚɟɦɨɫɬɶ
ɩɨɫɬɨɹɧɧɨɣ
İ
.
Ɉɞɧɚɤɨ ɛɟɡ ɭɱɟɬɚ ɯɚɪɚɤɬɟɪɚ ɢɡɦɟɧɟɧɢɹ ɫɪɟɞɵ (ɧɚɩɪɢɦɟɪ, ɫɤɨɪɨ
0
İ
ɫɪɟɞɵ ɛɨɥɶɲɟ ɷɥɟɤɬɪɢɱɟɫɤɨɣ
ɚ
ɫɬɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɨɞɧɨɝɨ ɜɢɞɚ ɷɧɟɪɝɢɢ ɜ ɞɪɭɝɢɟ) ɫɪɚɜɧɢɬɟɥɶɧɵɟ ɜɟɥɢɱɢɧɵ
.
ɹɜɥɹɸɬɫɹ ɧɟɫɨɢɡɦɟɪɢɦɵɦɢ
ɰɟɩɢ Ɉɦɚ ɩɨɞ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɨɣ ɧɭɠɧɨ ɩɨɧɢɦɚɬɶ ɫɢɥɭ
Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɜ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɡɚɦɤɧɭɬɨɣ
F/q = W
Ⱥ
ɚ ɧɟ ɗȾɋ ɢɫɬɨɱɧɢɤɚ. Ɉɬɫɸɞɚ ɫɥɟɞɭɟɬ, ɱɬɨ ɟɫɥɢ ɡɚɪɹɞ ɧɟ ɞɜɢɠɟɬɫɹ, ɬɨ ɷɧɟɪɝɢɸ
ɨɧ ɧɟ ɪɚɫɯɨɞɭɟɬ
ɨɛɪɚɡɭɹ ɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɨɩɪɟɞɟɥɟɧɧɨɣ ɧɚɩɪɹɠɟɧɧɨɫɬɢ
ȿ
ɫɬ
,
ȿɫɥɢ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ ɫɬɚɬɢɱɟɫɤɨɟ ɩɨɥɟ ɨɬɫɭɬɫɬɜɭɟɬ ɩɨ ɨɩɪɟɞɟɥɟ
ɧɢɸ, ɬɨ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ ɨɧɨ ɪɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɟɬ ɢ ɪɟɚɥɶɧɨ ɜɥɢɹɟɬ
-
-
,
.
-
ɧɚ ɩɪɨɰɟɫɫɵ
,
ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ. ȼ ɷɬɢɯ ɫɥɭɱɚɹɯ ɷɧɟɪɝɟɬɢɱɟɫɤɢɣ ɛɚ
145
-
ɥɚɧɫ(ɨɫɧɨɜɧɨɣ ɡɚɤɨɧ ɫɨɯɪɚɧɟɧɢɹ ɢ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ) ɦɨɠɟɬ ɛɵɬɶ ɭɞɨɜɥɟ
-
ɬɜɨɪɟɧ ɬɨɥɶɤɨ ɩɪɢ ɭɫɥɨɜɢɢ ɪɚɜɟɧɫɬɜɚ ɫɢɥ ɷɬɢɯ ɞɜɭɯ ɩɨɥɟɣ: ɫɬɚɬɢɱɟɫɤɨɝɨ ɢ ɫɬɚ
ɰɢɨɧɚɪɧɨɝɨ ɩɨɫɬɨɹɧɧɨɝɨ, ɜ ɨɬɥɢɱɢɟ ɨɬ ɩɟɪɟɦɟɧɧɨɝɨ ɤɜɚɡɢɫɬɚɰɢɨɧɚɪɧɨɝɨ
Ⱥɧɚɥɢɡɢɪɭɹ ɜɵɲɟɢɡɥɨɠɟɧɧɨɟ, ɡɚɦɟɬɢɦ
ɱɚɫɬɢɰɚɦ ɢ ɦɨɠɟɬ ɛɵɬɶ ɨɬɧɹɬɚ ɨɬ ɧɢɯ ɜ ɜɢɞɟ ɬɟɩɥɨɜɨɣ ɷɧɟɪɝɢɢ
ɛɵɬɶ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɬɨɤɚ ɛɟɡ ɧɟɤɨɬɨɪɨɝɨ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ
ɬɨɤɚ ɢɫɬɨɱɧɢɤ ɞɨɫɬɚɜɥɹɟɬ ɷɧɟɪɝɢɸ ɫɨ ɫɤɨɪɨɫɬɶɸ
ɪɹɞɨɜ/ɫ
ɰɟɩɢ
1Ⱦɠ/ɫ = ȼɬ.
ɱɢɫɥɨɦ ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚɪɹɞɨɜ
)·(Ⱦɠ/
,
ɹɜɥɹɟɬɫɹ ɟɞɢɧɢɰɟɣ ɢɡɦɟɪɟɧɢɹ ɦɨɳɧɨɫɬɢ ɢ ɧɚɡɵɜɚɟɬɫɹ ɜɚɬɬɨɦ ɢ ɪɚɜɧɚ
ɷɥɟɦ/.ɡɚɪɹɞ
) = Ⱦɠ/ɫ. 4.
ɋɤɨɪɨɫɬɶ, ɫ ɤɨɬɨɪɨɣ ɷɧɟɪɝɢɹ ɫɨɨɛɳɚɟɬɫɹ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɬɨɥɶɤɨ ɩɪɢ ɢɡɦɟɪɟɧɢɢ ɬɨɤɚ ɜ ɰɟɩɢ ɫ ɷɥɟɤɬɪɨɥɢɬɚɦɢ
,
ɩɪɟɞɫɬɚɜɥɹɸɳɢɯ ɫɨɛɨɣ ɫɭɦɦɭ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ
: 1.
ɗɧɟɪɝɢɹ ɩɟɪɟɞɚɟɬɫɹ ɡɚɪɹɠɟɧɧɵɦ
. 2.
. 3.
ɉɪɢ ɧɚɥɢɱɢɢ
I·E = (
ɱɢɫɥɨ ɷɥɟɦɟɧɬɚɪɧɵɯ ɡɚ
[8].
ɇɟ ɦɨɠɟɬ
ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɩɪɨɬɢɜɨɩɨɥɹɪɧɨ ɞɜɢɠɭɳɢɯɫɹ ɦɚɬɟɪɢɚɥɶɧɵɯ ɦɢɤɪɨɱɚɫɬɢɰ ɡɚ ɫɟ
ɤɭɧɞɭ, ɚɗȾɋɜȾɠ/ɷɥɟɦ. ɡɚɪɹɞ ɦɨɳɧɨɫɬɶ ɪɚɜɧɚ
ɝɢɟɣ ɩɨɬɨɤɚ Ƚɚɭɫɫɚ, ɜɟɥɢɱɢɧɚ ɤɨɬɨɪɨɣ
Ɋ
ɢ ɢɡɦɟɪɹɟɬɫɹ ɜɚɬɬɦɟɬɪɨɦ
W
I·E
ɢ ɦɨɠɟɬ ɛɵɬɶ ɧɚɡɜɚɧɚ ɷɧɟɪ
. 5.
ɉɨɫɤɨɥɶ
-
-
-
-
-
ɤɭ ɤɚɠɞɚɹ ɬɨɱɤɚ ɩɨɥɹ ɯɚɪɚɤɬɟɪɢɡɭɟɬɫɹ ɷɧɟɪɝɢɟɣ, ɚ ɪɚɡɧɨɫɬɶ ɩɨɬɟɧɰɢɚɥɨɜ ɞɜɭɯ
–
ɬɨɱɟɤ
ɫɭɳɧɨɫɬɢ ɫɬɚɬɢɱɟɫɤɨɝɨ ɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɨɥɟɣ
ɧɚɩɪɹɠɟɧɢɟɦ, ɨɱɟɜɢɞɧɨ,ɦɨɠɧɨ ɝɨɜɨɪɢɬɶ ɨ ɪɚɡɥɢɱɢɢ ɷɧɟɪɝɟɬɢɱɟɫɤɨɣ
.
ȼɫɬɚɬɢɱɟɫɤɨɦɩɨɥɟɷɧɟɪɝɢɹɩɟ
ɪɟɞɚɟɬɫɹ ɩɪɢ ɩɟɪɟɯɨɞɟ ɫ ɨɞɧɨɝɨ ɷɧɟɪɝɟɬɢɱɟɫɤɨɝɨ ɭɪɨɜɧɹ ɧɚ ɞɪɭɝɨɣ (ɦɢɤɪɨɢɡɦɟ
ɪɹɟɦɵɟ ɜɟɥɢɱɢɧɵ
ɩɪɨɜɨɞɧɢɤɚ ɤ ɞɪɭɝɨɣ ɩɨ ɞɥɢɧɟ ɩɪɨɜɨɞɧɢɤɚ
ɩɪɹɠɟɧɧɨɫɬɶ ɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɫɜɹɡɚɧɚ ɫ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɶɸ
ɚ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɫɬɚɰɢɨɧɚɪɧɨɝɨ
).
ȼ ɫɬɚɰɢɨɧɚɪɧɨɦ ɩɨɥɟ ɷɧɟɪɝɢɹ ɩɟɪɟɞɚɟɬɫɹ ɨɬ ɨɞɧɨɣ ɬɨɱɤɢ
(
ɦɚɤɪɨɢɡɦɟɪɹɟɦɵɟ ɜɟɥɢɱɢɧɵ
–
ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɢ ɫɤɨɪɨɫɬɶɸ ɢɨɧɢɡɚɰɢɢ. Ɍɚɤ
). ɇɚ-
İ
ɚ
ɱɬɨ ɜ ɰɟɩɹɯ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɫ ɷɥɟɤɬɪɨɥɢɬɚɦɢ ɢ ɪɚɫɬɜɨɪɚɦɢ ɪɚɫɫɱɢɬɚɬɶ ɷɧɟɪɝɟ
ɬɢɱɟɫɤɢɣ ɛɚɥɚɧɫ ɩɨ ɡɚɤɨɧɚɦ Ɉɦɚ
ɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ
.
(11)
ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ ɪɨɞɚ ɧɟ ɩɪɟɞ
-
-
,
-
-
146
9.4. Ɋɚɫɱɟɬ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɷɥɟɤɬɪɨɥɢɬɨɜ ɜ ɰɟɩɹɯ
ɩɨɫɬɨɹɧɧɨɝɨ (ɢɥɢ ɜɵɩɪɹɦɥɟɧɧɨɝɨ) ɬɨɤɚ
Ɉɫɧɨɜɧɵɦ ɡɚɤɨɧɨɦ ɞɥɹ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɜ ɰɟɩɹɯ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɹɜɥɹ
ɟɬɫɹ ɡɚɤɨɧ Ɉɦɚ
:
ϕ−ϕ
=
I
BA
I
R
′
E
=
+
rR
U
I
R
2
=⋅=
³
1
.;;; dSERI
(86)
S
Ʌɟɝɤɨ ɭɫɦɨɬɪɟɬɶ ɜɨ ɜɫɟɯ ɩɪɢɜɟɞɟɧɧɵɯ ɩɪɢɦɟɪɚɯ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɡɚɤɨɧɚ Ɉɦɚ
ɨɬɫɭɬɫɬɜɢɟ ɞɢɷɥɟɤɬɪɢɱɟɫɤɨɣ ɩɪɨɧɢɰɚɟɦɨɫɬɢ
İ
.
ɗɬɨ ɨɡɧɚɱɚɟɬ, ɱɬɨ ɡɚɤɨɧ Ɉɦɚ ɜ
ɚ
ɬɚɤɢɯ ɮɨɪɦɚɯ ɛɟɡ ɫɜɹɡɢ ɫ ɩɨɬɨɤɨɦ Ƚɚɭɫɫɚ ɢ ɡɚɤɨɧɚ Ʉɭɥɨɧɚ ɧɟ ɦɨɠɟɬ ɢɫɩɨɥɶɡɨ
ɜɚɬɶɫɹ ɞɥɹ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ
.
Ɋɚɫɫɦɚɬɪɢɜɚɹ ɢɡɜɟɫɬɧɵɟ ɫɯɟɦɵ ɡɚɦɟɳɟɧɢɹ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
Ʉ.Ɇ. ɉɨɥɢɜɚɧɨɜ ɩɨɤɚɡɚɥ
ɡɧɚɱɟɧɢɹ
U, I, P
ɨɬɧɨɫɢɬɟɥɶɧɨ ɜɧɟɲɧɟɣ ɰɟɩɢ ɬɨɥɶɤɨ ɬɨɝɞɚ, ɤɨɝɞɚ
ɧɚɩɨɦɧɢɦ, ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ Ʉɭɥɨɧɚ ɟɫɬɶ
[33],
ɱɬɨ ɜɫɟ ɭɪɚɜɧɟɧɢɹ ɷɬɢɯ ɫɯɟɦ ɞɚɸɬ ɨɞɢɧɚɤɨɜɵɟ
F/q, a q –
I = E/r,
ɟɞɢɧɢɱɧɵɣ ɩɨɥɨɠɢ
ɝɞɟ
ȿ
-
-
,
,
-
ɬɟɥɶɧɵɣ ɡɚɪɹɞ. ɉɪɢ ɷɬɨɦ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ ɞɜɢɠɭɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɨ
–
ɡɚɪɹɠɟɧɧɵɟ ɦɢɤɪɨɱɚɫɬɢɰɵ
ɦɨɫɬɶ. ȼɷɥɟɤɬɪɨɥɢɬɚɯ
–
ɢɨɧɧɚɹ ɩɪɨɜɨɞɢɦɨɫɬɶ: ɞɜɢɠɭɬɫɹ ɚɬɨɦɵ, ɝɪɭɩɩɵ ɚɬɨɦɨɜ
ɫ ɪɚɡɥɢɱɧɵɦɢ ɤɢɧɟɬɢɱɟɫɤɢɦɢ ɫɤɨɪɨɫɬɹɦɢ
ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ ɩɨɥɟɣ ɫɬɚɬɢɱɟɫɤɨɝɨ ɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ
,
ɷɥɟɤɬɪɨɥɢɬɚɯ
ɨɤɚɡɵɜɚɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɜɥɢɹɧɢɟ ɧɚ ɫɬɟɩɟɧɶ ɢɨɧɢɡɚɰɢɢ ɩɪɢ ɢɡ
ɦɟɧɟɧɢɢ ɜɟɥɢɱɢɧɵ ɜɧɟɲɧɟɝɨ ɩɨɥɹ
ɷɥɟɤɬɪɨɧɵ, ɬ. ɟ. ɜɨɡɧɢɤɚɟɬ ɷɥɟɤɬɪɨɧɧɚɹ ɩɪɨɜɨɞɢ
.
ɗɬɨ ɩɪɨɢɫɯɨɞɢɬ ɩɨɬɨɦɭ, ɱɬɨ ɩɪɨɰɟɫɫ
,
ɪɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɸɳɢɯ ɜ
.
Ⱥɜɬɨɪɭ ɧɚ ɛɚɡɟ ɜɵɹɜɥɟɧɧɵɯ ɡɚɤɨɧɨɦɟɪɧɨɫɬɟɣ ɭɞɚɥɨɫɶ ɪɚɡɪɚɛɨɬɚɬɶ ɪɚɫɱɟɬ
ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫ ɭɱɟɬɨɦ ɜɥɢɹɧɢɹ ɢɡɦɟɧɹɸɳɟɣɫɹ ɫɪɟɞɵ
ɇɚ ɪɢɫ
ɧɟɣɧɵɦ ɬɨɤɨɩɪɢɟɦɧɢɤɨɦ ɩɟɪɜɨɝɨ ɪɨɞɚ, ɚɧɚɪɢɫ
ɝɨ ɪɨɞɚ
. 30
ɩɪɟɞɫɬɚɜɥɟɧɚ ɫɯɟɦɚ ɢɡɦɟɪɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɫ ɥɢ
. 31 –
ɫ ɬɨɤɨɩɪɢɟɦɧɢɤɨɦ ɜɬɨɪɨ
.
İ
.
ɚ
-
-
-
-
147
Ɋɢɫ
IE
. 30.
ɋɯɟɦɚ ɢɡɦɟɪɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɩɟɪɜɨɝɨ ɪɨɞɚ
= .0dsE
S
³
Ʉɚɤ ɜɢɞɢɦ, ɜɫɯɟɦɟɪɢɫ
.
ɜɟɥɢɱɢɧɵ
ɷɥɟɤɬɪɨɧɨɜ
ȼɚɬɬɦɟɬɪ ɢɡɦɟɪɹɟɬ ɬɟɩɥɨɜɭɸ ɦɨɳɧɨɫɬɶ, ɩɨɥɭɱɟɧɧɭɸ ɨɬ ɞɜɢɠɭɳɢɯɫɹ
.
ȼɫɯɟɦɟɪɢɫ
ɬɨɪɧɵɟ ɜɟɥɢɱɢɧɵ. Ⱥɦɩɟɪɦɟɬɪ ɢɡɦɟɪɹɟɬ ɜɟɥɢɱɢɧɭ
. 31,
. 30
ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ ɢɡɦɟɪɹɸɬ ɫɤɚɥɹɪɧɵɟ
ɧɚɨɛɨɪɨɬ, ɚɦɩɟɪɦɟɬɪ ɢ ɜɨɥɶɬɦɟɬɪ ɢɡɦɟɪɹɸɬ ɜɟɤ
I
,
ɜɨɥɶɬɦɟɬɪ ɢɡɦɟɪɹɟɬ ɪɚɡ
+
ɧɨɫɬɶ ɩɚɞɟɧɢɣ ɧɚɩɪɹɠɟɧɢɣ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ
ɨɩɪɟɞɟɥɹɟɬ ɩɪɨɫɬɪɚɧɫɬɜɟɧɧɭɸ ɩɥɨɬɧɨɫɬɶ ɉ ɜɟɤɬɨɪɚ ɉɨɣɧɬɢɧɝɚ
IE
r
ɢ
r
.
+
,
ɩɨɞɟɥɟɧɧɨɝɨ ɧɚ
ȼɚɬɬɦɟɬɪ
–
-
-
Ɋɢɫ
. 31.
ɋɯɟɦɚ ɢɡɦɟɪɟɧɢɹ ɷɥɟɤɬɪɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɜ ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ
ɫɬɨɪ
³
S
≠ .0dsE
148
.
ɫ
2
, ɬ.
ɟ
. IC· E,
ɩɨɫɤɨɥɶɤɭ ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ (ɩɪɨɜɨɞɧɢɤɚɯ ɜɬɨɪɨɝɨ ɪɨɞɚ) ɷɥɟɤɬɪɨ
-
ɞɜɢɠɭɳɚɹ ɫɢɥɚ ɢɡɦɟɪɹɟɬɫɹ ɜ ɞɠɨɭɥɹɯ ɧɚ ɷɥɟɦɟɧɬɚɪɧɵɣ ɡɚɪɹɞ ɢ ɱɢɫɥɨɦ ɷɥɟɦɟɧ
ɬɚɪɧɵɯ ɡɚɪɹɞɨɜ, ɩɟɪɟɧɨɫɢɦɵɯ ɡɚ
ɱɬɨ ɬɵ ɢɡɦɟɪɹɟɲɶ
!»
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜɫɯɟɦɟɪɢɫ
ɡɧɚɱɧɨ ɨɩɪɟɞɟɥɹɸɬɫɹ ɩɨ ɨɫɧɨɜɧɨɦɭ ɡɚɤɨɧɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
= E/(R + r
I
+
ɫɯɟɦɟ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
ɨɬɦɟɱɟɧɨ
);
ij
–
ij
b
,
ɪɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɟɬ ɫɬɨɪɨɧɧɟɟ ɩɨɥɟ
A
= U
K
(
ɪɢɫ
ɷɥɟɤɬɪɨɥɢɬɢɱɟɫɤɨɟ ɪɚɜɧɨɜɟɫɢɟ ɦɨɠɟɬ ɧɚɫɬɭɩɢɬɶ
ɫɢɥ ɫɬɚɬɢɱɟɫɤɨɝɨ
ɫɬɨɪ
−= .dsEdsE
³³
SS
ɪɚɫɫɦɚɬɪɢɜɚɟɦɵɯ ɩɨɥɹɯ
ɢ ɫɬɚɰɢɨɧɚɪɧɨɝɨ ɩɨɥɟɣ, ɬ.ɟ
ɉɪɢ ɷɬɨɦ ɫɥɟɞɭɟɬ ɡɚɦɟɬɢɬɶ, ɱɬɨ ɩɪɨɰɟɫɫɵ, ɩɪɨɢɫɯɨɞɹɳɢɟ ɜ
,
ɪɟɡɤɨ ɨɬɥɢɱɚɸɬɫɹ, ɪɚɡɧɹɬɫɹ ɢ ɟɞɢɧɢɰɵ ɢɡɦɟɪɟɧɢɹ ɨɬ
. 30
;
1
. 31)
1
ɫɟɤɭɧɞɭ
. «
Ʌɟɝɤɨ ɢɡɦɟɪɹɬɶ, ɫɥɨɠɧɟɟ ɡɧɚɬɶ
ɷɧɟɪɝɟɬɢɱɟɫɤɢɟ ɩɚɪɚɦɟɬɪɵ ɷɥɟɦɟɧɬɨɜ ɨɞɧɨ
–
ɡɚɤɨɧɭ Ɉɦɚ
2
+++
2
11
2
11
³
=====
dsEUPgrUUIrIP
S
.0/;/
ɫ ɩɪɨɜɨɞɧɢɤɨɦ ɜɬɨɪɨɝɨ ɪɨɞɚ, ɤɚɤ ɜɵɲɟ ɛɵɥɨ
ɫɬɨɪ
dsE
S
³
ɬɨɥɶɤɨ ɩɪɢ ɭɫɥɨɜɢɢ ɪɚɜɟɧɫɬɜɚ
.
.0≠
ȼɷɬɢɯɭɫɥɨɜɢɹɯ
ɫɬɨɪ
= dsEdsE
³³
SS
ɢɥɢ
-
,
-
:
ȼ
ɦɢɤɪɨ
-
ɞɨ ɦɚɤɪɨɟɞɢɧɢɰ. ɉɨɷɬɨɦɭ ɡɚɤɨɧ Ɉɦɚ ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ ɪɨɞɚ ɢɫ
ɩɨɥɶɡɨɜɚɬɶ ɞɥɹ ɪɚɫɱɟɬɚ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɚɪɚɦɟɬɪɨɜ ɜ ɰɟɩɹɯ Ɉɦɚ ɫ ɷɥɟɤɬɪɨɥɢɬɚ
ɦɢ ɧɟ ɩɪɟɞɫɬɚɜɥɹɟɬɫɹ ɜɨɡɦɨɠɧɵɦ. Ɉɞɧɚɤɨ ɡɚɦɟɬɢɦ, ɜ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɷɥɟɤɬɪɨ
ɯɢɦɢɱɟɫɤɨɣ ɥɢɬɟɪɚɬɭɪɟ ɡɚɤɨɧ Ɉɦɚ ɮɨɪɦɭɥɢɪɭɟɬɫɹ ɢ ɞɥɹ ɠɢɞɤɨɫɬɟɣ ɜ ɜɢɞɟ
j = F/NA·Z+·n0+·(u++u–)E,
ɥɟɧɬɧɨɫɬɶ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢɨɧɨɜ ɜ ɟɞɢɧɢɰɟ ɨɛɴɟɦɚ ɷɥɟɤɬɪɨɥɢɬɚ
ɝɞɟ
F –
ɱɢɫɥɨ Ɏɚɪɚɞɟɹ
, N
–
ɱɢɫɥɨ Ⱥɜɨɝɚɞɪɨ
A
, u
ɢ
+
, Z
u
– ɜɚ-
+
–
–
[14]:
ɩɨɞ
ɜɢɠɧɨɫɬɶ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɩɨɥɨɠɢɬɟɥɶɧɵɯ ɢ ɨɬɪɢɰɚɬɟɥɶɧɵɯ ɢɨɧɨɜ. ɉɨ ɢɡɜɟɫɬ
ɧɵɦ ɩɪɢɱɢɧɚɦ ɷɬɨɬ ɡɚɤɨɧ ɧɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɜ ɩɪɨɦɵɲɥɟɧɧɨɣ ɷɥɟɤɬɪɨɬɟɯɧɢɤɟ
ɂɬɚɤ, ɚɦɩɟɪɦɟɬɪ
ɠɟɧɧɵɯ ɢɨɧɨɜ ɫɨɨɬɜɟɬɫɬɜɟɧɧɨ ɫɨɩɪɨɬɢɜɥɟɧɢɸ
ɷɧɟɪɝɢɢ ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɥɟɣ
ɧɨɫɬɶ ɩɚɞɟɧɢɣ ɧɚɩɪɹɠɟɧɢɣ (ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ
ɤɨɜ
I
ɢ
I
, ɬ.
ɟ
+
. I+ · r+ = I– · r– = U).
–
(pA)
ɮɢɤɫɢɪɭɟɬ ɬɨɤ
ɢɫɬɨɱɧɢɤɚ
I
ɞɜɢɠɭɳɢɯɫɹ ɩɨɥɨɠɢɬɟɥɶɧɨ ɡɚɪɹ
+
Z = r
I·E.
ȼɨɥɶɬɦɟɬɪ
r
+
ɢ ɡɚɬɪɚɱɟɧɧɨɣ ɫɢɫɬɟɦɨɣ
+
(pV)
ɢ
r
ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɯ ɢɦ ɬɨ
–
ɮɢɤɫɢɪɭɟɬ ɪɚɡ
.
-
-
-
-
-
-
-
-
149
ȼɚɬɬɦɟɬɪ
(
ɪ
W)
ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɩɪɢɧɹɬɵɦɢ ɟɞɢɧɢɰɚɦɢ ɢɡɦɟɪɟɧɢɹ, ɩɪɢɜɟ
ɞɟɧɧɵɦɢ ɜɵɲɟ, ɡɚɮɢɤɫɢɪɭɟɬ ɡɚɬɪɚɱɟɧɧɭɸ ɷɧɟɪɝɢɸ ɨɛɨɢɯ ɩɨɥɟɣ: ɫɬɚɬɢɱɟɫɤɨɝɨ ɢ
-
ɫɬɚɰɢɨɧɚɪɧɨɝɨ
ɧɢɢ ɧɟɥɶɡɹ ɫɦɟɲɢɜɚɬɶ ɮɢɡɢɱɟɫɤɭɸ ɫɭɬɶ ɫɥɚɝɚɟɦɵɯ ɷɧɟɪɝɢɣ
U –
I
+
ɷɧɟɪɝɢɹ ɜ ɮɨɪɦɟ ɪɚɛɨɬɵ
ɨɬɜɟɬɫɬɜɢɢ ɫ ɡɚɤɨɧɨɦ Ɉɦɚ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɞɥɹ ɩɪɨɜɨɞɧɢɤɨɜ ɩɟɪɜɨɝɨ ɪɨɞɚ
ɫɨɫɬɚɜɥɹɟɬ
ɱɟɧɧɚɹ ɢɫɬɨɱɧɢɤɨɦ ɧɚ ɩɪɟɨɛɪɚɡɨɜɚɧɢɟ ɫɪɟɞɵ
Ɋ
Ɋ
= I
W
2
· r
–
–
ɮɨɪɦɭɥɟ
ɟɬɫɹ
:
Ɋ
= I
W
, ɬ.
:
Ɋ
= I+ · U = I
+
– P+ = P
W
2
·R,
+
,
ɝɞɟ
r
ɟ
. I · E = PW = W
, I–U
2
· r+ = U2/r+; I
+
= I+ · U + Q,
AK
–
ɷɧɟɪɝɢɹ ɜ ɜɢɞɟ ɬɟɩɥɨɬɵ. ɗɬɚ ɷɧɟɪɝɢɹ ɜ ɫɨ
–
· U –
–
ɝɞɟ
ɷɧɟɪɝɢɹ ɜ ɮɨɪɦɟ ɬɟɩɥɨɬɵ, ɡɚɬɪɚ
İɚ,
ɢɥɢ
–
ɨɬɤɭɞɚ
ɤɨɧɬɪɨɥɢɪɭɟɬɫɹ ɢɡɦɟɧɹɸɳɟɣɫɹ ɫɪɟɞɨɣ
–
Ɋ
–
= I
2
–
· r
R=
;
Ɋ
–
ɢɡɦɟɪɹɟɬɫɹ ɜɚɬɬɦɟɬɪɨɦ ɢɥɢ ɨɩɪɟɞɟɥɹ
W
Ɋ
2+ .
/ I
W
Q = I– · U.
ȼɷɬɨɦɜɵɪɚɠɟ
I+ · UɢQ = I– · U;
(86)
ɦɨɠɟɬ ɛɵɬɶ ɨɩɪɟɞɟɥɟɧɚ ɩɨ
(87)
İ
ɢ ɨɩɪɟɞɟɥɹɟɬɫɹ ɬɟɩ
ɚ
ɥɨɜɨɣ ɷɧɟɪɝɢɟɣ, ɩɨɥɭɱɟɧɧɨɣ ɜ ɪɟɡɭɥɶɬɚɬɟ ɩɪɟɜɪɚɳɟɧɢɹ ɷɧɟɪɝɢɢ ɨɬ ɢɨɧɢɡɚɰɢɢ ɫɪɟ
ɞɵ (ɩɨɫɤɨɥɶɤɭ ɧɚɩɪɹɠɟɧɧɨɫɬɶ ɫɬɚɬɢɱɟɫɤɨɝɨ ɩɨɥɹ ɨɩɪɟɞɟɥɹɟɬɫɹ ɮɨɪɦɭɥɨɣ
(82).
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɜ ɷɥɟɤɬɪɨɥɢɬɚɯ ɩɨɞ ɜɨɡɞɟɣɫɬɜɢɟɦ ɢɫɬɨɱɧɢɤɚ ɩɨɫɬɨɹɧɧɨɣ
-
-
-
-
-
-
ɢɥɢ ɜɵɩɪɹɦɥɟɧɧɨɣ ɗȾɋ ɦɨɠɧɨ ɜɵɞɟɥɢɬɶ ɞɜɟ ɮɢɡɢɱɟɫɤɢɟ ɫɭɳɧɨɫɬɢ ɩɟɪɟɞɚɱɢ
ɷɧɟɪɝɢɢ ɬɨɤɨɩɪɢɟɦɧɢɤɭ
ɜɮɨɪɦɟɬɟɩɥɨɬɵ
[4; 16].
:
ɩɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ ɜ ɮɨɪɦɟ ɪɚɛɨɬɵ ɢ ɩɟɪɟɞɚɱɚ ɷɧɟɪɝɢɢ
ȼ ɫɥɭɱɚɟ ɦɚɤɪɨɫɤɨɩɢɱɟɫɤɨɝɨ ɬɟɥɚ ɩɪɢɪɚɳɟɧɢɟ ɤɢɧɟɬɢ
ɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɦɨɠɟɬ ɛɵɬɶ ɥɢɛɨ ɪɚɛɨɬɨɣ, ɥɢɛɨ ɬɟɩɥɨɬɨɣ. ȿɫɥɢ ɩɟɪɟɞɚɱɚ ɤɢɧɟ
ɬɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɩɪɨɢɫɯɨɞɢɬ ɜ ɦɚɤɪɨɧɚɩɪɚɜɥɟɧɧɨɣ ɮɨɪɦɟ, ɬɨ ɫɪɟɞɚ ɩɨɥɭɱɚɟɬ
(
ɷɧɟɪɝɢɸ ɜ ɜɢɞɟ ɪɚɛɨɬɵ
ɩɟɪɜɨɝɨ ɪɨɞɚ
Ɋ
= I+ · U).
+
ɜ ɧɚɲɟɦ ɫɥɭɱɚɟ ɧɚɩɪɚɜɥɟɧɧɨɟ ɞɜɢɠɟɧɢɟ ɜ ɩɪɨɜɨɞɧɢɤɚɯ
ȼ ɫɥɭɱɚɟ ɨɬɞɟɥɶɧɵɯ ɱɚɫɬɢɰ (ɧɚ ɦɢɤɪɨɭɪɨɜɧɟ) ɩɪɢɪɚɳɟɧɢɟ ɤɢɧɟɬɢɱɟɫɤɨɣ
ɷɧɟɪɝɢɢ ɜɫɟɝɞɚ ɹɜɥɹɟɬɫɹ ɬɟɩɥɨɬɨɣ
.
ȼ ɦɚɤɪɨɧɟɧɚɩɪɚɜɥɟɧɧɨɣ ɮɨɪɦɟ ɬɟɩɥɨɬɚ ɩɪɢ
ɩɟɪɟɯɨɞɟ ɱɚɫɬɢɰ ɫ ɨɞɧɨɝɨ ɭɪɨɜɧɹ ɧɚ ɞɪɭɝɨɣ ɫɜɹɡɚɧɚ ɫ ɧɚɩɪɹɠɟɧɧɨɫɬɶɸ ɫɬɚɬɢɱɟ
ɫɤɨɝɨ ɩɨɥɹ
ɉɨɫɤɨɥɶɤɭ ɩɚɪɚɦɟɬɪRɩɪɢ ɨɞɧɨɦ ɢ ɬɨɦ ɠɟ ɧɚɩɪɹɠɟɧɢɢ
ɬɟɪɢɡɭɟɬ ɩɨɥɧɭɸ ɷɧɟɪɝɢɸ
(
Ɋ
–
= I– · U).
(87)
U (
ɪɢɫ
. 30)
ɯɚɪɚɤ
ɜ ɪɚɫɫɦɚɬɪɢɜɚɟɦɨɣ ɫɢɫɬɟɦɟ, ɚɩɚɪɚɦɟɬɪ
r
–
–
-
-
-
-
150
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]