Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Электрические машины и микромашины. Задачи. Учебное пособие
.pdf
ɥɟɥɶɧɨɣ
Q
Q
Q
ɤɨɣ)
ɆȾɋɬɚɤɨɣɨɛɦɨɬɤɢɟɟɧɚɡɵɜɚɸɬɫɬɚɛɢɥɢɡɢɪɭɸɳɟɣ ɨɛɦɨɬ-
ɫɨɫɬɚɜɥɹɟɬɞɨɆȾɋɩɚɪɚɥɥɟɥɶɧɨɣɨɛɦɨɬɤɢȾɟɥɚɟɬɫɹɷɬɨɞɥɹ
ɝɚɪɚɧɬɢɪɨɜɚɧɧɨɝɨ ɩɨɥɭɱɟɧɢɹ ɩɚɞɚɸɳɟɣ ɫɤɨɪɨɫɬɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɬɟɞɥɹɝɚɪɚɧɬɢɢɭɫɬɨɣɱɢɜɨɣɪɚɛɨɬɵɞɜɢɝɚɬɟɥɹ
1.9.1. Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ
ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
Ɉɞɧɢɦ ɢɡ ɨɫɧɨɜɧɵɯ ɞɨɫɬɨɢɧɫɬɜ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
ɹɜɥɹɟɬɫɹ
ɜɨɡɦɨɠɧɨɫɬɶ ɩɥɚɜɧɨɝɨ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ
ɜɲɢɪɨɤɢɯɩɪɟɞɟɥɚɯɂɡɮɨɪɦɭɥɵ
UIR R
n
ɚɚ ɚɪ
ɫɎ
ɟ
ɜɢɞɧɨɱɬɨɱɚɫɬɨɬɭɜɪɚɳɟɧɢɹɦɨɠɧɨɪɟɝɭɥɢɪɨɜɚɬɶɬɪɟɦɹɫɩɨɫɨɛɚɦɢ
ȼɤɥɸɱɟɧɢɟɦ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹRap.
ɂɡɦɟɧɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ Ɏ.
ɂɡɦɟɧɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹUɧɚ ɡɚɠɢɦɚɯ ɨɛɦɨɬɤɢ ɹɤɨɪɹ
Ɉɛɵɱɧ
ɨ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɩɪɢ
ɩɨɫɬɨɹɧɧɨɦɦɨɦɟɧɬɟɫɬɚɬɢɱɟɫɤɨɝɨɫɨɩɪɨɬɢɜɥɟɧɢɹ
Ɇɫɬ = const
Ⱦɜɢɝɚɬɟɥɢɩɚɪɚɥɥɟɥɶɧɨɝɨɧɟɡɚɜɢɫɢɦɨɝɨ
ɢɫɦɟɲ
ɚɧɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Q
Ɋɢɫɋɤɨɪɨɫɬɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ
ɩɚɪɚɥɥɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹɩɪɢ
5
5
5
,
ɧɨɦ
5DS
!
DS
!5
DS
!5
DS
,D
DS
DS
ɪɟɝɭɥɢɪɨɜɚɧɢɢɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹɜɤɥɸɱɟɧɢɟɦ
ɪɟɨɫɬɚɬɚɜɰɟɩɶɹɤɨɪɹ
Q
,ɜ,ɜ
,
ɧɨɦ
Ɋɢɫɋɤɨɪɨɫɬɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɞɜɢɝɚɬɟɥɹɩɚɪɚɥɥɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ
ɩɪɢɪɟɝɭɥɢɪɨɜɚɧɢɢ
ɱɚɫɬɨɬɵɜɪɚɳɟɧɢɢɩɭɬɟɦ
ɢɡɦɟɧɟɧɢɹɦɚɝɧɢɬɧɨɝɨ
ɩɨɬɨɤɚ
,ɤɡ
Q
Q
88
,D
,
ɧɨɦ
Ɋɢɫɋɤɨɪɨɫɬɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɞɜɢɝɚɬɟɥɹɩɚɪɚɥɥɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ
ɩɪɢɪɟɝɭɥɢɪɨɜɚɧɢɢ
ɱɚɫɬɨɬɵɜɪɚɳɟɧɢɢɩɭɬɟɦ
ɢɡɦɟɧɟɧɢɹɧɚɩɪɹɠɟɧɢɹ
ɧɚɡɚɠɢɦɚɯɹɤɨɪɹ
,D
Q
ȼɤɥɸɱɟɧɢɟ ɪɟɨɫɬɚɬɚ ɜ ɰɟɩɶ ɹɤɨɪɹ. ɗɬɨɬɫɩɨɫɨɛɩɨɡɜɨɥɹɟɬɪɟɝɭ
ɥɢɪɨɜɚɬɶɱɚɫɬɨɬɭɜɪɚɳɟɧɢɹ ɬɨɥɶɤɨ ɜɧɢɡ ɨɬɯɨɥɨɫɬɨɝɨ ɯɨɞɚɉɪɢ ɷɬɨɦ
Raɪ,
ɱɟɦɛɨɥɶɲɟɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɬɟɦɫɢɥɶɧɟɟɭɦɟɧɶɲɚɟɬɫɹɱɚɫɬɨɬɚɜɪɚ
ɳɟɧɢɹɪɢɫ
ɂɡɦɟɧɟɧɢɟ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ. Ⱦɥɹ ɢɡɦɟɧɟɧɢɹɦɚɝɧɢɬɧɨɝɨ ɩɨ
ɬɨɤɚɧɟɨɛɯɨɞɢɦɨ ɢɡɦɟɧɹɬɶ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹɉɪɢ ɷɬɨɦ ɠɟɫɬɤɨɫɬɶɫɤɨ
ɪɨɫɬɧɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɢɦɟɧɹɟɬɫɹɏɚɪɚɤɬɟɪɢɫɬɢɤɢɧɟɹɜɥɹɸɬɫɹɩɚɪɚɥ
ɥɟɥɶɧɵɦɢ ɪɢɫ ɋɩɨɫɨɛ ɩɨɡɜɨɥɹɟɬɪɟɝɭɥɢɪɨɜɚɬɶɱɚɫɬɨɬɭ ɜɪɚɳɟ
ɧɢɢɜɨɫɧɨɜɧɨɦɜɜɟɪɯɨɬɧɨɦɢɧɚɥɶɧɨɣ
ɂɡɦɟɧɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɡɚɠɢɦɚɯ ɹɤɨɪɹ.Ⱦɥɹɞɚɧɧɨɝɨɫɩɨɫɨɛɚ
ɬɪɟɛɭɟɬɫɹɫɩɟɰɢɚɥɶɧɚɹɭɫɬɚɧɨɜɤɚɩɨɡɜɨɥɹɸɳɚɹɢɡɦɟɧɹɬɶɧɚɩɪɹɠɟɧɢɟ
ɧɚɹɤɨɪɟɞɜɢɝɚɬɟɥɹɨɫɬɚɜɥɹɹɟɝɨɧɟɢɡɦɟɧɧɵɦɧɚɨɛɦɨɬɤɟɜɨɡɛɭɠɞɟɧɢɹ
Ɍɚɤɤɚɤɩɪɟɜɵɲɟɧɢɟɧɨɦɢɧɚɥɶɧɨɝɨɧɚɩɪɹɠɟɧɢɹɧɟɠɟɥɚɬɟɥɶɧɨɫɩɨɫɨɛ
ɩɪɢɦɟɧɹɟɬɫɹɞɥɹɪɟɝɭɥɢɪɨɜɚɧɢɹɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɜɧɢɡɨɬɧɨɦɢɧɚɥɶ
ɧɨɣɋɤɨɪɨɫɬɧɵɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɩɪɟɞɫɬɚɜɥɹɸɬɫɟɦɟɣɫɬɜɨɩɚɪɚɥɥɟɥɶ
ɧɵɯɩɪɹɦɵɯɪɢɫ
ɋɭɳɟɫɬɜɭɟɬɣ ɫɩɨɫɨɛ ±
ɋɭɬɶɟɝɨɡɚɤɥɸɱɚɟɬɫɹɜɬɨɦɱɬɨɱɚɫɬɨɬɭɜɪɚɳɟɧɢɹɞɜɢɝɚɬɟɥɹɪɟɝɭ
ɳɟɧɢɹ.
ɢɦɩɭɥɶɫɧɨɟ ɪɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ ɜɪɚ-
ɥɢɪɭɸɬɧɟɜɟɥɢɱɢɧɨɣɩɨɫɬɨɹɧɧɨɩɨɞɜɨɞɢɦɨɝɨɧɚɩɪɹɠɟɧɢɹɚɞɥɢɬɟɥɶɧɨ
ɫɬɶɸ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ ɧɨɦɢɧɚɥɶɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ Ƚɥɚɜɧɨɟ ɞɨɫɬɨɢɧ
ɫɬɜɨɫɩɨɫɨɛɚ±ɦɟɧɶɲɟɟɩɨɬɪɟɛɥɟɧɢɟɷɧɟɪɝɢɢɩɨɫɤɨɥɶɤɭɜɩɟɪɢɨɞɤɨɝɞɚ
ɷɥɟɤɬɪɨɧɧɵɣɤɥɸɱɡɚɤɪɵɬɩɨɬɪɟɛɥɹɟɦɵɣɬɨɤɪɚɜɟɧɧɭɥɸ
Q
Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹ
ɩɪɨɬɢɜɥɟɧɢɹ
ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ
ɠɟɤɚɤɢɜɞɜɢɝɚɬɟɥɟɩɚɪɚɥɥɟɥɶɧɨɝɨɧɟ
ɡɚɜɢɫɢɦɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
,
ɧɨɦ
,
ɧɨɦ
,D
ɜɤɥɸɱɟɧɢɟɦ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨ-
ɜ ɰɟɩɶɹɤɨɪɹ ɢ ɢɡɦɟɧɟɧɢɟɦ
ɜɵɩɨɥɧɹɟɬɫɹ ɬɚɤ
Ɋɟɝɭɥɢɪɨɜɚɧɢɟ ɱɚɫɬɨɬɵ ɜɪɚ
ɳɟɧɢɹ
ɢɡɦɟɧɟɧɢɟɦ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚɨɫɭ
Ɋɢɫɋɤɨɪɨɫɬɧɵɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ±ɩɪɢ
ɧɨɪɦɚɥɶɧɨɣɫɯɟɦɟɜɤɥɸɱɟɧɢɹ
±ɩɪɢɲɭɧɬɢɪɨɜɚɧɢɢ
ɨɛɦɨɬɤɢɜɨɡɛɭɠɞɟɧɢɹ±ɩɪɢ
ɲɭɧɬɢɪɨɜɚɧɢɢɨɛɦɨɬɤɢɹɤɨɪɹ
ɳɟɫɬɜɥɹɟɬɫɹɨɞɧɢɦɢɡɞɜɭɯɫɩɨɫɨɛɨɜɥɢɛɨ
ɲɭɧɬɢɪɨɜɚɧɢɟɦ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ
ɥɢɛɨɲɭɧɬɢɪɨɜɚɧɢɟɦɨɛɦɨɬɤɢɹɤɨɪɹ
ɉɪɢ ɲɭɧɬɢɪɨɜɚɧɢɢ ɨɛɦɨɬɤɢ ɜɨɡ
ɛɭɠɞɟɧɢɹ ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ ɭɦɟɧɶɲɚɟɬ
ɫɹ ȼ ɪɟɡɭɥɶɬɚɬɟ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɭɜɟ
ɥɢɱɢɜɚɟɬɫɹɪɢɫ
ɉɪɢɲɭɧɬɢɪɨɜɚɧɢɢɹɤɨɪɹɬɨɤɢɩɨɬɨɤɜɨɡɛɭɠɞɟɧɢɹɜɨɡɪɚɫɬɚɸɬ
Ⱦ
0
ȼ
ɋ
Ƚ
Ɇ
R
ɚ ɱɚɫɬɨɬɚɜɪɚɳɟɧɢɹ ɩɚɞɚɟɬ ɋɨɩɪɨɬɢɜɥɟɧɢɟ
ɧɚɯɨɞɢɬɫɹ ɩɪɚɤɬɢɱɟ
ɲ.ɚ
ɫɤɢ ɩɨɞ ɩɨɥɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ ɫɟɬɢ ɩɨɷɬɨɦɭ ɟɝɨ ɜɟɥɢɱɢɧɚ ɞɨɥɠɧɚ
ɛɵɬɶɡɧɚɱɢɬɟɥɶɧɨɣ
1.9.2. Ɍɨɪɦɨɡɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
Ɍɨɪɦɨɠɟɧɢɟ ɧɟɨɛɯɨ
ɞɢɦɨ ɜ ɬɟɯ ɫɥɭɱɚɹɯ ɤɨɝɞɚ
ɬɪɟɛɭɟɬɫɹ ɛɵɫɬɪɨ ɨɫɬɚɧɨɜɢɬɶ
ɪɚɛɨɱɢɣ ɦɟɯɚɧɢɡɦ ɢɥɢ ɪɟɡɤɨ
ɭɦɟɧɶɲɢɬɶɱɚɫɬɨɬɭɟɝɨ ɜɪɚɳɟ
ɧɢɹ Ɋɚɡɥɢɱɚɸɬ
(ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ)
ɬɨɪɦɨɠɟɧɢɟ
ɧɢɟɦ
ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟ
ɝɟɧɟɪɚɬɨɪɧɨɟ
ɬɨɪɦɨɠɟɧɢɟ
ɩɪɨɬɢɜɨɜɤɥɸɱɟ-
ɟɧɟɪɚɬɨɪɧɵɣ
ɪɟɠɢɦ
K
n1
n2
Q
n
0
D
Ⱥ
Ɇɫɬ
ɜɢɝɚɬɟɥɶɧɵɣ
ɪɟɠɢɦ
ɧɢɟ
Ɉɛɵɱɧɨɬɨɪɦɨɡɧɵɟɪɟ
ɠɢɦɵ ɪɚɫɫɦɚɬɪɢɜɚɸɬɩɪɢ ɩɨɫ
ɊɢɫɌɨɪɦɨɡɧɵɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɞɜɢɝɚɬɟɥɹɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɬɨɹɧɧɨɦ ɦɨɦɟɧɬɟɫɬɚɬɢɱɟɫɤɨɝɨ
ɫɨɩɪɨɬɢɜɥɟɧɢɹ
(Ɇɫɬ= const).
Ƚɟɧɟɪɚɬɨɪɧɨɟ ɪɟɤɭɩɟɪɚɬɢɜɧɨɟɬɨɪɦɨɠɟɧɢɟ ȿɫɥɢɞɜɢɝɚɬɟɥɶ
ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɪɚɫɤɪɭɬɢɬɶ ɞɨ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɜɵɲɟ
n
ɱɚɫɬɨɬɵ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ
ɗȾɋ ɦɚɲɢɧɵ ɫɬɚɧɟɬ ɛɨɥɶɲɟ
0
ɧɚɩɪɹɠɟɧɢɹɢɬɨɤɢɡɦɟɧɢɬɫɜɨɟɧɚɩɪɚɜɥɟɧɢɟ
UE UcnɎ
I
ɚ
ɚɟ
RR
ɚɚ
ɬɟ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɣɞɟɬ ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ ɫɨɡɞɚɫɬ ɬɨɪɦɨɡɧɨɣ
ɦɨɦɟɧɬ ɚ ɜɵɪɚɛɨɬɚɧɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɬɢɬɫɹ ɜ ɫɟɬɶ
Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɟɧɟɪɚɬɨɪɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɹɜɥɹɸɬɫɹ
ɩɪɨɞɨɥɠɟɧɢɟɦɯɚɪɚɤɬɟɪɢɫɬɢɤɞɜɢɝɚɬɟɥɶɧɨɝɨɪɟɠɢɦɚɜɨɛɥɚɫɬɶɨɬɪɢɰɚ
ɬɟɥɶɧɵɯɦɨɦɟɧɬɨɜɪɢɫɝɪɚɮɢɤ
Ⱦɜɢɝɚɬɟɥɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟ ɦɨɠɟɬ ɩɟɪɟɣɬɢ
ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ
ɢɛɨɫ ɭɜɟɥɢɱɟɧɢɟ ɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹ ɬɨɤ ɹɤɨ
ɪɹ ɪɚɜɧɵɣ ɬɨɤɭɜɨɡɛɭɠɞɟɧɢɹ ɭɦɟɧɶɲɚɟɬɫɹɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤɭɦɟɧɶ
ɲɚɟɬɫɹɢ
ɗȾɋɧɢɤɨɝɞɚɧɟɫɬɚɧɟɬɛɨɥɶɲɟɧɚɩɪɹɠɟɧɢɹɫɟɬɢȾɥɹɩɟɪɟɜɨ
ɞɚ ɬɚɤɨɝɨ ɞɜɢɝɚɬɟɥɹɜ ɪɟɠɢɦɝɟɧɟɪɚɬɨɪɚ ɟɝɨɩɪɟɜɪɚɳɚɸɬ ɜ ɞɜɢɝɚɬɟɥɶ
Ⱦ
ə
Ⱦ
ə
ɧɟɡɚɜɢɫɢɦɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɨ ɞɜɭɦ
ɫɯɟɦɚɦȼ ɩɟɪɜɨɦɫɥɭɱɚɟ ɜɰɟɩɶ ɹɤɨɪɹ ɜɜɨɞɹɬɞɨɩɨɥɧɢɬɟɥɶɧɨɟ ɫɨɩɪɨ
R
ɬɢɜɥɟɧɢɟ
ɢ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɫɨ ɡɧɚɱɟɧɢɹ
ɜɜɟɫɬɢɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɪɢɫɝɪɚɮɢɤɱɚɫɬɨɬɚɜɪɚɳɟɧɢɹɭɩɚɞɟɬɞɨɧɭɥɹȼɬɨɱɤɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɫɬɚɧɨɜɢɬɫɹ©ɦɹɝɱɟªɪɢɫɝɪɚɮɢɤ
ap1
n
ɫɧɢɠɚɟɬɫɹ ɞɨ ɡɧɚɱɟɧɢɹ n2 ȿɫɥɢ
1
R
ap2
> R
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɫɬɚɧɟɬ ɟɳɟ©ɦɹɝɱɟª
ap1
Dɞɜɢ
ɝɚɬɟɥɶɫɥɟɞɭɟɬɨɬɤɥɸɱɢɬɶɨɬɫɟɬɢ
ȼɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɦɟɧɹɸɬ ɩɨɥɹɪɧɨɫɬɶ ɢɫɬɨɱɧɢɤɚ ɧɚ ɤɥɟɦɦɚɯ
ɹɤɨɪɹ Ɍɨɤ ɦɟɧɹɟɬ ɫɜɨɣ ɡɧɚɤ ɪɟɡɤɨ ɭɜɟɥɢɱɢɜɚɟɬɫɹɦɚɲɢɧɚ ɧɚɱɢɧɚɟɬ
ɪɚɡɜɢɜɚɬɶɡɧɚɱɢɬɟɥɶɧɵɣ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬɬ ɋɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ
ɪɟɡɭɥɶɬɚɬɟɱɟɝɨ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɢɧɬɟɧɫɢɜɧɨ ɭɦɟɧɶɲɚɟɬɫɹɪɢɫ
ɝɪɚɮɢɤ Ⱦɥɹɨɝɪɚɧɢɱɟɧɢɹɛɪɨɫɤɚɬɨɤɚɜɰɟɩɶɹɤɨɪɹɜɜɨɞɹɬɞɨɛɚɜɨɱ
ɧɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟɉɪɢɞɨɫɬɢɠɟɧɢɢɬɨɱɤɢ
Ʉɞɜɢɝɚɬɟɥɶɨɬɤɥɸɱɚɸɬɨɬ
ɫɟɬɢɂɧɚɱɟɨɧɧɚɱɧɟɬɜɪɚɳɚɬɶɫɹɜɨɛɪɚɬɧɭɸɫɬɨɪɨɧɭɋɬɨɱɤɢɡɪɟɧɢɹ
ɛɵɫɬɪɨɬɵ ɨɫɬɚɧɨɜɚ ɞɚɧɧɵɣ ɫɩɨɫɨɛ ɹɜɥɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɷɮɮɟɤɬɢɜɧɵɦ
ȼɫɟɜɵɲɟ ɫɤɚɡɚɧɧɨɟɫɩɪɚɜɟɞɥɢɜɨ ɢɞɥɹ
ɜɨɡɛɭɠɞɟɧɢɹ
ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ
Ɉȼ
ɜɢɝɚɬɟɥɶ
ȿɚ,D
,ɚ
5ɞ
Ɍɨɪɦɨɡ
Ɋɢɫɋɯɟɦɚɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɬɨɪɦɨɠɟɧɢɹɞɜɢɝɚɬɟɥɹ
ɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Ɋɢɫɋɯɟɦɚɞɢɧɚɦɢɱɟɫɤɨɝɨ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
,ɚ
Ɉȼ
ȿɚ,D
ɜɢɝɚɬɟɥɶ
5ɞ
Ɍɨɪɦɨɡ
ɬɨɪɦɨɠɟɧɢɹɞɜɢɝɚɬɟɥɹ
Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɉɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ
R
ɨɛɦɨɬɤɭ ɹɤɨɪɹ ɨɬɤɥɸɱɚɸɬ ɨɬ ɫɟɬɢ ɢ ɡɚɦɵɤɚɸɬ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɞ
ɪɢɫɉɨɞ ɞɟɣɫɬɜɢɟɦɩɪɨɬɢɜɨɗȾɋɬɨɤɦɟɧɹɟɬɫɜɨɟɧɚɩɪɚɜ
ɥɟɧɢɟ
E
R
Ⱦ
ɚ
R
ȼ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɱɚ
ɦɚɲɢɧɚ
I
ɚ
ɚɞ
ɪɚɡɜɢɜɚɟɬ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬɬɨɱɤɚ
ɫɬɨɬɚɜɪɚɳɟɧɢɹɭɦɟɧɶɲɚɟɬɫɹɞɨɧɭɥɹɝɪɚɮɢɤɪɢɫ
Ⱦɥɹ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ
ɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ
ɨɞɧɨɜɪɟɦɟɧɧɨ ɫ ɩɨɞɤɥɸɱɟɧɢɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ Rɞ
ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶ-
ɪɢɫ ɫɥɟɞɭɟɬ ɩɨɦɟɧɹɬɶ ɡɚɠɢɦɵ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɱɬɨɛɵ
ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɢ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚɨɫɬɚɥɢɫɶ ɩɪɟɠɧɢɦɢɌɨɥɶɤɨ ɜ
ɷɬɨɦɫɥɭɱɚɟɦɚɲɢɧɚɛɭɞɟɬɪɚɡɜɢɜɚɬɶɬɨɪɦɨɡɧɨɣɦɨɦɟɧɬɂɛɨɟɫɥɢ
ɩɨɦɟɧɹɬɶɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɢɜɨɛɦɨɬɤɟɜɨɡɛɭɠɞɟɧɢɹɢɜ ɨɛɦɨɬɤɟɹɤɨ
ɪɹɧɚɩɪɚɜɥɟɧɢɟɦɨɦɟɧɬɚɧɟɢɡɦɟɧɢɬɫɹ
Ȼɟɫɤɨɧɬɚɤɬɧɵɟɞɜɢɝɚɬɟɥɢɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɨɛɵɱɧɨɝɨ ɢɫɩɨɥɧɟɧɢɹ ɢɦɟɸɬ ɰɟɧ
ɧɨɟ ɤɚɱɟɫɬɜɨ ± ɜɨɡɦɨɠɧɨɫɬɶ ɲɢɪɨɤɨ ɢ ɩɥɚɜɧɨ ɪɟɝɭɥɢɪɨɜɚɬɶ ɱɚɫɬɨɬɭ
ɜɪɚɳɟɧɢɹ ȼɦɟɫɬɟ ɫ ɬɟɦ ɨɧɢ ɨɛɥɚɞɚɸɬ ɫɭɳɟɫɬɜɟɧɧɵɦ ɧɟɞɨɫɬɚɬɤɨɦ
ɨɛɭɫɥɨɜɥɟɧɧɵɦ ɳɟɬɨɱɧɨɤɨɥɥɟɤɬɨɪɧɵɦ ɭɡɥɨɦ ɪɚɞɢɨɩɨɦɟɯɢ ɢɫɤɪɟ
ɧɢɟɢɬɞ
ɇɨ ɟɫɬɶɞɜɢɝɚɬɟɥɢ ɨɛɥɚɞɚɸɳɢɟɞɨɫɬɨɢɧɫɬɜɚɦɢ ɞɜɢɝɚɬɟɥɟɣ ɩɨ
ɫɬɨɹɧɧɨɝɨɬɨɤɚɢɫɜɨɛɨɞɧɵɟɨɬɢɯɧɟɞɨɫɬɚɬɤɨɜɌɚɤɢɟɞɜɢɝɚɬɟɥɢɧɚɡɵ
ɜɚɸɬɫɹ
ɪɢɫ ɡɚɦɟɧɹɟɬɫɹ ɩɨɥɭɩɪɨɜɨɞɧɢɤɨ
ɜɵɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ
ɪɨɦ ɭɩɪɚɜɥɹɟɦɵɦɫɢɝɧɚɥɚɦɢ
ɱɢɤɚ ɩɨɥɨɠɟɧɢɹ ɪɨɬɨɪɚ
ɦɟɯɚɧɢɱɟɫɤɢɣ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɶ
ɨɬɥɢɱɢɟɨɬɨɛɵɱɧɵɯɤɨɥɥɟɤɬɨɪɧɵɯɞɜɢɝɚ
ɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɢɦɟɟɬ ɧɟɩɨɞɜɢɠ
ɧɭɸ ɨɛɦɨɬɤɭ ɹɤɨɪɹ ɢ ɜɪɚɳɚɸɳɭɸɫɹ ɫɢ
ɫɬɟɦɭɜɨɡɛɭɠɞɟɧɢɹɨɛɵɱɧɨɜɜɢɞɟɩɨɫɬɨɹɧɧɨɝɨɦɚɝɧɢɬɚ
ɛɟɫɤɨɧɬɚɤɬɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚȻȾɉɌ
ɓɟɬɨɱɧɨɤɨɥɥɟɤɬɨɪɧɵɣ ɭɡɟɥɜ ɧɢɯ
ID
ɉɉ ± ɢɧɜɟɪɬɨ
f(D)ɨɬɞɚɬ
ȾɉɊ ɗɥɟɤɬɪɨ
ɗɆɉ ɜ
ɉɉ
Ɋɢɫɋɬɪɭɤɬɭɪɧɚɹ
ɗɆɉ
D
ɫɯɟɦɚȻȾɉɌ
ɉɊ
ɂɫɩɨɥɧɢɬɟɥɶɧɵɟɞɜɢɝɚɬɟɥɢɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ɂɫɩɨɥɧɢɬɟɥɶɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ (ɂȾ) ɧɚɡɵɜɚɸɬɫɹ ɷɥɟɤɬɪɨɦɟɯɚ
ɧɢɱɟɫɤɢɟɭɫɬɪɨɣɫɬɜɚ ɩɪɟɨɛɪɚɡɭɸɳɢɟɷɥɟɤɬɪɢɱɟɫɤɢɣɫɢɝɧɚɥɜɦɟɯɚɧɢ
ɱɟɫɤɨɟɜɪɚɳɟɧɢɟɜɚɥɚ
Ƚɥɚɜɧɵɟ ɬɪɟɛɨɜɚɧɢɹɩɪɟɞɴɹɜɥɹɟɦɵɟ ɤ ɢɫɩɨɥɧɢɬɟɥɶɧɵɦ ɞɜɢɝɚ
ɬɟɥɹɦ
ɨɬɫɭɬɫɬɜɢɟ ɫɚɦɨɯɨɞɚ – ɜɪɚɳɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɩɪɢ ɨɬɫɭɬɫɬɜɢɢ
x
ɫɢɝɧɚɥɚ ɭɩɪɚɜɥɟɧɢɹ;
x ɲɢɪɨɤɢɣ ɞɢɚɩɚɡɨɧ ɪɟɝɭɥɢɪɨɜɚɧɢɹ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ;
x ɭɫɬɨɣɱɢɜɨɫɬɶ ɪɚɛɨɬɵ ɜɨ ɜɫɟɦ ɞɢɚɩɚɡɨɧɟ ɭɝɥɨɜɵɯ ɫɤɨɪɨɫɬɟɣ;
x ɜɵɫɨɤɨɟ ɛɵɫɬɪɨɞɟɣɫɬɜɢɟ;
x ɦɚɤɫɢɦɚɥɶɧɚɹ ɥɢɧɟɣɧɨɫɬɶ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɪɟɝɭɥɢɪɨɜɨɱɧɵɯ ɯɚ-
ɪɚɤɬɟɪɢɫɬɢɤ.
ɋɭɳɟɫɬɜɭɟɬɞɜɚ ɫɩɨɫɨɛɚɭɩɪɚɜɥɟɧɢɹɢɫɩɨɥɧɢɬɟɥɶɧɵɦɢɞɜɢɝɚɬɟ
ɥɹɦɢɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ɹɤɨɪɧɨɟɪɢɫɢɩɨɥɸɫɧɨɟɪɢɫ
Ɏ
8
ɜ
ə
8
Ɋɢɫɋɯɟɦɚɜɤɥɸɱɟɧɢɹ
ɢɫɩɨɥɧɢɬɟɥɶɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɩɪɢ ɹɤɨɪɧɨɦ ɭɩɪɚɜɥɟɧɢɢ
ɜ
,
ɭ
ɭ
5ɞ
Ɋɢɫɋɯɟɦɚɜɤɥɸɱɟɧɢɹ
ɢɫɩɨɥɧɢɬɟɥɶɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɩɪɢ ɩɨɥɸɫɧɨɦ ɭɩɪɚɜɥɟɧɢɢ
əɤɨɪɧɨɟɭɩɪɚɜɥɟɧɢɟ
ɚɜɧɟɧɢɟ
ɍɪ
ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤm = f(Q)ɩɪɢD= const
ɪɢɫɚ
m
DQ
m ± ɨɬɧɨɫɢɬɟɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚD = Uɭ/U
ɝɞɟ
ɫɢɝɧɚɥɚ
Q±ɨɬɧɨɫɢɬɟɥɶɧɚɹɱɚɫɬɨɬɚɜɪɚɳɟɧɢɹ
ɍɪɚɜɧɟɧɢɟ
ɪɟɝɭɥɢɪɨɜɨɱɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤQ = f(D)ɩɪɢ
m = const ɪɢɫɛ
m
Ɇɟɯɚɧɢɱɟɫɤ
m
QQDQ
ɚɹ ɦɨɳɧɨɫɬɶ
ɪɢɫ
QD
ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ
8ɭ
Ɏ
ə
,
ɜ
8ɜ
± ɤɨɷɮɮɢɰɢɟɧɬ
ɜ
ɪ
ɦɯ
P
P
ɢɪɟɝɭɥɢɪɨɜɨɱɧɵɟɛɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɢɫɩɨɥɧɢɬɟɥɶɧɨɝɨɞɜɢɝɚɬɟɥɹɩɨɫɬɨɹɧɧɨɝɨ
D
ɚ ɛ
ɊɢɫɆɟɯɚɧɢɱɟɫɤɢɟɚ
ɬɨɤɚɩɪɢɹɤɨɪɧɨɦɭɩɪɚɜɥɟɧɢɢ
Q
Q
ɉɨɥɸɫɧɨɟɭɩɪɚɜɥɟɧɢɟ
ɍɪɚɜɧɟɧɢɟ
ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤm = f(Q)ɩɪɢD= const
ɪɢɫɚ
ɍɪɚɜɧɟɧɢɟ
ɪɟɝɭɥɢɪɨɜɨɱɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤQ = f(D)ɩɪɢ
m = constɪɢɫɛ
QD D
P
DDQ
m
ɪ
ɦɟɯ
D
ɊɢɫɁɚɜɢɫɢɦɨɫɬɶ
ɦɟɯɚɧɢɱɟɫɤɨɣɦɨɳɧɨɫɬɢ
ɨɬɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɩɪɢ
ɹɤɨɪɧɨɦɭɩɪɚɜɥɟɧɢɢ
D
D
Q
m
Ɇɟɯɚɧɢɱɟɫɤɚɹ ɦɨɳɧɨɫɬɶ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ
DQ D Q
ɪɢɫ
ɊɢɫɆɟɯɚɧɢɱɟɫɤɢɟɚɢɪɟɝɭɥɢɪɨɜɨɱɧɵɟ
ɛɯɚɪɚɤɬɟɪɢɫɬɢɤɢɢɫɩɨɥɧɢɬɟɥɶɧɨɝɨɞɜɢɝɚɬɟɥɹ
ɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚɩɪɢɩɨɥɸɫɧɨɦɭɩɪɚɜɥɟɧɢɢ
D
ɚ
Q
Q
ɛ
P
ɪ
ɦɟɯ
D
D
ɊɢɫɁɚɜɢɫɢɦɨɫɬɶ
ɦɟɯɚɧɢɱɟɫɤɨɣɦɨɳɧɨɫɬɢ
ɨɬɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɩɪɢ
ɩɨɥɸɫɧɨɦɭɩɪɚɜɥɟɧɢɢ
D
ɪ
ɦɯ
Q
ɍɧɢɜɟɪɫɚɥɶɧɵɟɤɨɥɥɟɤɬɨɪɧɵɟɞɜɢɝɚɬɟɥɢ
ə
a
D
ɪ
ɍɧɢɜɟɪɫɚɥɶɧɵɦɢ ɤɨɥɥɟɤɬɨɪɧɵɦɢ ɞɜɢɝɚɬɟɥɹɦɢ (ɍɄȾ ɧɚɡɵɜɚ
ɸɬɫɹɞɜɢɝɚɬɟɥɢɤɨɬɨɪɵɟɦɨɝɭɬɪɚɛɨɬɚɬɶɨɬɫɟɬɟɣɩɨɫɬɨɹɧɧɨɝɨɢɩɟɪɟ
ɦɟɧɧɨɝɨɬɨɤɚɪɢɫɗɬɢɞɜɢɝɚɬɟɥɢɧɚɯɨɞɹɬɲɢɪɨɤɨɟɩɪɢɦɟɧɟɧɢɟ
ɜɜɵɫɨɤɨɫɤɨɪɨɫɬɧɵɯ ɩɪɢɜɨɞɚɯ ɤɨɮɟɦɨɥɤɢɩɵɥɟɫɨɫɵ ɷɥɟɤɬɪɨɛɪɢɬɜɵ
ɢ ɬɩ ɬ ɤ ɩɨɡɜɨɥɹɸɬ ɩɪɢɩɢɬɚɧɢɢ ɨɬ ɫɟɬɢ Ƚɰɩɨɥɭɱɚɬɶ ɜɟɫɶɦɚ
ɡɧɚɱɢɬɟɥɶɧɵɟ ɭɝɥɨɜɵɟ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ ɞɨ ɨɛɦɢɧ ɱɟɝɨ
ɧɟɜɨɡɦɨɠɧɨɞɨɛɢɬɶɫɹ ɫ ɩɨɦɨɳɶɸɫɢɧɯɪɨɧɧɵɯ ɢ ɚɫɢɧɯɪɨɧɧɵɯɦɚɲɢɧ
ɩɪɢɱɚɫɬɨɬɟȽɰ
K
,D
FRVM
Q
Ɇ
ɗȾɋɜɪɚɳɟ
Ɋɢɫɋɯɟɦɚ
ɜɤɥɸɱɟɧɢɹɍɄȾ
ȿ
U,
DD
ɜ
Ɇ
ɊɢɫɊɚɛɨɱɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɍɄȾ
ɩɪɢɪɚɛɨɬɟɨɬɫɟɬɢɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ɩɪɢɪɚɛɨɬɟɨɬɫɟɬɢɩɟɪɟɦɟɧɧɨɝɨɬɨɤɚ
ɇɈɆ
Ɇ
ɇɈɆ
ȿɫɥɢ ɩɪɟɧɟɛɪɟɱɶ ɧɚɫɵɳɟɧɢɟɦ ɢ
ɨɬɟɪɹɦɢ ɜ ɫɬɚɥɢ ɭɱɟɫɬɶ
ɩ
ɧɢɹ ɜɵɪɚɡɢɬɶ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɱɟ
8
[,M
DD
,
M
Ɋɢɫȼɟɤɬɨɪɧɚɹ
ɞɢɚɝɪɚɦɦɚɍɄȾɩɪɢɪɚɛɨɬɟ
ɧɚɩɟɪɟɦɟɧɧɨɦɬɨɤɟ
ɪɟɡ ɬɨɤ ɢ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɟ ɚɤɬɢɜɧɵɟ ɢ
ɪɟɚɤɬɢɜɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɭɪɚɜɧɟɧɢɟ
ɧɚɩɪɹɠɟɧɢɹɦɨɠɧɨɩɪɢɜɟɫɬɢɤɜɢɞɭ
Ɏ
UEIrjIx
ɜɪ ɚ ɚ ɚ ɚ
ɝɞɟ raɢxa ± ɚɤɬɢɜɧɵɟ ɢ ɪɟɚɤɬɢɜɧɵɟ
ɫɨɩɪɨɬɢɜɥɟɧɢɹɹɤɨɪɧɨɣɰɟɩɢ
ɇɚɪɢɫ ɩɨɫɬɪɨɟɧɚɜɟɤɬɨɪɧɚɹ
ɞɢɚɝɪɚɦɦɚ
ɍɄȾɩɪɢɪɚɛɨɬɟɨɬɫɟɬɢɩɟɪɟɦɟɧɧɨɝɨɬɨɤɚ
Ɋɚɛɨɬɚ
ɍɄȾ ɨɬ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ ɧɢɱɟɦɧɟ ɨɬɥɢɱɚɟɬɫɹɨɬ
ɪɚɛɨɬɵ ɨɛɵɱɧɨɝɨ ɞɜɢɝɚɬɟɥɹ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɚ ɩɪɢ ɪɚɛɨɬɟ ɨɬ ɫɟɬɢ
ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɟɫɬɶ ɬɪɢ ɨɫɨɛɟɧɧɨɫɬɢ
1) ɩɭɥɶɫɚɰɢɹ ɜɪɚɳɚɸɳɟɝɨ
ɦɨɦɟɧɬɚ, 2) ɜɤɥɸɱɟɧɢɟ ɜ ɫɟɬɶ ɩɟɪɟɦɟɧɧɨɝɨ ɬɨɤɚ ɥɢɲɶ ɱɚɫɬɢ ɜɢɬɤɨɜ
ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, 3) ɯɭɞɲɢɟ ɭɫɥɨɜɢɹ ɤɨɦɦɭɬɚɰɢɢ.
Ɍɚɯɨɝɟɧɟɪɚɬɨɪɵɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ɍɚɯɨɝɟɧɟɪɚɬɨɪɚɦɢ (ɌȽ) ɧɚɡɵɜɚɸɬɫɹɷɥɟɤɬɪɢɱɟɫɤɢɟ ɦɚɲɢɧɵɧɟ
ɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ ɩɪɟɨɛɪɚɡɭɸɳɢɟ ɦɟɯɚɧɢɱɟɫɤɨɟ ɜɪɚɳɟɧɢɟ ɜ ɷɥɟɤ
ɬɪɢɱɟɫɤɢɣɫɢɝɧɚɥ
Ƚɥɚɜɧɨɟ ɬɪɟɛɨɜɚɧɢɟɩɪɟɞɴɹɜɥɹɟɦɨɟ ɤ ɬɚɯɨɝɟɧɟɪɚɬɨɪɚɦ ɡɚɤɥɸ
ɱɚɟɬɫɹ ɜ ɥɢɧɟɣɧɨɫɬɢ ɜɵɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ
ɡɚɜɢɫɢɦɨɫɬɢ ɦɟɠɞɭ ɜɵɯɨɞɧɵɦ ɧɚɩɪɹɠɟɧɢɟɦ
ɜɪɚɳɟɧɢɹ
n
Ukn
ɝɞɟk–ɤɨɷɮɮɢɰɢɟɧɬɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɫɬɢ
Ɉɫɧɨɜɧɨɟ ɧɚɡɧɚɱɟɧɢɟɬɚɯɨɝɟɧɟSɚɬɨSɨɜ ± ɢɡɦɟɪɟɧɢɟ ɱɚɫɬɨɬɵ
ɜɪɚɳɟɧɢɹɤɚɤɨɝɨɥɢɛɨɜɚɥɚ
Ɍɚɯɨɝɟɧɟɪɚɬɨɪɵ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚɩɨ ɤɨɧɫɬɪɭɤɰɢɢ ɢɩɪɢɧɰɢɩɭ
ɞɟɣɫɬɜɢɹ ɩɪɟɞɫɬɚɜɥɹɸɬ ɫɨɛɨɣɧɟɛɨɥɶɲɨɣ ɝɟɧɟɪɚɬɨɪɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ
ɜɫɟɝɞɚ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦɈɱɟɧɶ ɱɚɫɬɨɢɯ ɜɨɡɛɭɠɞɚɸɬ ɨɬ
ɩɨɫɬɨɹɧɧɵɯɦɚɝɧɢɬɨɜ
ȼ ɨɛɳɟɦ ɫɥɭɱɚɟ ɜɵɯɨɞɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɬɚɯɨɝɟɧɟɪɚɬɨɪɚ ɩɨ
ɫɬɨɹɧɧɨɝɨɬɨɤɚɢɦɟɟɬɜɢɞɪɢɫ
ɫɎnU
'
ɟɨ ɳ
U
ɫ knr
ɟɪɹ ɚɦ
ɫ
± ɩɨɫɬɨɹɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ
ɝɞɟ
ɟ
ɗȾɋ Ɏ
ɩɪɢ
ɨ
R
ɧ
±ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ ɜ
ɪɟɠɢɦɟɯɨɥɨɫɬɨɝɨɯɨɞɚ
ɜɪɚɳɟɧɢɹ
'
U
–ɩɚɞɟɧɢɟɧɚɩɪɹɠɟ
ɳ
ɧɢɹ ɜ ɳɟɬɨɱɧɨɦ ɤɨɧɬɚɤɬɟ
ɤɨɷɮɮɢɰɢɟɧɬ ɪɟɚɤɰɢɢ ɹɤɨɪɹ
n–ɱɚɫɬɨɬɚ
k
ɪɹ
r
ɫɨɩɪɨɬɢɜɥɟɧɢɟɫɨɛɫɬɜɟɧɧɨɨɛɦɨɬɤɢ
R
ɹɤɨɪɹ
±ɫɨɩɪɨɬɢɜɥɟɧɢɟɧɚɝɪɭɡ
ɧ
8
±
–
ɚɦ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɬɚɯɨɝɟɧɟɪɚɬɨɪɚ
ɤɢ
U ɢ ɭɝɥɨɜɨɣ ɫɤɨɪɨɫɬɶɸ
5ɧ
Ɋɢɫȼɵɯɨɞɧɵɟ
ɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ɂɨɧɚ
ɧɟɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ
5ɧ
5
ɧ
5ɧ
Q
ɉɨɝɪɟɲɧɨɫɬɢɬɚɯɨɝɟɧɟɪɚɬɨɪɚ
ɫɥɚɜɥɢɜɚɟɬɫɹ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɜ ɩɟɪɟɯɨɞɧɨɦ ɤɨɧɬɚɤɬɟ ɦɟɠɞɭ
ɳɟɬɤɨɣɢ ɤɨɥɥɟɤɬɨɪɨɦ
ɫɥɚɜɥɢɜɚɟɬɫɹɪɚɡɦɚɝɧɢɱɢɜɚɸɳɢɦ ɞɟɣɫɬɜɢɟɦ ɩɨɩɟɪɟɱɧɨɣɪɟɚɤɰɢɢ ɹɤɨ
Ɍɟɦɩɟɪɚɬɭɪɧɚɹ ɩɨɝɪɟɲɧɨɫɬɶ ɫɜɹɡɚɧɚɫɢɡɦɟɧɟɧɢɟɦɫɨɩɪɨɬɢɜɥɟɧɢɹ
ɪɹ
ɨɛɦɨɬɤɢɹɤɨɪɹɢ ɨɫɨɛɟɧɧɨ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɟɫɥɢɩɨɫɥɟɞɧɹɹɢɦɟ
ɟɬɫɹ ɉɪɢ ɭɜɟɥɢɱɟɧɢɢ ɬɟɦɩɟɪɚɬɭɪɵ ɦɟɞɢ ɧɚ ɋɟɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ
ɭɜɟɥɢɱɢɜɚɟɬɫɹ ɧɚ
ɜɟɧɫɬɜɨɜɵɯɨɞɧɵɯɧɚɩɪɹɠɟɧɢɣɩɪɢ ɜɪɚɳɟɧɢɢ ɹɤɨɪɹ ɫɨɞɧɨɣ ɢ ɬɨɣɠɟ
ɱɚɫɬɨɬɨɣ ɜ ɪɚɡɧɵɯɧɚɩɪɚɜɥɟɧɢɹɯ ȼɨɡɧɢɤɚɟɬ ɢɡɡɚɫɦɟɳɟɧɢɹ ɳɟɬɨɤɫ
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣ ɧɟɣɬɪɚɥɢ ɢ ɩɨɹɜɥɟɧɢɹ ɩɪɨɞɨɥɶɧɨɣ ɪɟɚɤɰɢɹ ɹɤɨɪɹ
ɤɨɬɨɪɚɹ ɧɨɫɢɬ ɧɚɦɚɝɧɢɱɢɜɚɸɳɢɣ ɯɚɪɚɤɬɟɪ ɩɪɢ ɨɞɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ
ɜɪɚɳɟɧɢɹ ɢ ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɢɣ ɩɪɢ ɞɪɭɝɨɦ
ɧɚɩɪɹɠɟɧɢɹ
ɩɨɫɬɨɹɧɧɨɝɨ
ɤɨɧɟɱɧɵɦɱɢɫɥɨɤɨɥɥɟɤɬɨɪɧɵɯɩɥɚɫɬɢɧɜɢɛɪɚɰɢɟɣɳɟɬɨɤ
ȼɨɩɪɨɫɵ
Ʉɚɤɨɜɚɪɨɥɶɤɨɥɥɟɤɬɨɪɚɜɦɚɲɢɧɟɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ"
Ʉɚɤɨɜɚɪɨɥɶɳɟɬɨɤɜɦɚɲɢɧɟɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ"
ɑɟɦ ɨɬɥɢɱɚɟɬɫɹ ɩɪɨɫɬɚɹ ɩɟɬɥɟɜɚɹ ɨɛɦɨɬɤɚ ɨɬ ɩɪɨɫɬɨɣ
ɜɨɥɧɨɜɨɣ"
Ʉɚɤ ɧɚ ɩɪɚɤɬɢɤɟ ɨɩɪɟɞɟɥɢɬɶ ɩɨɥɨɠɟɧɢɟ ɳɟɬɨɤ ɧɚ ɥɢɧɢɢ
ɝɟɨɦɟɬɪɢɱɟɫɤɨɣɧɟɣɬɪɚɥɢ"
ɑɬɨɧɚɡɵɜɚɟɬɫɹɪɟɚɤɰɢɟɣɹɤɨɪɹɦɚɲɢɧɵɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ"
Ɉɬ ɱɟɝɨɡɚɜɢɫɢɬ ɯɚɪɚɤɬɟɪɪɟɚɤɰɢɢ ɹɤɨɪɹɩɪɨɞɨɥɶɧɚɹ ɢɥɢ
ɩɨɩɟɪɟɱɧɚɹ"
Ʉɚɤɨɟɞɟɣɫɬɜɢɟɨɤɚɡɵɜɚɟɬɩɨɩɟɪɟɱɧɚɹɪɟɚɤɰɢɹɹɤɨɪɹ"
Ʉɨɝɞɚ ɩɪɨɹɜɥɹɟɬɫɹ ɢɫɤɚɠɚɸɳɟɟ ɚ ɤɨɝɞɚ ɪɚɡɦɚɝɧɢɱɢɜɚɸ
ɳɟɟɞɟɣɫɬɜɢɟɩɨɩɟɪɟɱɧɨɣɪɟɚɤɰɢɢɹɤɨɪɹ"
Ɉɬɱɟɝɨɡɚɜɢɫɢɬɜɟɥɢɱɢɧɚɪɟɚɤɰɢɢɹɤɨɪɹ"
Ʉɨɝɞɚ ɩɨɹɜɥɹɟɬɫɹ ɧɚɦɚɝɧɢɱɢɜɚɸɳɚɹ ɚ ɤɨɝɞɚ ɪɚɡɦɚɝɧɢɱɢ
ɜɚɸɳɚɹɩɪɨɞɨɥɶɧɚɹɪɟɚɤɰɢɹɹɤɨɪɹ"
ɉɨɱɟɦɭɩɪɨɢɫɯɨɞɢɬɤɨɦɦɭɬɚɰɢɹɬɨɤɚɜɨɛɦɨɬɤɚɯɹɤɨɪɹ"
Ɉɬɱɟɝɨɡɚɜɢɫɢɬɤɚɱɟɫɬɜɨɤɨɦɦɭɬɚɰɢɢ"
Ʉɚɤɨɟ ɜɧɟɲɧɟɟ ɦɚɝɧɢɬɧɨɟ ɩɨɥɟɩɪɢɫɭɬɫɬɜɭɟɬ ɜ ɡɨɧɟ ɤɨɦ
ɦɭɬɚɰɢɢ"
ɹɜɥɹɟɬɫɹ ɫɩɟɰɢɮɢɱɟɫɤɨɣ ɩɨɝɪɟɲɧɨɫɬɶɸ ɬɚɯɨɝɟɧɟɪɚɬɨɪɚ
ɬɨɤɚ Ɉɧɚ ɨɛɭɫɥɚɜɥɢɜɚɟɬɫɹ ɡɭɛɱɚɬɵɦ ɫɬɪɨɟɧɢɟ ɹɤɨɪɹ
. ɇɟɥɢɧɟɣɧɨɫɬɶ ɜɵɯɨɞɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɨɛɭ
Ⱥɫɢɦɦɟɬɪɢɹ ɜɵɯɨɞɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹɧɟɪɚ
Ɂɨɧɚ ɧɟɱɭɜɫɬɜɢɬɟɥɶɧɨɫɬɢ ɨɛɭ
ɉɭɥɶɫɚɰɢɹ ɜɵɯɨɞɧɨɝɨ
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]