Добавил:
ivanov666
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Электрические машины и микромашины. Задачи. Учебное пособие
.pdf
ȿɫɥɢ
W
ɤ
ɟɪ = –ɟ
ɬɨɤɢɡɦɟɧɹɟɬɫɹɩɨ ɥɢɧɟɣɧɨɦɭɡɚɤɨɧɭɚɤɨɦɦɭɬɚ
ɤ
ɰɢɸ ɧɚɡɵɜɚɸɬɥɢɧɟɣɧɨɣ Ɉɧɚɹɜɥɹɟɬɫɹ ɧɚɢɛɨɥɟɟ ɛɥɚɝɨɩɪɢɹɬɧɨɣ ɢɫ
ɤɪɟɧɢɟɩɨɞɳɟɬɤɨɣɨɬɫɭɬɫɬɜɭɟɬ
ȿɫɥɢ
ɟɪ > ɟ
ɬɨɤ ɩɪɨɯɨɞɢɬ ɧɭɥɟɜɨɟ ɡɧɚɱɟɧɢɟ ɩɨɡɞɧɟɟ ɱɟɦ ɩɪɢ
ɤ
ɥɢɧɟɣɧɨɣ ɤɨɦɦɭɬɚɰɢɢ Ɍɚɤɭɸ ɤɨɦɦɭɬɚɰɢɸ ɧɚɡɵɜɚɸɬ ɡɚɦɟɞɥɟɧɧɨɣ
ɪɢɫ Ɉɧɚ ɹɜɥɹɟɬɫɹ ɧɚɢɦɟɧɟɟɛɥɚɝɨɩɪɢɹɬɧɨɣɬ ɤɩɨɞ ɫɛɟɝɚɸ
ɳɢɦɤɪɚɟɦɳɟɬɤɢɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɢɧɬɟɧɫɢɜɧɨɟɢɫɤɪɟɧɢɟ ɱɬɨ ɨɩɚɫ
ɧɨɞɥɹɦɚɲɢɧɵ
ɟɪ < ɟ
ȿɫɥɢ
ɬɨɤɩɪɨɯɨɞɢɬɧɭɥɟɜɨɟɡɧɚɱɟɧɢɟɪɚɧɶɲɟɱɟɦ ɩɪɢ
ɤ
ɥɢɧɟɣɧɨɣ ɤɨɦɦɭɬɚɰɢɢ Ɍɚɤɭɸ ɤɨɦɦɭɬɚɰɢɸ ɧɚɡɵɜɚɸɬ ɭɫɤɨɪɟɧɧɨɣ
ɪɢɫ Ɂɞɟɫɶ ɦɨɠɟɬ ɜɨɡɧɢɤɧɭɬɶ ɢɫɤɪɟɧɢɟ ɧɚ ɧɚɛɟɝɚɸɳɟɦ ɤɪɚɟ
ɳɟɬɤɢɈɞɧɚɤɨɷɬɨɧɟɨɫɨɛɟɧɧɨɨɩɚɫɧɨɬɤɳɟɬɤɚ ɧɚɛɟɝɚɹ ɧɚ ɢɫɤɪɵ
ɝɚɫɢɬɢɯ
,
W7
,D
ɊɢɫȽɪɚɮɢɤɢɡɦɟɧɟɧɢɹɬɨɤɚ
ɜɩɪɨɰɟɫɫɟɤɨɦɦɭɬɚɰɢɢ
ɊɢɫȽɪɚɮɢɤɢɬɨɤɚ
ɜɤɨɦɦɭɬɢɪɭɟɦɨɣɫɟɤɰɢɢ
±ɩɪɢɥɢɧɟɣɧɨɣɤɨɦɦɭɬɚɰɢɢ
±ɩɪɢɡɚɦɟɞɥɟɧɧɨɣɤɨɦɦɭɬɚɰɢɢ
±ɩɪɢɭɫɤɨɪɟɧɧɨɣɤɨɦɦɭɬɚɰɢɢ
7ɤ
Ⱦɥɹ ɭɥɭɱɲɟɧɢɹ ɤɨɦɦɭɬɚɰɢɢ ɜ ɦɚɲɢɧɚɯ ɦɨɳɧɨɫɬɶɸ ɛɨɥɟɟ
ɤȼɬ ɭɫɬɚɧɚɜɥɢɜɚɸɬ ɞɨɩɨɥɧɢɬɟɥɶɧɵɟ ɩɨɥɸɫɚ Ɉɧɢ ɫɨɡɞɚɸɬ ɜ ɡɨɧɟ
ɤɨɦɦɭɬɚɰɢɢɦɚɝɧɢɬɧɨɟɩɨɥɟɬɚɤɨɣɜɟɥɢɱɢɧɵɢɧɚɩɪɚɜɥɟɧɢɹɩɪɢɤɨɬɨ
ɪɨɦ ɜɤɨɦɦɭɬɢɪɭɸɳɟɣ ɫɟɤɰɢɢ ɢɧɞɭɰɢɪɭɟɬɫɹ
ɗȾɋ ɟɤ = –ɟ
Ɉɛɦɨɬɤɭ
ɪ
ɞɨɛɚɜɨɱɧɵɯ ɩɨɥɸɫɨɜ ɜɤɥɸɱɚɸɬ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɨɛɦɨɬɤɨɣ ɹɤɨɪɹ
ɟ
ɚɦɚɝɧɢɬɧɭɸɰɟɩɶɜɵɩɨɥɧɹɸɬɧɟɧɚɫɵɳɟɧɧɨɣȼɷɬɨɦɫɥɭɱɚɟ
ɨɤɚɡɵ
ɤ
ɜɚɟɬɫɹ ɩɪɨɩɨɪɰɢɨɧɚɥɶɧɨɣ ɬɨɤɭ ɹɤɨɪɹ ɱɬɨ ɨɛɟɫɩɟɱɢɜɚɟɬ ɚɜɬɨɦɚɬɢɱɟ
ɟ
ɢɟ
ɫɤɭɸɤɨɦɩɟɧɫɚɰɢɸ
.
ɤ
ɪ
ɍɪɚɜɧɟɧɢɹɧɚɩɪɹɠɟɧɢɹ
ȿ
ɢɭɪɚɜɧɟɧɢɹɦɨɦɟɧɬɨɜɦɚɲɢɧɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ƚɟɧɟɪɚɬɨɪɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚȼɭɫɬɚɧɨɜɢɜɲɟɦɫɹɪɟɠɢɦɟɭɪɚɜ
ɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹ
UE IR
ɚɚɚ
ɝɞɟ
ȿɚ – ɗȾɋɢɧɞɭɰɢɪɨɜɚɧɧɚɹɜɨɛɦɨɬɤɟɹɤɨɪɟɪɟɡɭɥɶɬɢɪɭɸɳɢɦ ɦɚɝ
R
ɧɢɬɧɵɦɩɨɥɟɦ ɝɟɧɟɪɚɬɨɪɚ
±ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢɤɨɬɨɪɨɟ
a
ɫɤɥɚɞɵɜɚɟɬɫɹɢɡɫɨɩɪɨɬɢɜɥɟɧɢɹɨɛɦɨɬɤɢɹɤɨɪɹɞɪɭɝɢɯɨɛɦɨɬɨɤɜɤɥɸ
ɱɟɧɧɵɯ ɜ ɟɝɨ ɰɟɩɶ ɧɚɩɪɢɦɟɪ ɨɛɦɨɬɤɢ ɞɨɛɚɜɨɱɧɵɯ ɩɨɥɸɫɨɜ ɩɟɪɟ
ɯɨɞɧɨɝɨɫɨɩɪɨɬɢɜɥɟɧɢɹɦɟɠɞɭɳɟɬɤɨɣɢɤɨɥɥɟɤɬɨɪɨɦ
ɗȾɋ
ɹɤɨɪɹɨɩɪɟɞɟɥɹɟɬɫɹɩɨɮɨɪɦɭɥɟ
ɫ nɎ
ɚɟ
ɝɞɟ
ɫɟ = pN/(60a)±ɩɨɫɬɨɹɧɧɵɣɤɨɷɮɮɢɰɢɟɧɬɨɩɪɟɞɟɥɹɟɦɵɣɢɫɤɥɸɱɢ
ɬɟɥɶɧɨɤɨɧɫɬɪɭɤɰɢɟɣɦɚɲɢɧɵ
ɍɪɚɜɧɟɧɢɟɦɨɦɟɧɬɨɜɧɚɜɚɥɭɝɟɧɟɪɚɬɨɪɚ
dȦ
ɆɆɆj,
r
ɩɞ ɨ ɚ
ɝɞɟ
Ɇ
±ɦɨɦɟɧɬɩɟɪɜɢɱɧɨɝɨɞɜɢɝɚɬɟɥɹɆ0±ɦɨɦɟɧɬɯɨɥɨɫɬɨɝɨɯɨɞɚ
ɩɞ
j ± ɦɨɦɟɧɬ ɢɧɟɪɰɢɢ ɜɪɚɳɚɸɳɢɯɫɹ ɱɚɫɬɟɣ Ɇ
dt
± ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ
ɚ
ɦɨɦɟɧɬɝɟɧɟɪɚɬɨɪɚ
ɫɦ = pN/(2Sa) ± ɩɨɫɬɨɹɧɧɵɣ ɤɨɷɮɮɢɰɢɟɧɬ ɡɚɜɢɫɹɳɢɣ ɬɨɥɶɤɨ ɨɬ
ɝɞɟ
McIɎ
a ɦ a
ɤɨɧɫɬɪɭɤɬɢɜɧɵɯɩɚɪɚɦɟɬɪɨɜɦɚɲɢɧɵ
Z
ȼɭɫɬɚɧɨɜɢɜɲɟɦɫɹɪɟɠɢɦɟ
= constɉɨɷɬɨɦɭ
ɆɆɆ
ɩɞ ɨ ɚ
Ⱦɜɢɝɚɬɟɥɶɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚȼɭɫɬɚɧɨɜɢɜɲɟɦɫɹɪɟɠɢɦɟɭɪɚɜ
ɧɟɧɢɟɧɚɩɪɹɠɟɧɢɹ
UE IR.
ɚɚɚ
ɍɪɚɜɧɟɧɢɟɦɨɦɟɧɬɨɜɧɚɜɚɥɭɞɜɢɝɚɬɟɥɹ
r r
ɆɆɆM ɆɆ j
ɚɨ j ɨ
ɝɞɟ
Ɇ
±ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣɜɪɚɳɚɸɳɢɣɦɨɦɟɧɬɨɛɭɫɥɨɜɥɟɧɧɵɣɜɡɚɢ
ɚ
dȦ
dt
ɦɨɞɟɣɫɬɜɢɟɦɬɨɤɚ ɹɤɨɪɹ ɫɪɟɡɭɥɶɬɢɪɭɸɳɢɦɦɚɝɧɢɬɧɵɦ ɩɨɬɨɤɨɦ ɪɚɫ
Ɇ
ɫɱɢɬɵɜɚɟɬɫɹɩɨɮɨɪɦɭɥɟ
ɦɵɣɞɥɹ ɩɨɤɪɵɬɢɹ ɦɟɯɚɧɢɱɟɫɤɢɯɩɨɬɟɪɶɢ ɩɨɬɟɪɶɜ ɫɬɚɥɢ ɹɤɨɪɹ
ɩɨɥɟɡɧɵɣ ɦɨɦɟɧɬ ɫɨ ɫɬɨɪɨɧɵ ɧɚɝɪɭɡɤɢ
±ɦɨɦɟɧɬɯɨɥɨɫɬɨɝɨɯɨɞɚɧɟɨɛɯɨɞɢ
ɨ
Ɇ
M
± ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ
j
2
ɜɨɡɧɢɤɚɸɳɢɣɩɪɢɢɡɦɟɧɟɧɢɢɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹ
±
ɋɭɦɦɭ
ɥɟɧɢɹ Ɇ
ɉɪɢ
Ɇ
ɢɆ2 ɧɚɡɵɜɚɸɬɦɨɦɟɧɬɨɦ ɫɬɚɬɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜ-
ɨ
ɫɬ
n = const ɦɨɦɟɧɬ Mj = 0Ɍɨɝɞɚ
ɆɆ
ɚɫɬ
ɉɨɫɥɟɞɧɟɟ ɪɚɜɟɧɫɬɜɨ ɬɪɭɞɧɨ ɧɚɡɜɚɬɶ ɭɪɚɜɧɟɧɢɟɦ ɨɞɧɚɤɨ ɨɧɨ
ɭɬɜɟɪɠɞɚɟɬ
ȼ ɭɫɬɚɧɨɜɢɜɲɟɦɫɹ ɪɟɠɢɦɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ,
ɪɚɡɜɢɜɚɟɦɵɣ ɞɜɢɝɚɬɟɥɟɦ, ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɦɨɦɟɧɬɨɦ ɫɬɚɬɢɱɟɫɤɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ
ɗɬɨɡɧɚɱɢɬ ɱɬɨ ɧɢɢɡɦɟɧɟɧɢɟɩɢɬɚɸɳɟɝɨɧɚɩɪɹɠɟɧɢɹɧɢɢɡɦɟ
ɧɟɧɢɟɫɨɩɪɨɬɢɜɥɟɧɢɹɹɤɨɪɧɨɣɰɟɩɢɧɢɱɬɨɞɪɭɝɨɟ ɧɟ ɦɨɠɟɬ ɢɡɦɟɧɢɬɶ
ɦɨɦɟɧɬɞɜɢɝɚɬɟɥɹɆɨɦɟɧɬɞɜɢɝɚɬɟɥɹɦɨɠɧɨɢɡɦɟɧɢɬɶɬɨɥɶɤɨɢɡɦɟɧɟ
ɧɢɟɦɧɚɝɪɭɡɤɢɧɚɟɝɨɜɚɥɭ
ɍɫɥɨɜɢɟɫɬɚɬɢɱɟɫɤɨɣɭɫɬɨɣɱɢɜɨɫɬɢ
Ⱦɥɹ
ɭɫɬɨɣɱɢɜɨɣɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɧɟɨɛɯɨɞɢɦɨɱɬɨɛɵ ɜɩɟɪɟ
ɯɨɞɧɵɟɪɟɠɢɦɵɜɵɩɨɥɧɹɥɨɫɶɭɫɥɨɜɢɟ
dM dM
ɫɬ ɚ
!
.
dn dn
ɗɬɨɦ
ɭɭɫɥɨɜɢɸɫɨɨɬɜɟɬɫɬɜɭɟɬɬɨɥɶɤɨɝɪɚɮɢɤɚ
Ⱦɟɣɫɬɜɢɬɟɥɶɧɨ ɟɫɥɢɩɪɨɢɡɨɣɞɟɬ ɫɥɭɱɚɣɧɨɟɭɦɟɧɶɲɟɧɢɟ ɱɚɫɬɨ
n ɞɨn
ɬɵɜɪɚɳɟɧɢɹɨɬ
x ɧɚ ɪɢɫ
ɩɪɨɬɢɜɥɟɧɢɹɧɚɜɚɥɭɩɨɹɜɢɬɫɹɩɨɥɨɠɢɬɟɥɶɧɵɣɞɢɧɚɦɢɱɟɫɤɢɣɦɨɦɟɧɬ
ɬɨ
1
ɚ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɫɬɚɧɟɬ ɛɨɥɶɲɟ ɦɨɦɟɧɬɚ ɫɨ
ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɝɨ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɱɧɟɬ ɭɜɟɥɢɱɢɜɚɬɶɫɹ ɞɨ
ɬɟɯɩɨɪɩɨɤɚɧɟɭɫɬɚɧɨɜɢɬɫɹɩɪɟɠɧɟɟɪɚɜɧɨɜɟɫɢɟɦɨɦɟɧɬɨɜ
x ɧɚ ɪɢɫ
ɛ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹɫɬɚɧɟɬ ɦɟɧɶɲɟ ɦɨɦɟɧɬɚɫɨ
ɩɪɨɬɢɜɥɟɧɢɹɧɚ ɜɚɥɭ ɩɨɹɜɢɬɫɹɨɬɪɢɰɚɬɟɥɶɧɵɣ ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ
ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɝɨ ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɧɚɱɧɟɬ ɩɪɨɝɪɟɫɫɢɜɧɨ
ɭɦɟɧɶɲɚɬɶɫɹɞɨɬɟɯɩɨɪɩɨɤɚɞɜɢɝɚɬɟɥɶɧɟɨɫɬɚɧɨɜɢɬɫɹɢɥɢɧɟ ɧɚɱɧɟɬ
ɜɪɚɳɚɬɶɫɹɜɨɛɪɚɬɧɭɸɫɬɨɪɨɧɭ
ɚ
Ⱥ
Ɇ
Ɇ
ɫɬ
ɚ
ɛ
Ɇɚ
Ⱥ
Ɇɫɬ
Q
QQ
ɊɢɫɄɜɨɩɪɨɫɭɭɫɬɨɣɱɢɜɨɣɚɢɧɟɭɫɬɨɣɱɢɜɨɣɛɪɚɛɨɬɵɞɜɢɝɚɬɟɥɹ
Q
Q
QQ
Q
ɉɪɢ ɫɥɭɱɚɣɧɨɦɭɜɟɥɢɱɟɧɢɢ ɱɚɫɬɨɬɵ ɜɪɚɳɟɧɢɹ ɨɬ nɞɨn2ɩɪɨ
ɰɟɫɫɩɨɣɞɟɬɜɨɛɪɚɬɧɨɦɧɚɩɪɚɜɥɟɧɢɢ
Ɍɚɤɢɦ ɨɛɪɚɡɨɦ ɞɥɹɭɫɬɨɣɱɢɜɨɣ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹɧɟɨɛɯɨɞɢɦɨ
ɱɬɨɛɵɩɪɢɭɦɟɧɶɲɟɧɢɢɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɧɚɜɟɥɢɱɢɧɭ
ɦɨɦɟɧɬɩɨɥɭɱɚɥ ɩɨɥɨɠɢɬɟɥɶɧɨɟ ɩɪɢɪɚɳɟɧɢɟ
-dM
ɦɟɧɬ±ɨɬɪɢɰɚɬɟɥɶɧɨɟ
ɢɧɚɨɛɨɪɨɬ
ɫɬ
dM
dnɜɪɚɳɚɸɳɢɣ
ɚ ɫɬɚɬɢɱɟɫɤɢɣɦɨ
ɚ
ɋɩɨɫɨɛɵɜɨɡɛɭɠɞɟɧɢɹɦɚɲɢɧɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ȼ ɡɚɜɢɫɢɦɨɫɬɢɨɬ ɫɩɨɫɨɛɚ ɫɨɟɞɢɧɟɧɢɹ ɨɛɦɨɬɤɢ ɝɥɚɜɧɵɯɩɨɥɸ
ɫɨɜ ɫ ɨɛɦɨɬɤɨɣ ɹɤɨɪɹ ɪɚɡɥɢɱɚɸɬ ɫɥɟɞɭɸɳɢɟ ɦɚɲɢɧɵ ɩɨɫɬɨɹɧɧɨɝɨ
ɬɨɤɚ
ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ± ɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹ ɩɨɥɭ
ɱɚɟɬɩɢɬɚɧɢɟɨɬɩɨɫɬɨɪɨɧɧɟɝɨɢɫɬɨɱɧɢɤɚɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ɫ ɩɚɪɚɥɥɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ±ɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹɟɟ
ɧɚɡɵɜɚɸɬ
ɟɟɧɚɡɵɜɚɸɬ
ɪɹ
ɛɭɠɞɟɧɢɹɩɨɫɥɟɞɨɜɚɬɟɥɶɧɚɹɢɩɚɪɚɥɥɟɥɶɧɚɹ
ɲɭɧɬɨɜɨɣɩɨɞɤɥɸɱɚɟɬɫɹɩɚɪɚɥɥɟɥɶɧɨɹɤɨɪɸ
ɫ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ±ɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹ
ɫɟɪɢɟɫɧɨɣɜɤɥɸɱɚɟɬɫɹɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɫɨɛɦɨɬɤɨɣɹɤɨ
ɫɨ ɫɦɟɲɚɧɧɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ±ɢɦɟɸɬɫɹɞɜɟɨɛɦɨɬɤɢɜɨɡ
ɋɦɟɲɚɧɧɨɟ ɜɨɡɛɭɠɞɟɧɢɟ ɦɨɠɟɬ ɛɵɬɶ
ɧɵɦ.
ȼɩɟɪɜɨɦ ɫɥɭɱɚɟ ɦɚɝɧɢɬɧɵɟɩɨɬɨɤɢ ɫɨɡɞɚɧɧɵɟ ɩɚɪɚɥɥɟɥɶɧɨɣɢ
ɫɨɝɥɚɫɧɵɦɢɥɢɜɫɬɪɟɱ-
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣ ɨɛɦɨɬɤɚɦɢ ɫɨɜɩɚɞɚɸɬ ɜɨ ɜɬɨɪɨɦ ɫɥɭɱɚɟ ɨɧɢ
ɧɚɩɪɚɜɥɟɧɵɜɫɬɪɟɱɧɨ
Ʉɪɨɦɟɩɟɪɜɨɝɨɨɫɬɚɥɶɧɵɟɝɟɧɟɪɚɬɨɪɵɨɬɧɨɫɹɬɫɹɤ
ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ.
ɝɟɧɟɪɚɬɨɪɚɦ
ɋɚɦɨɜɨɡɛɭɠɞɟɧɢɟɝɟɧɟɪɚɬɨɪɨɜɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ⱦɥɹɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɝɟɧɟɪɚɬɨɪɨɜ ɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ ɧɟɨɛɯɨɞɢ
ɦɵɫɥɟɞɭɸɳɢɟɭɫɥɨɜɢɹ
ɇɚɥɢɱɢɟ ɨɫɬɚɬɨɱɧɨɝɨ ɦɚɝɧɢɬɧɨɝɨ ɩɨɬɨɤɚ
ȿɫɥɢ ɟɝɨ
ɧɟɬ, ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ ɫɥɟɞɭɟɬ ɩɨɞɤɥɸɱɢɬɶ ɧɚ ɤɨɪɨɬɤɨɟ ɜɪɟɦɹ
ɤ ɩɨɫɬɨɪɨɧɧɟɦɭ ɢɫɬɨɱɧɢɤɭ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ.
ɋɨɝɥɚɫɧɨɟ ɧɚɩɪɚɜɥɟɧɢɟ ɨɫɬɚɬɨɱɧɨɝɨ ɩɨɬɨɤɚ ɫ ɩɨɬɨ
ɤɨɦ ɫɨɡɞɚɧɧɵɦɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹȼ ɩɪɨɬɢɜɧɨɦ ɫɥɭɱɚɟ ɫɥɟ-
ɞɭɟɬ ɩɨɦɟɧɹɬɶ ɦɟɫɬɚɦɢ ɡɚɠɢɦɵ ɥɢɛɨ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ, ɥɢɛɨ
ɨɛɦɨɬɤɢ ɹɤɨɪɹ (ɧɨ ɧɟ ɬɟ ɢ ɞɪɭɝɢɟ ɫɪɚɡɭ!).
ɋɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɜɨɡɛɭɠɞɟɧɢɹ ɞɨɥɠɧɨ ɛɵɬɶ
ɦɟɧɶɲɟɤɪɢɬɢɱɟɫɤɨɝɨ
ɉɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɦɨɠɧɨɨɩɢɫɚɬɶ ɫɥɟɞɭɸɳɢɦ ɭɪɚɜɧɟ
ɧɢɟɦ
di
ɜ
dt
ɝɞɟ
eiRL ,
eɢi
± ɦɝɧɨɜɟɧɧɵɟ ɡɧɚɱɟɧɢɹ ɗȾɋɢɬɨɤɚɜɨɡɛɭɠɞɟɧɢɹRɢL±
ɜ
ɜ
ɫɭɦɦɚɪɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɢ ɫɭɦɦɚɪɧɚɹ ɢɧɞɭɤɬɢɜɧɨɫɬɶ ɤɨɧɬɭɪɚ ©ɨɛ
ɦɨɬɤɚɹɤɨɪɹ±ɨɛɦɨɬɤɚɜɨɡɛɭɠɞɟɧɢɹª
Ⱦɜɚɱɥɟɧɚ ɭɪɚɜɧɟɧɢɹɦɨɠɧɨɢɡɨɛɪɚɡɢɬɶɝɪɚɮɢɱɟɫɤɢɜ ɜɢɞɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ
iɜRɪɢɫ ɉɪɨɰɟɫɫɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹɛɭɞɟɬɢɞɬɢɞɨɬɨɱɤɢɢɯ
ɫɬɢɤɢ
ɩɟɪɟɫɟɱɟɧɢɢ±ɬ
Ⱥ
e = f(iɜ) ɢ ɜɨɥɶɬɚɦɩɟɪɧɨɣɯɚɪɚɤɬɟɪɢ
ȿɫɥɢ ɭɜɟɥɢɱɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜɨɥɶɬ
ɚɦɩɟɪɧɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɣɞɟɬ ɤɪɭɱɟ ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ
ɡɚɤɨɧɱɢɬɫɹ ɜ ɬ
A’ ɉɪɢ ɧɟɤɨɬɨɪɨɦ ɬɚɤ ɧɚɡɵɜɚɟɦɨɦ ɤɪɢɬɢɱɟɫɤɨɦ
ɫɨɩɪɨɬɢɜɥɟɧɢɢɩɪɹɦɚɹ ɈȺ ɛɭɞɟɬɩɪɚɤɬɢɱɟɫɤɢ ɫɨɜɩɚɞɚɬɶ ɫɧɚɱɚɥɶɧɨɣ
ɭ
E
N
ɥɢɧɟɣɧɨɣ ɱɚɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ȼ ɷɬɨɦ ɫɥɭɱɚɟ
e § iɜR
ɢɩɪɨɰɟɫɫɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹɫɬɚɧɨɜɢɬɫɹɧɟɜɨɡɦɨɠɧɵɦ
ɤɪ
(
Lɜ5ɤɪ
Ⱥޖ
ȿ
ɨɫɬ
H
ɊɢɫɏɚɪɚɤɬɟɪɢɡɦɟɧɟɧɢɹɬɨɤɚɜɨɡɛɭɠɞɟɧɢɹɢɗȾɋ
ɜɩɪɨɰɟɫɫɟɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ
Ⱥ
Lɜ5
L
ɜ
ɟ=f(iɜ)
di e i R
ɜɜ
dt L
8 ȿ
Lɜ
Ƚɟɧɟɪɚɬɨɪɵɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
Ɉɫɧɨ
ɜɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ ɨɩɪɟɞɟɥɹɸɳɢɦɢ ɫɜɨɣɫɬɜɚ ɝɟɧɟ
ɪɚɬɨɪɨɜɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚɹɜɥɹɸɬɫɹɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ±ɡɚɜɢɫɢɦɨɫɬɶU0 = f(iɜ)ɩɪɢIa = 0ɪɢɫ
x
ɉɪɢ
ɯɨɥɨɫɬɨɦ ɯɨɞɟɤɨɝɞɚ ɰɟɩɶɧɚɝɪɭɡɤɢ ɪɚɡɨɦɤɧɭɬɚ ɧɚɩɪɹɠɟ
ɧɢɟɧɚɤɥɟɦɦɚɯɪɚɜɧɨ
ɧɢɹɝɟɧɟɪɚɬɨɪɚɩɨɞɞɟɪɠɢɜɚɟɬɫɹɩɨɫɬɨɹɧɧɨɣɧɚɩɪɹɠɟɧɢɟɩɪɢɯɨɥɨɫɬɨɦ
ɯɨɞɟɡɚɜɢɫɢɬɬɨɥɶɤɨɨɬɜɟɥɢɱɢɧɵɦɚɝɧɢɬɧɨɝɨɩɨɬɨɤɚɬɟɨɬɜɟɥɢɱɢɧɵ
ɬɨɤɚɜɨɡɛɭɠɞɟɧɢɹɉɨɷɬɨɦɭ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɧɨɣɯɚɪɚɤɬɟɪɢɫɬɢɤɟ
8
ɗȾɋU0 = E = cenɎ.ɉɨɫɤɨɥɶɤɭɱɚɫɬɨɬɚɜɪɚɳɟ
U0 = f(iɜ)ɩɨɞɨɛɧɚɦɚɝɧɢɬ
Ɏ = f(iɜ)
(8
8
ȿ
F
8
8 IL
8 IL
D
ɜ
8
ɨɫɬ
Ɋɢɫɏɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɯɨɥɨɫɬɨɝɨɯɨɞɚɝɟɧɟɪɚɬɨɪɚ
ɩɪɚɤɬɢɱɟɫɤɢɥɸɛɨɝɨ
ɫɩɨɫɨɛɚɜɨɡɛ
ɠɞɟɧɢɹ
Lɜ
Ɋɢɫɇɚɝɪɭɡɨɱɧɚɹ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɝɟɧɟɪɚɬɨɪɚ
ɧɟɡɚɜɢɫɢɦɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
L
x
ɧɚɝɪɭɡɨɱɧɚɹ±ɡɚɜɢɫɢɦɨɫɬɶU = f(iɜ)ɩɪɢIa = I
= constɏɚ
ɧɨɦ
ɪɚɤɬɟɪɢɫɬɢɤɚ ɩɪɨɯɨɞɢɬ ɧɢɠɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɢɡɡɚ
ɜɧɭɬɪɟɧɧɟɝɨ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɢ ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɟɝɨ ɞɟɣɫɬɜɢɹ
ɩɨɩɟɪɟɱɧɨɣɪɟɚɤɰɢɢɹɤɨɪɹɪɢɫ
ȿɫɥɢ ɨɬ ɬ
ɥɨɠɢɬɶ ɨɬɪɟɡɨɤ
ɚ ɫɨɨɬɜɟɬɫɬɜɭɸɳɟɣ ɧɟɤɨɬɨɪɨɦɭ ɧɚɩɪɹɠɟɧɢɸ8 ɨɬ
ab ɪɚɜɧɵɣ ɜɧɭɬɪɟɧɧɟɦɭ ɩɚɞɟɧɢɸ ɧɚɩɪɹɠɟɧɢɹ IaRa,
ɩɪɨɜɟɫɬɢɨɬɪɟɡɨɤbc, ɬɨɩɨɥɭɱɢɦɯɚɪɚɤɬɟɪɢɫɬɢɱɟɫɤɢɣɬɪɟɭɝɨɥɶɧɢɤabc
ȼ ɧɟɦ ɤɚɬɟɬ
ɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɜ ɦɚɫɲɬɚɛɟ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ
bc ɨɬɪɚɠɚɟɬ ɪɚɡɦɚɝɧɢɱɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɩɨɩɟɪɟɱ-
ɚ ɨɬɪɟɡɨɤbk – ɪɚɡ-
ɦɚɝɧɢɱɢɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɩɨɩɟɪɟɱɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɜ ɦɚɫɲɬɚɛɟ
ɧɚɩɪɹɠɟɧɢɹ
ɫɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦɢ
x
ɜɧɟɲɧɹɹ±ɡɚɜɢɫɢɦɨɫɬɶU = f(I)ɩɪɢiɜ = constɞɥɹɝɟɧɟɪɚɬɨɪɚ
Rɜ = constɞɥɹ ɝɟɧɟɪɚɬɨɪɚɩɚɪɚɥɥɟɥɶ
ɧɨɝɨɢɫɦɟɲɚɧɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
8
Ɋɢɫȼɧɟɲɧɹɹɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
ɝɟɧɟɪɚɬɨɪɚɧɟɡɚɜɢɫɢɦɨɝɨ
ɢɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
,
ɧɨɦ
,
8
,
Ɋɢɫȼɧɟɲɧɢɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɝɟɧɟɪɚɬɨɪɨɜ
ɫɦɟɲɚɧɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɧɨɦ
ȼɧɟɲɧɹɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɝɟɧɟɪɚɬɨɪɚ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟ
ɧɢɹ ɪɚɫɩɨɥɚɝɚɟɬɫɹ ɧɢɠɟ ɜɧɟɲɧɟɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɝɟɧɟɪɚɬɨɪɚ ɧɟɡɚɜɢ
ɫɢɦɨɝɨɜɨɡɛɭɠɞɟɧɢɹɪɢɫɤɪɢɜɚɹɗɬɨɩɪɨɢɫɯɨɞɢɬɩɨɬɨɦɭɱɬɨ
ɤɞɜɭɦɩɪɢɱɢɧɚɦɭɦɟɧɶɲɚɸɳɢɦɧɚɩɪɹɠɟɧɢɟɜɝɟɧɟɪɚɬɨɪɟɫɧɟɡɚɜɢ
ɫɢɦɵɦɜɨɡɛɭɠɞɟɧɢɟɦɜɧɭɬɪɟɧɧɟɟɩɚɞɟɧɢɟɧɚɩɪɹɠɟɧɢɹɢ ɪɚɡɦɚɝɧɢɱɢ
ɜɚɸɳɟɟ ɞɟɣɫɬɜɢɟ ɩɨɩɟɪɟɱɧɨɣ ɪɟɚɤɰɢɢ ɹɤɨɪɹ ɞɨɛɚɜɥɹɟɬɫɹ ɬɪɟɬɶɹ ±
ɭɦɟɧɶɲɟɧɢɟɬɨɤɚɜɨɡɛɭɠɞɟɧɢɹɢɛɨ
iɜ = U/R
ɧɢɸɨɫɧɨɜɧɨɝɨɦɚɝɧɢɬɧɨɝɨɩɨɬɨɤɚɭɦɟɧɶɲɟɧɢɸ
ɱɬɨɩɪɢɜɨɞɢɬɤɨɫɥɚɛɥɟ
ɜ
ɗȾɋɚ ɫɥɟɞɨɜɚɬɟɥɶ
ɧɨɢɧɚɩɪɹɠɟɧɢɹɧɚɡɚɠɢɦɚɯɝɟɧɟɪɚɬɨɪɚ
ȼɧɟɲɧɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢɝɟɧɟɪɚɬɨɪɨɜɫɦɟɲɚɧɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɡɚɜɢɫɹɬɨɬɫɨɨɬɧɨɲɟɧɢɹ
ɆȾɋɩɚɪɚɥɥɟɥɶɧɨɣɢɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɣɨɛɦɨ
ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ Ɉɛɵɱɧɨ ɨɫɧɨɜɧɨɣ ɹɜɥɹɟɬɫɹ ɩɚɪɚɥɥɟɥɶɧɚɹ ɨɛɦɨɬɤɚ
,
ɜɨɡɛɭɠɞɟɧɢɹɉɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸɨɛɦɨɬɤɭɜɵɛɢɪɚɸɬɫɬɚɤɢɦɪɚɫɱɟɬɨɦ
ɱɬɨɛɵ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɣ ɧɚɝɪɭɡɤɟ ɟɟ
ɹɤɨɪɹ ɢ ɜɧɭɬɪɟɧɧɟɟ ɩɚɞɟɧɢɟ ɧɚɩɪɹɠɟɧɢɹ ȼ ɷɬɨɦ ɫɥɭɱɚɟ
ɪɚɤɬɟɪɢɫɬɢɤɚ
ɢɦɟɟɬɜɢɞɤɪɢɜɨɣɧɚɪɢɫ
ɆȾɋ ɤɨɦɩɟɧɫɢɪɨɜɚɥɚ ɪɟɚɤɰɢɸ
ɜɧɟɲɧɹɹ ɯɚ-
ȿɫɥɢ ɭɫɢɥɢɬɶ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɨɛɦɨɬɤɭ ɜɧɟɲɧɹɹ ɯɚɪɚɤɬɟɪɢ
ɫɬɢɤɚɩɪɢɨɛɪɟɬɟɬɜɢɞ ɤɪɢɜɨɣ ɪɢɫ ɉɪɢ ɜɫɬɪɟɱɧɨɦ ɜɤɥɸɱɟɧɢɢ
ɨɛɦɨɬɨɤ ɧɚɩɪɹɠɟɧɢɟ ɝɟɧɟɪɚɬɨɪɚ ɫ ɪɨɫɬɨɦ ɧɚɝɪɭɡɤɢ ɧɚɱɧɟɬ ɫɢɥɶɧɨ
ɭɦɟɧɶɲɚɬɶɫɹ ɤɪɢɜɚɹ Ɍɚɤɨɟ ɜɤɥɸɱɟɧɢɟɩɪɢɦɟɧɹɸɬ ɜɫɩɟɰɢɚɥɶɧɵɯ
ɫɥɭɱɚɹɯ ɤɨɝɞɚ ɬɪɟɛɭɟɬɫɹ ɩɨɥɭɱɢɬɶ ɤɪɭɬɨɩɚɞɚɸɳɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ
ɧɚɩɪɢɦɟɪɜɫɜɚɪɨɱɧɵɯɝɟɧɟɪɚɬɨɪɚɯɩɪɨɠɟɤɬɨɪɧɵɯɭɫɬɚɧɨɜɤɚɯɢɬɞ
ɪɟɝɭɥɢɪɨɜɨɱɧɚɹ±ɡɚɜɢɫɢɦɨɫɬɶiɜ = f(I)ɩɪɢU = constɪɢɫ
x
L
ɜ
,
ɧɨɦ
ɊɢɫɊɟɝɭɥɢɪɨɜɨɱɧɵɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɝɟɧɟɪɚɬɨɪɨɜɪɚɡɥɢɱɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
±ɩɚɪɚɥɥɟɥɶɧɨɝɨɢɧɟɡɚɜɢɫɢɦɨɝɨ
±ɫɦɟɲɚɧɧɨɝɨɫɧɨɪɦɚɥɶɧɨɣɫɟɪɢɟɫɧɨɣ
ɨɛɦɨɬɤɨɣ±ɫɦɟɲɚɧɧɨɝɨɫɭɫɢɥɟɧɧɨɣ
ɫɟɪɢɟɫɧɨɣɨɛɦɨɬɤɨɣ
,
Ɋɟɝɭɥɢɪɨɜɨɱɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɤɚɡɵɜɚɸɬ ɤɚɤ ɫɥɟɞɭɟɬ ɢɡɦɟ
ɧɹɬɶɬɨɤɜɨɡɛɭɠɞɟɧɢɹɫɢɡɦɟɧɟɧɢɟɦɧɚɝɪɭɡɤɢɱɬɨɛɵɧɚɩɪɹɠɟɧɢɟɝɟɧɟ
ɪɚɬɨɪɚ ɨɫɬɚɜɚɥɨɫɶ ɩɨɫɬɨɹɧɧɵɦ ɉɨɥɭɱɚɟɬɫɹ ɱɬɨ ɪɟɝɭɥɢɪɨɜɨɱɧɵɟ ɯɚ
ɪɚɤɬɟɪɢɫɬɢɤɢɹɜɥɹɸɬɫɹɡɟɪɤɚɥɶɧɵɦɨɬɨɛɪɚɠɟɧɢɟɦɜɧɟɲɧɢɯ
Ⱦɜɢɝɚɬɟɥɢɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ
ɂɡ
ɜɧɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɫ ɭɱɟɬɨɦ ɮɨɪɦɭɥɵ
ɭɪɚ
ɦɨɠɧɨɩɨɥɭɱɢɬɶɧɟɫɤɨɥɶɤɨɨɱɟɧɶɩɨɥɟɡɧɵɯɮɨɪɦɭɥɚɢɦɟɧɧɨ
UE
I;
ɚ
ɚ
R
ɚ
Ⱦɜɢɝɚɬɟɥɢɦɨɳɧɨɫɬɶɸɛɨɥɟɟ ɤȼɬ ɩɭɫɤɚɸɬɫ ɩɨɦɨɳɶɸ ɩɭɫɤɨ
ɜɨɝɨ
ɪɟɨɫɬɚɬɚɩɨɞɛɢɪɚɹɜɟɥɢɱɢɧɭ
II
ɩɧɨɦ
U
dy
RR
ɚɩɪ
UIR
n
R
ɬɚɤɱɬɨɛɵ
ɩɪ
c Ɏ
ɟ
ɚɚ
ɗȾɋ
Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨɬɨɤɚ ɦɨɳɧɨɫɬɶɸɦɟɧɟɟ ɤȼɬ ɩɭɫɤɚɸɬ
Q
ɩɪɹɦɵɦ ɜɤɥɸɱɟɧɢɟɦ ɜ ɫɟɬɶ ɩɨɫɤɨɥɶɤɭ ɨɧɢ ɨɛɥɚɞɚɸɬ ɨɬɧɨɫɢɬɟɥɶɧɨ
ɛɨɥɶɲɢɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ ɹɤɨɪɧɨɣ ɰɟɩɢ ɚ ɢɯ ɩɭɫɤɨɜɨɣ ɬɨɤ ɫɪɚɜɧɢ
ɬɟɥɶɧɨɧɟɜɟɥɢɤ
Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚɤɚɤ ɢɝɟɧɟɪɚɬɨɪɵ ɛɵɜɚɸɬ ɩɚɪɚɥ
ɥɟɥɶɧɨɝɨ ɧɟɡɚɜɢɫɢɦɨɝɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɢ ɫɦɟɲɚɧɧɨɝɨ ɜɨɡɛɭɠɞɟ
ɧɢɹɈ ɤɚɱɟɫɬɜɟɞɜɢɝɚɬɟɥɟɣ ɫɭɞɹɬɩɨ ɢɯ ɪɚɛɨɱɢɦɢ ɦɟɯɚɧɢɱɟɫɤɢɦɯɚ
ɪɚɤɬɟɪɢɫɬɢɤɚɦ
Ⱦɜɢɝɚɬɟɥɶɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Ɋɚɛɨɱɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɢɫ ɩɪɟɞɫɬɚɜɥɹɸɬɫɨɛɨɣ ɡɚɜɢ
ɫɢɦɨɫɬɢɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɦɨɦɟɧɬɚ ɩɨɬɪɟɛɥɹɟɦɨɣ ɦɨɳɧɨɫɬɢ ɬɨɤɚɢ
ɄɉȾ ɨɬ ɩɨɥɟɡɧɨɣ ɦɨɳɧɨɫɬɢ ɩɪɢɩɨɫɬɨɹɧɧɨɦ ɧɚɩɪɹɠɟɧɢɢɢ ɬɨɤɟɜɨɡ
ɛɭɠɞɟɧɢɹ
0,
ɞɜɢɝɚɬɟɥɹɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
n, M, P1,I, K = f(P2)ɩɪɢU
Q0,D3K
Q
K
Q
0,D
Ɋ
Ɋ
Ɋ
Ɋ
ɊɢɫɊɚɛɨɱɢɟɯɚɪɚɤɬɟɪɢɫɬɢɤɢ
ɧɨɦ
= const, I
ɧɨɦ
Q
= const
ɜ.ɧɨɦ
0
ɊɢɫɆɟɯɚɧɢɱɟɫɤɢɟ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ
ɩɚɪɚɥɥɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɧɨɦ
5DS
5
!
DS
5
!5
DS
DS
5
!5
DS
DS
0
ɉɪɢɫɧɹɬɢɢɪɚɛɨɱɢɯɯɚɪɚɤɬɟɪɢɫɬɢɤɭɫɬɚɧɚɜɥɢɜɚɸɬɧɨɦɢɧɚɥɶɧɵɣ
ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ
ɧɨɦɢɧɚɥɶɧɨɦ ɬɨɤɟ ɹɤɨɪɹɨɛɟɫɩɟɱɢɜɚɟɬ ɜɪɚɳɟɧɢɟ ɞɜɢɝɚɬɟɥɹɫ ɧɨɦɢ-
ɢ
ɧɚɥɶɧɨɣ ɱɚɫɬɨɬɨɣ
± ɬɨɤ ɤɨɬɨɪɵɣ ɩɪɢ ɧɨɦɢɧɚɥɶɧɨɦ ɧɚɩɪɹɠɟɧɢɢ
Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɢɫ ɩɨɤɚɡɵɜɚɸɬ ɡɚɜɢɫɢ
ɦɨɫɬɢɱɚɫɬɨɬɵɜɪɚɳɟɧɢɹɨɬɜɟɥɢɱɢɧɵɦɨɦɟɧɬɚ
I
= const, Rap = constɝɞɟ R
ɜ
±ɪɟɝɭɥɢɪɨɜɨɱɧɨɟɫɨɩɪɨɬɢɜɥɟɧɢɟɜɰɟɩɢ
ap
n = f(M) ɩɪɢ U = const,
ɹɤɨɪɹ
UIR R Ɇ RR
n
ɚɚ ɚɪ ɚ ɚɪ
ɫɎ ɫɫ Ɏ
ɟɟɦ
U
ɫɫ Ɏ
ɟɦ
Rap = 0 ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɧɚɡɵɜɚɟɬɫɹ ɟɫɬɟɫɬɜɟɧɧɨɣ ɩɪɢ
S
ɉɪɢ
Rap > 0±ɢɫɤɭɫɫɬɜɟɧɧɨɣ
Ⱦɜɢɝɚɬɟɥɶɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɉɪɢ ɷɤɫɩɥɭɚɬɚɰɢɢ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ
ɧɚɞɨɩɨɦɧɢɬɶɨɞɧɨɩɪɚɜɢɥɨ
ɞɜɢɝɚɬɟɥɶ ɧɟɥɶɡɹ ɨɫɬɚɜɥɹɬɶ ɛɟɡ ɧɚɝɪɭɡɤɢ,
ɬ. ɤ. ɨɧ ɢɞɟɬ ɜ ɪɚɡɧɨɫ, ɬ. ɟ. ɱɚɫɬɨɬɚ ɜɪɚɳɟɧɢɹ ɪɟɡɤɨ ɜɨɡɪɚɫɬɚɟɬ, ɜɨ
ɜɪɚɳɚɸɳɢɯɫɹ ɱɚɫɬɹɯ ɦɚɲɢɧɵ ɜɨɡɧɢɤɚɸɬ ɛɨɥɶɲɢɟ ɞɢɧɚɦɢɱɟɫɤɢɟ ɭɫɢɥɢɹ, ɱɬɨ ɦɨɠɟɬ ɩɪɢɜɟɫɬɢ ɤ ɪɚɡɪɵɜɭ ɛɚɧɞɚɠɟɣ, ɩɨɪɱɟ ɨɛɦɨɬɤɢ ɢ ɜɵɯɨɞɭ ɞɜɢɝɚɬɟɥɹ ɢɡ ɫɬɪɨɹ.
ɉɨɷɬɨɣɩɪɢɱɢɧɟɩɪɢɪɚɛɨɬɟɫɞɜɢɝɚɬɟɥɟɦɧɟ
ɫɥɟɞɭɟɬɭɦɟɧɶɲɚɬɶɧɚɝɪɭɡɤɭɦɟɧɟɟóɧɨɦɢɧɚɥɶɧɨɝɨɡɧɚɱɟɧɢɹ
ɇɚɪɢɫ ɩɨɤɚɡɚɧɵ ɪɚɛɨɱɢɟɚɧɚ ɪɢɫ ɦɟɯɚɧɢɱɟɫɤɢɟɯɚ
ɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Q0,D3K
Q
K
0
Ɋ
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ
Ⱦɜɢɝɚɬɟ
ɧɨɦ
ɊɢɫɊɚɛɨɱɢɟ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ
ɥɶɫɦɟɲɚɧɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
Ɋ,D
Q
Ɋ
ɧɨɦ
Ɋ
0
ɯɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ
ɧɨɦ
ɊɢɫɆɟɯɚɧɢɱɟɫɤɢɟ
ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ
ɜɨɡɛɭɠɞɟɧɢɹ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹ ɡɚɜɢɫɹɬɨɬ ɫɨɨɬɧɨɲɟɧɢɹ
0
5
5
DS
5
DS
ɧɨɦ
ɆȾɋɨɛɦɨ
D
!
!5
0
DS
ɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ Ɉɛɵɱɧɨ ɨɞɧɚ ɢɡ ɧɢɯ ɹɜɥɹɟɬɫɹ ɝɥɚɜɧɨɣ ɞɪɭɝɚɹ ±
ɜɫɩɨɦɨɝɚɬɟɥɶɧɨɣ
ɏɚɪɚɤɬɟɪɢɫɬɢɤɢɞɜɢɝɚɬɟɥɹɡɚɧɢɦɚɸɬɩɪɨɦɟɠɭɬɨɱɧɨɟɩɨɥɨɠɟɧɢɟ
ɦɟɠɞɭ ɪɚɫɫɦɨɬɪɟɧɧɵɦɢ ɜɵɲɟ ɩɪɢɛɥɢɠɚɹɫɶ ɥɢɛɨ ɤ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ
ɞɜɢɝɚɬɟɥɹɩɚɪɚɥɥɟɥɶɧɨɝɨɥɢɛɨɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨɜɨɡɛɭɠɞɟɧɢɹ
ɋɬɪɨɝɨ ɝɨɜɨɪɹ ɞɜɢɝɚɬɟɥɢ ɱɢɫɬɨ ɩɚɪɚɥɥɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ
ɜɵɩɭɫɤɚɸɬɫɹ ɪɟɞɤɨ Ʉɚɤ ɩɪɚɜɢɥɨɨɧɢ ɫɧɚɛɠɚɸɬɫɹɧɟɛɨɥɶɲɨɣ ɩɨɫɥɟ
ɞɨɜɚɬɟɥɶɧɨɣ ɨɛɦɨɬɤɨɣ ɜɨɡɛɭɠɞɟɧɢɹ ɜɤɥɸɱɚɟɦɨɣ ɫɨɝɥɚɫɧɨ ɫ ɩɚɪɚɥ
Соседние файлы в предмете [НЕСОРТИРОВАННОЕ]