EP / Теория ЭП Драчев

3.1.11. ɍɩɪɚɠɧɟɧɢɹ ɞɥɹ ɫɚɦɨɩɪɨɜɟɪɤɢ (ɪɚɫɱɟɬɵ ɜɵɩɨɥɧɹɸɬɫɹ ɜ ɨɬɧɨɫɢɬɟɥɶɧɵɯ ɟɞɢɧɢɰɚɯ)

3.1.11.1.Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ Ȧɇ / 2. ɉɪɢɧɹɬɶ r = 0,05, Ɏ =1.

3.1.11.2.Ɉɩɪɟɞɟɥɢɬɶ RȾɈȻ ɜ ɰɟɩɢ Ⱦɇȼ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ ɜɪɚɳɟɧɢɹ Ȧɇ / 2. ɉɪɢɧɹɬɶ r=0,1, U=1, Ɏ=1.

3.1.11.3.Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ ɩɪɢ U=1, Ɇ=1, Ɏ=1 ɜɜɟɫɬɢ ɜ ɰɟɩɶ ɹɤɨɪɹ RȾɈȻ=0,5. ɉɪɢɧɹɬɶ r = 0,05.

3.1.11.4.Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ ɩɪɢ Ɏ=1, RȾɈȻ=0,5 ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ Ɇ=2. ɉɪɢɧɹɬɶ r = 0,05.

3.1.11.5.Ɉɩɪɟɞɟɥɢɬɶ Rɞɨɛ ɜ ɰɟɩɢ ɹɤɨɪɹ Ⱦɇȼ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɪɢ Ɇ=1 ɫɤɨɪɨɫɬɶ Ȧ = – 1. ɉɪɢɧɹɬɶ Ɏ=1, r = 0,05.

3.1.11.6.Ɉɩɪɟɞɟɥɢɬɶ ɫɤɨɪɨɫɬɶ ɢ ɬɨɤ ɞɜɢɝɚɬɟɥɹ ɩɪɢ U = 1, Ɇ = 1, Ɏ = 0,5. ɉɪɢ-

ɧɹɬɶ r=0,1.

3.1.11.7.Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ U =

0,5, Ɇ = 1, Ɏ = 1, r = 0,05, RȾɈȻ = 0,5.

3.1.11.8. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ

U = 0,5, Ɇ =1, Ɏ = 1, RȾɈȻ = 1. ɉɪɢɧɹɬɶ r = 0,05.

3.1.11.9. Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ = 0,5, Ȧɋ = 0,5. ȼɨɡɪɨɫ Ɇɋ =1,5. ɇɚ ɫɤɨɥɶɤɨ ɧɭɠɧɨ ɭɜɟɥɢɱɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɞɜɢɝɚɬɟɥɟ, ɱɬɨɛɵ ɜɨɫɫɬɚɧɨɜɢɬɶ ɫɤɨɪɨɫɬɶ, ɟɫɥɢ r

=0,05?

3.1.11.10.Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ = 0,5, Ȧɋ = 1. Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɟɫɥɢ Ɇɋ ɜɨɡɪɨɫ ɜ 2 ɪɚɡɚ, ɚ r = 0,05?

3.1.11.11.Ⱦɇȼ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ Ɇɋ =1, Ȧɋ = 0,5.Ɉɩɪɟɞɟɥɢɬɶ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɞɜɢɝɚɬɟɥɟ, ɧɟɨɛɯɨɞɢɦɨɟ ɞɥɹ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ, ɟɫɥɢ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɭɦɟɧɶɲɢɥɫɹ ɞɨ 0,8 ɩɪɢ r=0,1.

3.1.11.12.ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɢ ɬɨɤ Ⱦɇȼ, ɟɫɥɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɜɨɡɪɨɫɥɨ ɧɚ 0,1. ɉɪɢɧɹɬɶ Ɇɋ = 1, r = 0,05.

3.1.11.13. Ɉɩɪɟɞɟɥɢɬɶ ɛɪɨɫɨɤ ɬɨɤɚ ɹɤɨɪɹ,	ɟɫɥɢ ɩɪɢ	ɪɚɛɨɬɟ Ⱦɇȼ	ɫ
Ɇɋ = 0,5 ɢ Ȧɋ = 0,5 ɧɚɩɪɹɠɟɧɢɟ ɫɤɚɱɤɨɦ ɫɧɢɡɢɥɨɫɶ ɧɚ 0,1.		ɉɪɢɧɹɬɶ Ɏ =	1,
r = 0,05.
3.1.11.14. Ɉɩɪɟɞɟɥɢɬɶ ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ,	ɟɫɥɢ ɩɪɢ Ɇɋ = 0,5, Ȧɋ = 0,95,
U = 1 ɩɨɬɨɤ ɭɦɟɧɶɲɢɥɫɹ ɞɨ Ɏ = 0,8.

3.1.11.15.ɉɪɢ ɩɟɪɟɜɨɞɟ Ⱦɇȼ, ɪɚɛɨɬɚɜɲɟɝɨ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɛɪɨɫɨɤ ɬɨɤɚ ɹɤɨɪɹ ɫɨɫɬɚɜɢɥ 2,5. Ɉɩɪɟɞɟɥɢɬɶ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɧɨɣ ɰɟɩɢ ɞɜɢɝɚɬɟɥɹ.

3.1.11.16.ɉɪɢ ɩɟɪɟɜɨɞɟ Ⱦɇȼ, ɪɚɛɨɬɚɜɲɟɝɨ ɛɟɡ ɧɚɝɪɭɡɤɢ ɧɚ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ, ɜ ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɹɤɨɪɹ R=1,2. Ɉɩɪɟɞɟɥɢɬɶ ɜɟɥɢɱɢɧɭ ɬɨɤɚ ɹɤɨɪɹ ɜ ɦɨɦɟɧɬ ɩɟɪɟɤɥɸɱɟɧɢɹ.

3.1.11.17. Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɬɨɤ ɢ	ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ
U = - 0,5, Ɇ = 1, r = 0,05, Ɏ = 1.

3.1.11.18.Ɉɩɪɟɞɟɥɢɬɶ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɦɨɦɟɧɬ, ɬɨɤ ɢ ɫɤɨɪɨɫɬɶ Ⱦɇȼ, ɟɫɥɢ

U = 0, Ɇ = 0,5, r = 0,05.

3.1.11.19.Ɉɩɪɟɞɟɥɢɬɶ ɩɪɢɛɥɢɠɟɧɧɨ ɦɢɧɢɦɚɥɶɧɨɟ ɜɪɟɦɹ ɩɭɫɤɚ Ⱦɇȼ, ɟɫɥɢ ɌȾ =1 ɫ, Ɇɋ = 0,5.

81

3.1.11.20.ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɜɪɟɦɹ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ, ɟɫɥɢ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ ɭɦɟɧɶɲɢɬɶ ɜɞɜɨɟ, ɚ Ⱦɇȼ ɪɚɛɨɬɚɥ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ?

3.1.11.21.ɇɚ ɫɤɨɥɶɤɨ ɢɡɦɟɧɢɬɫɹ ɫɤɨɪɨɫɬɶ ɫɩɭɫɤɚ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ Ⱦɇȼ, ɟɫɥɢ ɭɜɟɥɢɱɢɬɶ ɜɞɜɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɰɟɩɢ ɹɤɨɪɹ? ɭɦɟɧɶɲɢɬɶ ɜɞɜɨɟ ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ?

3.2. ɗɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɟ ɫɜɨɣɫɬɜɚ ɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ)

3.2.1.ɍɪɚɜɧɟɧɢɹ ɢ ɫɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ Ⱦɉȼ

ȼɨɬɥɢɱɢɟ ɨɬ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ Ⱦɇȼ ɜ ɞɜɢɝɚɬɟɥɹɯ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ (Ⱦɉȼ) ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɜɤɥɸɱɚɟɬɫɹ ɜ ɰɟɩɶ ɹɤɨɪɹ. Ɍɨɤ ɹɤɨɪɹ ɨɞɧɨɜɪɟɦɟɧɧɨ ɹɜɥɹɟɬɫɹ ɬɨɤɨɦ ɜɨɡɛɭɠɞɟɧɢɹ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɫɯɟɦɚ Ⱦɉȼ ɩɪɟɞɫɬɚɜɥɟɧɚ ɧɚ ɪɢɫ. 3.30.

Ⱦɜɢɝɚɬɟɥɢ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭ-

Uɠɞɟɧɢɹ ɜɨ ɜɫɩɨɦɨɝɚɬɟɥɶɧɵɯ ɦɟɯɚɧɢɡɦɚɯ

LM

ɩɪɨɤɚɬɧɵɯ ɫɬɚɧɨɜ, ɜ ɤɪɚɧɨɜɨɦ ɯɨɡɹɣɫɬɜɟ

RȾɈȻ

ɩɨɫɬɟɩɟɧɧɨ ɜɵɬɟɫɧɹɸɬɫɹ ɛɨɥɟɟ ɩɪɨɫɬɵɦ

ɢ ɞɟɲɟɜɵɦ ɚɫɢɧɯɪɨɧɧɵɦ ɞɜɢɝɚɬɟɥɟɦ ɡɚ

Ɇ

I

ɫɱɟɬ

ɢɯ

ɛɨɥɶɲɟɣ ɩɪɨɫɬɨɬɵ

ɢ

ɥɭɱɲɢɯ

ɷɧɟɪɝɟɬɢɱɟɫɤɢɯ ɩɨɤɚɡɚɬɟɥɟɣ.

Ɋɢɫ. 3.30. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɫɯɟɦɚ

ɋɨɯɪɚɧɹɸɬ

Ⱦɉȼ

ɫɜɨɢ ɩɨɡɢɰɢɢ

ɜ ɦɚɝɢɫɬɪɚɥɶɧɨɦ

ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ

ɷɥɟɤɬɪɨɬɪɚɧɫɩɨɪɬɟ, ɬɪɚɦɜɚɟ,

ɜɧɭɬɪɢɡɚ-

ɜɨɡɛɭɠɞɟɧɢɹ

ɜɨɞɫɤɨɦ

ɬɪɚɧɫɩɨɪɬɟ

ɛɥɚɝɨɞɚɪɹ

ɫɜɨɢɦ

ɞɨɫɬɨɢɧɫɬɜɚɦ:

–ɞɥɹ ɩɢɬɚɧɢɹ ɞɨɫɬɚɬɨɱɧɨ ɢɦɟɬɶ ɨɞɢɧ ɩɪɨɜɨɞ (ɬɪɨɥɥɟɣ);

–ɧɟ ɛɨɢɬɫɹ ɛɨɥɶɲɢɯ ɫɧɢɠɟɧɢɣ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɨɦ ɭɞɚɥɟɧɢɢ ɭɫɬɚɧɨɜɨɤ ɨɬ ɢɫɬɨɱɧɢɤɚ ɩɢɬɚɧɢɹ (ɩɨɬɨɤ ɧɟ ɡɚɜɢɫɢɬ ɨɬ ɧɚɩɪɹɠɟɧɢɹ);

–ɥɭɱɲɟ ɜɵɞɟɪɠɢɜɚɸɬ ɩɟɪɟɝɪɭɡɤɢ ɧɚ ɩɨɞɴɟɦɟ, ɨɛɥɚɞɚɹ ɛɨɥɶɲɟɣ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɩɨ ɦɨɦɟɧɬɭ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ Ⱦɇȼ ɩɪɢ ɨɞɢɧɚɤɨɜɨɣ ɫ ɧɢɦ ɩɟɪɟɝɪɭɡɨɱɧɨɣ ɫɩɨɫɨɛɧɨɫɬɶɸ ɩɨ ɬɨɤɭ;

–ɪɚɡɜɢɜɚɟɬ ɩɪɢɦɟɪɧɨ ɩɨɫɬɨɹɧɧɭɸ ɦɨɳɧɨɫɬɶ (ɦɚɥɵɣ ɝɪɭɡ – ɜɵɫɨɤɚɹ ɫɤɨɪɨɫɬɶ, ɬɹɠɟɥɵɣ ɝɪɭɡ – ɦɟɞɥɟɧɧɚɹ ɫɤɨɪɨɫɬɶ), ɧɟɨɛɯɨɞɢɦɭɸ ɞɥɹ ɬɪɚɧɫɩɨɪɬɧɵɯ ɦɚɲɢɧ;

–ɛɨɥɟɟ ɧɚɞɟɠɧɵ ɡɚ ɫɱɟɬ ɛɨɥɶɲɨɝɨ ɫɟɱɟɧɢɹ ɩɪɨɜɨɞɨɜ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɦɚɥɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ɦɟɠɞɭ ɜɢɬɤɚɦɢ.

ȼɤɥɸɱɟɧɢɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɜ ɰɟɩɶ ɹɤɨɪɹ, ɦɨɳɧɨɫɬɶ ɤɨɬɨɪɨɣ ɧɚ ɞɜɚ ɩɨɪɹɞɤɚ ɜɵɲɟ, ɱɟɦ ɦɨɳɧɨɫɬɶ ɜɨɡɛɭɠɞɟɧɢɹ, ɫɨɡɞɚɟɬ ɭɫɥɨɜɢɹ ɞɥɹ ɮɨɪɫɢɪɨɜɚɧɧɨɝɨ ɢɡɦɟɧɟɧɢɹ ɩɨɬɨɤɚ ɞɜɢɝɚɬɟɥɹ. ȼ ɞɢɧɚɦɢɤɟ ɩɪɢɯɨɞɢɬɫɹ ɭɱɢɬɵɜɚɬɶ ɜɥɢɹɧɢɟ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ, ɜɨɡɧɢɤɚɸɳɢɯ ɩɪɢ ɛɵɫɬɪɵɯ ɢɡɦɟɧɟɧɢɹɯ ɩɨɬɨɤɚ.

ɉɨɜɟɞɟɧɢɟ Ⱦɉȼ ɨɩɢɫɵɜɚɟɬɫɹ ɬɟɦɢ ɠɟ ɭɪɚɜɧɟɧɢɹɦɢ ɞɥɹ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ, ɱɬɨ ɢ Ⱦɇȼ. ɂɯ ɨɬɥɢɱɢɟ – ɜ ɫɩɨɫɨɛɟ ɫɨɡɞɚɧɢɹ ɩɨɬɨɤɚ.

Ɉɫɧɨɜɧɵɟ ɭɪɚɜɧɟɧɢɹ Ⱦɉȼ ɛɟɡ ɭɱɟɬɚ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ [1]:

U E I R (Lə	LɈȼ )	dI	w			dɎ	; ȿ = ɤɎ(I)·Ȧ; Ɇ = ɤɎ(I)·I.
				ȼ
		dt				dt

Ɉɩɭɫɤɚɹ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɭɪɚɜɧɟɧɢɣ, ɩɨɫɬɪɨɢɦ ɫɬɪɭɤɬɭɪɧɭɸ ɫɯɟɦɭ (ɪɢɫ. 3.31).

82

ɋɬɪɭɤɬɭɪɧɚɹ ɫɯɟɦɚ ɹɤɨɪɧɨɣ ɰɟɩɢ ɨɫɬɚɥɚɫɶ ɩɪɟɠɧɟɣ (ɫɦ. ɪɢɫ. 3.31), ɨɬɫɭɬɫɬɜɭɟɬ ɤɨɧɬɭɪ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ, ɬɨɤ ɹɤɨɪɹ ɜɵɩɨɥɧɹɟɬ ɮɭɧɤɰɢɸ ɬɨɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢ ɫɨɡɞɚɟɬ ɧɚɦɚɝɧɢɱɢɜɚɸɳɭɸ ɫɢɥɭ ɜ ɦɚɝɧɢɬɧɨɣ ɰɟɩɢ ɞɜɢɝɚɬɟɥɹ. ɇɚ ɜɯɨɞɟ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ – ɬɨɤ ɹɤɨɪɹ, ɧɚ ɜɵɯɨɞɟ – ɩɨɬɨɤ ɞɜɢɝɚɬɟɥɹ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ R ɹɤɨɪɧɨɣ ɰɟɩɢ ɜɤɥɸɱɚɟɬ ɜ ɫɟɛɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ rɈȼ

R rə rOB RȾɈȻ ,

(3.47)

ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ ɩɨɫɬɨɹɧɧɚɹ ɜɪɟɦɟɧɢ ɹɤɨɪɧɨɣ ɰɟɩɢ ɭɱɢɬɵɜɚɟɬ ɫɭɦɦɚɪɧɭɸ ɢɧɞɭɤɬɢɜɧɨɫɬɶ ɨɛɦɨɬɨɤ ɹɤɨɪɹ ɢ ɜɨɡɛɭɠɞɟɧɢɹ

Lə	LOB		.	(3.48)
Ɍə	R

ɉɨ ɫɬɪɭɤɬɭɪɧɨɣ ɫɯɟɦɟ ɦɨɠɧɨ ɢɡɭɱɚɬɶ ɩɨɜɟɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ ɜ ɫɬɚɬɢɤɟ ɢ ɞɢɧɚɦɢɤɟ. ɉɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɢɯ ɭɱɟɬɚ ɜɢɯɪɟɜɵɯ ɬɨɤɨɜ ɧɭɠɧɨ ɨɛɪɚɬɢɬɶɫɹ ɤ ɛɨɥɟɟ ɩɨɥɧɵɦ ɭɱɟɛɧɵɦ ɩɨɫɨɛɢɹɦ [1, 14].

U

E

I

M MC

1/R

1

Ȧ

1 Tə p

J p

Ɏ

I

ɎɊɢɫ. 3.31. ɋɬɪɭɤɬɭɪɧɚɹ

wȼ·ɪ	ɫɯɟɦɚ Ⱦɉȼ

3.2.2. ȿɫɬɟɫɬɜɟɧɧɵɟ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ

ɍɪɚɜɧɟɧɢɹ ɦɟɯɚɧɢɱɟɫɤɢɯ ɢ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɜ ɨɛɳɟɦ ɜɢɞɟ ɨɞɢɧɚɤɨɜɵ ɞɥɹ ɜɫɟɯ ɞɜɢɝɚɬɟɥɟɣ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ (3.11).

	U		R	M.
Ȧ	kɎ		kɎ 2

Ⱦɥɹ Ⱦɉȼ ɩɨɬɨɤ ɹɜɥɹɟɬɫɹ ɮɭɧɤɰɢɟɣ ɬɨɤɚ ɹɤɨɪɹ Ɏ = f(I) ɢ ɜɫɟ ɩɪɨɰɟɫɫɵ, ɩɪɨɬɟɤɚɸɳɢɟ ɜ ɦɚɲɢɧɟ, ɨɩɪɟɞɟɥɹɸɬɫɹ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ (ɪɢɫ. 3.32).

	U		R M
				.
Ȧ	kɎ I		kɎ I 2

ɇɚ ɪɢɫ. 3.32 ɩɪɢɜɟɞɟɧɵ ɬɚɤɠɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɜɢɝɚɬɟɥɹ. ɉɪɢ ɬɨɤɚɯ ɹɤɨɪɹ I < Iɇ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɢɦɟɸɬ ɜɢɞ ɝɢɩɟɪɛɨɥɵ ɢ ɩɪɢ ɫɬɪɟɦɥɟɧɢɢ ɦɨɦɟɧɬɚ ɢ ɬɨɤɚ ɤ ɧɭɥɸ ɚɫɢɦɩɬɨɬɢɱɟɫɤɢ ɩɪɢɛɥɢɠɚɸɬɫɹ ɤ ɨɫɢ ɨɪɞɢɧɚɬ. ɉɪɢ I = 0 ɩɨɬɨɤ Ɏ = 0 ɢ ɫɤɨɪɨɫɬɶ ɫɬɪɟɦɢɬɫɹ ɤ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɱɬɨɛɵ ɗȾɋ

83

ɭɪɚɜɧɨɜɟɫɢɥɚ ɩɪɢɥɨɠɟɧɧɨɟ ɧɚɩɪɹɠɟɧɢɟ. Ɋɟɚɥɶɧɨ ɫɭɳɟɫɬɜɭɟɬ ɨɫɬɚɬɨɱɧɵɣ ɩɨɬɨɤ ɎɈɋɌ, ɢ ɫɤɨɪɨɫɬɶ ɧɟ ɪɚɜɧɚ ɛɟɫɤɨɧɟɱɧɨɫɬɢ, ɧɨ ɨɫɬɚɟɬɫɹ ɨɱɟɧɶ ɜɵɫɨɤɨɣ.

Ⱦɉȼ ɞɨɥɠɟɧ ɢɦɟɬɶ ɝɚɪɚɧɬɢɪɨɜɚɧɧɵɣ ɦɢɧɢɦɭɦ ɧɚɝɪɭɡɤɢ (~0.4 Ɇɇ), ɢɧɚɱɟ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɛɭɞɟɬ ɛɨɥɶɲɟ ɦɚɤɫɢɦɚɥɶɧɨ ɞɨɩɭɫɬɢɦɨɣ ɩɨ ɭɫɥɨɜɢɹɦ ɦɟɯɚɧɢɱɟɫɤɨɣ ɩɪɨɱɧɨɫɬɢ.

Ɏ	Ȧ	Ȧ
Ɏɇ
	Ȧɇ
I	I	M
Iɇ	Iɇ	Mɇ

Ɋɢɫ. 3.32. Ʉɪɢɜɚɹ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ, ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ ɢ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ

ɉɪɢ I > Iɇ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɡɨɧɟ ɧɚɫɵɳɟɧɢɹ, ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɞɨɛɧɵ Ⱦɇȼ, ɧɨ ɠɟɫɬɤɨɫɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɩɟɪɟɦɟɧɧɚ

ȕ kɎ 2	var .	(3.49)
R

ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ ɢɡɦɟɧɹɸɬɫɹ ɚɧɚɥɨɝɢɱɧɨ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ Ⱦɇȼ (ɪɢɫ. 3.33).

		U R
							M .
Ȧ		kɎ I				kɎ I 2
Ȧ	Ȧ
								Ȧ
								Ɏɇ>Ɏ
ɟɫɬ
						ɟɫɬ
UĻ						RĹ		ɟɫɬ
M							M	M
ɚ – UĻĻ						ɛ – RĹĹ		ɜ – ɎĻ

Ɋɢɫ. 3.33. ɂɫɤɭɫɫɬɜɟɧɧɵɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ⱦɉȼ ɩɪɢ: ɚ) ɭɦɟɧɶɲɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ; ɛ) ɭɜɟɥɢɱɟɧɢɢ ɫɨɩɪɨɬɢɜɥɟɧɢɹ;

ɜ) ɭɦɟɧɶɲɟɧɢɢ ɩɨɬɨɤɚ

ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɫɦɟɳɚɸɬɫɹ ɩɪɢɦɟɪɧɨ ɩɚɪɚɥɥɟɥɶɧɨ ɟɫɬɟɫɬɜɟɧɧɨɣ, ɩɪɢ ɜɜɟɞɟɧɢɢ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɢɡɦɟɧɹɸɬ ɧɚɤɥɨɧ, ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɬɨɤɚ ɫɤɨɪɨɫɬɶ ɜɨɡɪɚɫɬɚɟɬ (ɞɥɹ ɷɬɨɝɨ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɭɸ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ ɲɭɧɬɢɪɭɸɬ ɞɨɛɚɜɨɱɧɵɦ ɫɨɩɪɨɬɢɜɥɟɧɢɟɦ).

3.2.3. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɉȼ

Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɚɡɞɟɥɟ. Ɉɫɭɳɟɫɬɜɥɟɧɢɟ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɨɜ ɞɜɢɝɚɬɟɥɟɣ ɞɪɭɝɨɝɨ

84

ɫɩɨɫɨɛɚ ɜɨɡɛɭɠɞɟɧɢɹ ɫɜɹɡɚɧɨ ɫ ɩɨɞɤɥɸɱɟɧɢɟɦ ɨɛɦɨɬɨɤ ɜɨɡɛɭɠɞɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɧɟɨɛɯɨɞɢɦɭɸ ɜɟɥɢɱɢɧɭ ɩɨɬɨɤɚ. ɋɩɨɫɨɛɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɨɫɬɚɸɬɫɹ ɩɪɟɠɧɢɦɢ:

–ɜɨɡɜɪɚɬ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ – ɪɟɤɭɩɟɪɚɰɢɹ;

–ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ;

–ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ.

Ɋɚɫɫɦɨɬɪɢɦ, ɤɚɤ ɨɫɭɳɟɫɬɜɥɹɸɬɫɹ ɷɬɢ ɫɩɨɫɨɛɵ ɭ Ⱦɉȼ.

Ɋɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ). ɍɫɥɨɜɢɟ ɊɌ – ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɛɨɥɶɲɟ ɩɪɢɥɨɠɟɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ ȿ > U. ȿɫɥɢ ɗȾɋ ɛɭɞɟɬ ɪɚɜɧɨ ɩɪɢɥɨɠɟɧɧɨɦɭ ɧɚɩɪɹɠɟɧɢɸ, ɬɨ ɩɪɢ I = 0, Ɏ = 0, Ȧ = f ɢ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ, ɞɥɹ ɪɟɠɢɦɚ ɊɌ ɜ ɟɫɬɟɫɬɜɟɧɧɨɣ ɫɯɟɦɟ ɜɤɥɸɱɟɧɢɹ Ⱦɉȼ ɧɟɨɛɯɨɞɢɦɚ Ȧ > f, ɢ ɪɟɠɢɦ ɊɌ ɧɟɜɨɡɦɨɠɟɧ.

ȼ ɭɫɬɚɧɨɜɤɚɯ ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɩɨɞɜɢɠɧɨɝɨ ɫɨɫɬɚɜɚ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɊɌ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɢɫɤɥɸɱɚɟɬɫɹ ɢɡ ɫɯɟɦɵ ɢ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ ɞɨɩɨɥɧɢɬɟɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ. ɇɨ ɷɬɨ ɩɨɥɭɱɚɟɬɫɹ Ⱦɇȼ!

Ɋɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ). Ɋɟɠɢɦ ɉȼ ɚɧɚɥɨɝɢɱɟɧ ɉȼ Ⱦɇȼ. Ɉɫɨɛɟɧɧɨɫɬɶ ɫɨɫɬɨɢɬ ɜ ɬɨɦ, ɤɚɤ ɩɨɞɤɥɸɱɢɬɶ ɨɛɦɨɬɤɭ ɜɨɡɛɭɠɞɟɧɢɹ. ɉɪɢ ɢɡɦɟɧɟɧɢɢ ɩɨɥɹɪɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɩɨɬɨɤ ɦɚɲɢɧɵ ɧɟ ɞɨɥɠɟɧ ɦɟɧɹɬɶ ɧɚɩɪɚɜɥɟɧɢɹ, ɨɛɦɨɬɤɚ ɞɨɥɠɧɚ ɛɵɬɶ ɜɤɥɸɱɟɧɚ ɜ ɰɟɩɶ, ɝɞɟ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɧɟ ɦɟɧɹɟɬɫɹ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɟɟ ɦɟɫɬɨ – ɡɚ ɪɟɜɟɪɫɨɪɨɦ (ɪɢɫ. 3.34).ɉɪɢ ɜɤɥɸɱɟɧɢɢ Ʉȼ ɢ ɩɪɢ ɜɤɥɸɱɟɧɢɢ Ʉɇ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɢɡɦɟɧɹɟɬɫɹ, ɚ ɬɨɤ ɜ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟ ɢɡɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɹ, ɧɟ ɦɟɧɹɟɬ ɧɚɩɪɚɜɥɟɧɢɹ ɢ ɩɨɬɨɤ. ɉɪɢ ɪɚɛɨɬɟ ɞɜɢɝɚɬɟɥɹ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜ ɨɞɧɨɦ ɢɡ ɧɚɩɪɚɜɥɟɧɢɣ ɩɟɪɟɤɥɸɱɟɧɢɟɦ ɤɨɧɬɚɤɬɨɪɨɜ Ʉȼ ɢ Ʉɇ ɢɡɦɟɧɹɟɬɫɹ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ, ɚ ɨɬɤɥɸɱɟɧɢɟ ɤɨɧɬɚɤɬɨɪɚ Ʉɉȼ ɜɜɨɞɢɬ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɯɨɞɢɬ ɜ ɪɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ. ɏɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɟɪɟɯɨɞɚ ɜ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɞɥɹ ɬɨɪɦɨɠɟɧɢɹ ɧɚ ɜɵɛɟɝɟ ɩɪɢɜɟɞɟɧɵ ɧɚ ɪɢɫ. 3.34. Ⱦɨɫɬɨɢɧɫɬɜɚ ɢ ɧɟɞɨɫɬɚɬɤɢ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɩɨɞɪɨɛɧɨ ɪɚɫɫɦɨɬɪɟɧɵ ɜ ɪɚɡɞɟɥɟ 3.1.6.

			Ȧ
		U
Ʉȼ	Ʉɇ
		LɆ RȾɈȻ	ɉȼ
				Ɇ
	Ɇ			MC ɉȼ
		Ʉɉȼ
Ʉɇ	Ʉȼ

Ɋɢɫ. 3.34. ɋɯɟɦɚ Ⱦɉȼ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɪɟɠɢɦɚ ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ

Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ). ɇɚ ɩɪɚɤɬɢɤɟ ɩɪɢɦɟɧɹɸɬɫɹ ɞɜɟ ɫɯɟɦɵ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ:

–ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ;

–ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ.

85

ɚ) Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ ɜɵɩɨɥɧɹɟɬ-

ɫɹ ɩɨɞɤɥɸɱɟɧɢɟɦ ɨɛɦɨɬɤɢ ɜɨɡɛɭɠɞɟɧɢɹ ɤ ɨɬɞɟɥɶɧɨɦɭ ɢɫɬɨɱɧɢɤɭ ɩɢɬɚɧɢɹ. ȼ ɱɚɫɬɧɨɫɬɢ ɷɬɢɦ ɢɫɬɨɱɧɢɤɨɦ ɦɨɠɟɬ ɫɥɭɠɢɬɶ ɫɟɬɶ, ɤ ɤɨɬɨɪɨɣ ɨɛɦɨɬɤɚ ɩɨɞɤɥɸɱɚɟɬɫɹ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ. Ɍɚɤɚɹ ɫɯɟɦɚ ɩɨ ɫɜɨɢɦ ɦɟɯɚɧɢɱɟɫɤɢɦ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ ɩɨɜɬɨɪɹɟɬ ɫɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ.

ɇɚ ɪɢɫ. 3.35 ɩɪɢɜɟɞɟɧɚ ɫɯɟ-

ɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ

RȾɌ

ɄɌ

ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ. ȼ

LM

ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜɤɥɸɱɟɧ

ɄɅ

ɤɨɧɬɚɤɬɨɪ ɄɅ ɢ ɹɤɨɪɧɚɹ ɰɟɩɶ

Ɇ

ɩɨɞɤɥɸɱɟɧɚ ɤ ɫɟɬɢ. Ⱦɥɹ ɩɟɪɟɯɨ-

ɞɚ ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪ-

Rȼ

ɄɌ

ɦɨɠɟɧɢɹ ɨɬɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ

ɄɅ ɢ ɜɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɄɌ.

Ɉɛɦɨɬɤɚ

ɜɨɡɛɭɠɞɟɧɢɹ

ɤɨɧɬɚɤ-

Ɋɢɫ. 3.35. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ

ɬɨɦ ɄɌ

ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ

ɫɨ-

ɩɪɨɬɢɜɥɟɧɢɟ Rȼ ɩɨɞɤɥɸɱɚɟɬɫɹ ɤ

ɬɨɪɦɨɠɟɧɢɹ ɫ ɧɟɡɚɜɢɫɢɦɵɦ ɜɨɡɛɭɠɞɟɧɢɟɦ

ɫɟɬɢ. ɐɟɩɶ ɹɤɨɪɹ ɞɪɭɝɢɦ ɤɨɧɬɚɤ-

ɬɨɦ ɄɌ ɡɚɦɵɤɚɟɬɫɹ ɧɚ ɫɨɩɪɨ-

U

ɬɢɜɥɟɧɢɟ RȾɌ. ɉɨɫɥɟ ɩɟɪɟɤɥɸ-

ɱɟɧɢɹ

ɜɨ

ɜɪɚɳɚɸɳɟɦɫɹ

ɩɨ

RȾɌ ɄɌ

ɢɧɟɪɰɢɢ ɹɤɨɪɟ ɧɚɜɨɞɢɬɫɹ ɗȾɋ,

L

ɜɨɡɧɢɤɚɸɳɢɣ ɬɨɤ ɫɨɜɩɚɞɚɟɬ ɩɨ

ɄɅ

ɄɅ

Ɇ

ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɗȾɋ ɢ ɜɨ ɜɡɚɢ-

Ɇ

ɦɨɞɟɣɫɬɜɢɢ ɫ ɩɨɬɨɤɨɦ ɫɨɡɞɚɟɬ-

ɄɌ

ɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ.

ȼɟɥɢɱɢɧɚ ɩɨɬɨɤɚ ɡɚɜɢɫɢɬ ɨɬ

Ɋɢɫ. 3.36. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ

ɬɨɤɚ ɜ

ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ.

ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ

Ⱦɥɹ ɫɨɡɞɚɧɢɹ ɩɨɬɨɤɚ, ɛɥɢɡɤɨɝɨ ɤ

ɧɨɦɢɧɚɥɶɧɨɦɭ Ɏ § Ɏɇ,

ɩɨ ɨɛ-

ɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɧɟɨɛɯɨɞɢɦɨ ɩɪɨɩɭɫɬɢɬɶ ɧɨɦɢɧɚɥɶɧɵɣ ɬɨɤ ɞɜɢɝɚɬɟɥɹ Iɇ. Ɋɚɫɯɨɞ ɦɨɳɧɨɫɬɢ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɫɨɫɬɚɜɥɹɟɬ ~Ɋɇ (ɞɥɹ ɞɜɢɝɚɬɟɥɹ ɧɟɡɚɜɢɫɢɦɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ – 0,02…0,05 Ɋɇ). ɂɡ ɷɬɢɯ ɫɨɨɛɪɚɠɟɧɢɣ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɫɨɩɪɨɬɢɜɥɟɧɢɟ Rȼ = Uɇ / Iȼ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ ɩɨ ɡɚɞɚɧɧɨɦɭ ɧɚɱɚɥɶɧɨɦɭ ɬɨɪɦɨɡɧɨɦɭ ɦɨɦɟɧɬɭ.

Ⱦɨɫɬɨɢɧɫɬɜɚ ɢ ɧɟɞɨɫɬɚɬɤɢ ɪɚɫɫɦɨɬɪɟɧɵ ɩɨɞɪɨɛɧɨ ɜ ɩ. 3.1.6.

ɛ) Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ (ɪɢɫ.3.36) ɲɢɪɨɤɨ ɢɫ-

ɩɨɥɶɡɭɟɬɫɹ ɜ ɤɪɚɧɨɜɵɯ ɦɟɯɚɧɢɡɦɚɯ. ȼ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɜɤɥɸɱɟɧ ɤɨɧɬɚɤɬɨɪ ɄɅ ɢ ɹɤɨɪɧɚɹ ɰɟɩɶ ɩɨɞɤɥɸɱɟɧɚ ɤ ɫɟɬɢ. Ⱦɥɹ ɩɟɪɟɯɨɞɚ ɜ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɶ ɤɨɧɬɚɤɬɨɪɨɦ ɄɅ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ.

ȼɤɥɸɱɚɟɬɫɹ ɤɨɧɬɚɤɬɨɪ ɄɌ ɢ ɫɨɛɢɪɚɟɬɫɹ ɤɨɧɬɭɪ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. Ɉɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɤɨɧɬɚɤɬɚɦɢ ɄɌ ɱɟɪɟɡ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ RȾɌ ɫɨɟɞɢɧɹɟɬɫɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨ ɫ ɰɟɩɶɸ ɹɤɨɪɹ ɬɚɤɢɦ ɨɛɪɚɡɨɦ, ɱɬɨɛɵ ɧɚɩɪɚɜɥɟɧɢɟ ɬɨɤɚ ɜ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɫɨɜɩɚɥɨ ɫ ɧɚɩɪɚɜɥɟɧɢɟɦ ɬɨɤɚ ɜ ɩɪɟɞɵɞɭɳɟɦ ɪɟɠɢɦɟ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɨɫɬɚɬɨɱɧɨɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɞɜɢɝɚɬɟɥɹ. Ⱦɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɜ ɪɟɠɢɦ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ.

86

ɍɫɥɨɜɢɹ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɝɟɧɟɪɚɬɨɪɚ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ:

1.ɇɚɥɢɱɢɟ ɨɫɬɚɬɨɱɧɨɝɨ ɩɨɬɨɤɚ ɎɈɋɌ.

2.Ɍɨɤ, ɜɨɡɧɢɤɚɸɳɢɣ ɜ ɰɟɩɢ, ɞɨɥɠɟɧ ɫɨɡɞɚɜɚɬɶ ɩɨɬɨɤ, ɫɨɜɩɚɞɚɸɳɢɣ ɩɨ ɧɚ-

ɩɪɚɜɥɟɧɢɸ ɫ ɎɈɋɌ.

3. ɗȾɋ, ɧɚɜɨɞɢɦɚɹ ɜ ɞɜɢɝɚɬɟɥɟ ɞɨɥɠɧɚ ɛɵɬɶ ɛɨɥɶɲɟ ɩɚɞɟɧɢɹ ɧɚɩɪɹɠɟɧɢɹ ɜ ɰɟɩɢ ɹɤɨɪɹ

ȿ > I (rə + rɈȼ + RȾɌ).

ɉɪɢ ɜɵɩɨɥɧɟɧɢɢ ɷɬɢɯ ɭɫɥɨɜɢɣ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟ ɩɪɨɢɫɯɨɞɢɬ ɫɥɟɞɭɸɳɢɦ ɨɛɪɚɡɨɦ. Ɉɫɬɚɬɨɱɧɨɟ ɧɚɦɚɝɧɢɱɢɜɚɧɢɟ ɞɜɢɝɚɬɟɥɹ ɎɈɋɌ ɩɪɢ ɜɪɚɳɟɧɢɢ ɹɤɨɪɹ ɧɚɜɨɞɢɬ ɗȾɋ ȿɈɋɌ (ɪɢɫ. 3.37), ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɤɨɬɨɪɨɣ ɩɨ ɹɤɨɪɸ ɢ ɨɛɦɨɬɤɟ ɜɨɡɛɭɠɞɟɧɢɹ ɩɪɨɬɟɤɚɟɬ ɬɨɤ I1. ɗɬɨɬ ɬɨɤ ɫɨɡɞɚɺɬ ɨɫɧɨɜɧɨɣ ɦɚɝɧɢɬɧɵɣ ɩɨɬɨɤ Ɏ, ɤɨɬɨɪɵɣ, ɫɨɜɩɚɞɚɹ ɩɨ ɧɚɩɪɚɜɥɟɧɢɸ ɫ ɨɫɬɚɬɨɱɧɵɦ ɩɨɬɨɤɨɦ, ɩɪɢɜɟɞɺɬ ɤ ɭɜɟɥɢɱɟɧɢɸ ɗȾɋ ɞɨ ȿ1. ɗɬɨ ɜ ɫɜɨɸ ɨɱɟɪɟɞɶ ɩɨɜɥɟɱɺɬ ɡɚ ɫɨɛɨɣ ɭɜɟɥɢɱɟɧɢɟ ɬɨɤɚ ɞɨ I2. Ɍɚɤɨɣ ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɛɭɞɟɬ ɩɪɨɞɨɥɠɚɬɶɫɹ ɞɨ ɬɟɯ ɩɨɪ, ɩɨɤɚ ɗȾɋ ɧɟ ɫɪɚɜɧɹɟɬɫɹ ɫ ɫɭɦɦɚɪɧɵɦ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɰɟɩɢ ɹɤɨɪɹ

ȿ= I (rə + rɈȼ + RȾɌ)

ɜɬɨɱɤɟ ɭɫɬɚɧɨɜɢɜɲɟɝɨɫɹ ɪɟɠɢɦɚ ɪɚɛɨɬɵ.

ɍɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɡɚɜɢɫɢɬ ɨɬ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ ɢ ɨɬ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɹɤɨɪɧɨɣ ɰɟɩɢ. ɉɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ R1 ɭɫɬɚɧɨɜɢɜɲɢɣɫɹ ɪɟɠɢɦ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɬɨɱɤɚɦ 1,2,3 ɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ I R1. ɍɜɟɥɢɱɟɧɢɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R2 > R1 ɩɪɢɜɨɞɢɬ ɤ ɭɦɟɧɶɲɟɧɢɸ ɬɨɤɚ ɢ ɦɨɦɟɧɬɚ, ɭɫɬɚɧɨɜɢɜɲɢɟɫɹ ɪɟɠɢɦɵ ɩɟɪɟɯɨɞɹɬ ɜ ɬɨɱɤɢ 4,5 ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ IR2. Ɉɛɪɚɬɢɬɟ ɜɧɢɦɚɧɢɟ, ɱɬɨ ɩɪɢ ɫɨɩɪɨɬɢɜɥɟɧɢɢ R2 ɢ ɫɤɨɪɨɫɬɢ Ȧ3 < Ȧ2 ɧɟ ɩɪɨɢɫɯɨɞɢɬ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ, ɬɨɤ ɧɟ ɩɪɨɬɟɤɚɟɬ, ɦɨɦɟɧɬ ɨɬɫɭɬɫɬɜɭɟɬ, ɬɨɪɦɨɠɟɧɢɟ ɧɟ ɨɛɟɫɩɟɱɢɜɚɟɬɫɹ. Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɧɚɱɢɧɚɟɬɫɹ ɧɟ ɫ ɧɭɥɟɜɨɣ, ɚ ɫ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨɫɬɢ (ɫɦ. ɪɢɫ. 3.37). Ɇɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɥɭɱɚɸɬɫɹ ɧɟɥɢɧɟɣɧɵɦɢ. Ʉɚɠɞɨɦɭ ɫɨɩɪɨɬɢɜɥɟɧɢɸ R ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɜɨɹ ɤɪɢɬɢɱɟɫɤɚɹ ɫɤɨɪɨɫɬɶ ȦɄɊ.

ȿ IR	IR2	IR1		Ȧ
		Ȧ1		ȦɄɊ1
ȿ2		1		ȦɄɊ2
	5	Ȧ2
ȿ1		2		ȦɄɊ3	Ɇ
	4	Ȧ3		Ɇɋ
	3
ȿɈɋɌ
			I	2
I1		I2		1

Ɋɢɫ. 3.37. ɉɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ ɢ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ

ȿɫɥɢ ɫɨɛɪɚɬɶ ɫɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɩɪɢ ɫɩɭɫɤɟ ɝɪɭɡɚ, ɬɨ ɩɨɫɥɟ ɨɬɩɭɫɤɚ ɬɨɪɦɨɡɚ ɝɪɭɡ ɛɭɞɟɬ ɩɚɞɚɬɶ ɞɨ ɤɪɢɬɢɱɟɫɤɨɣ ɫɤɨɪɨ

87

ɫɬɢ, ɩɪɢ ɤɨɬɨɪɨɣ ɧɚɱɧɟɬɫɹ ɩɪɨɰɟɫɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɹ, ɜɨɡɧɢɤɧɟɬ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ, ɢ ɤɪɚɧ ɢɫɩɵɬɚɟɬ ɞɢɧɚɦɢɱɟɫɤɢɣ ɭɞɚɪ. ɗɬɨɬ ɧɟɞɨɫɬɚɬɨɤ ɤɨɦɩɟɧɫɢɪɭɟɬɫɹ ɜɨɡɦɨɠɧɨɫɬɶɸ ɫɩɭɫɤɚ ɝɪɭɡɚ ɩɪɢ ɫɧɹɬɢɢ ɧɚɩɪɹɠɟɧɢɹ ɩɢɬɚɧɢɹ ɤɪɚɧɚ. Ɍɚɤɨɣ ɜɢɞ ɬɨɪɦɨɠɟɧɢɹ ɦɨɠɟɬ ɢɫɩɨɥɶɡɨɜɚɬɶɫɹ ɤɚɤ ɚɜɚɪɢɣɧɵɣ. ɋɯɟɦɭ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɫ ɫɚɦɨɜɨɡɛɭɠɞɟɧɢɟɦ ɱɚɫɬɨ ɧɚɡɵɜɚɸɬ ɫɯɟɦɨɣ ɛɟɡɨɩɚɫɧɨɝɨ ɫɩɭɫɤɚ.

3.2.4. Ɋɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ Ⱦɉȼ

Ɋɚɫɱɟɬ ɟɫɬɟɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. ɇɟɥɢɧɟɣɧɚɹ ɡɚɜɢɫɢɦɨɫɬɶ Ɏ = f (I)

ɩɪɟɞɨɩɪɟɞɟɥɹɟɬ ɪɚɫɱɟɬ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɦ ɦɟɬɨɞɨɦ.

Ⱦɥɹ ɪɚɫɱɺɬɚ ɢɫɩɨɥɶɡɭɸɬɫɹ ɤɚɬɚɥɨɠɧɵɟ ɞɚɧɧɵɟ ɞɜɢɝɚɬɟɥɹ: PH, UH, IH, nH, Șɇ, JȾȼ ɢ ɤɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ: n, P, M, Ș = f (I). ɉɪɟɞɜɚɪɢɬɟɥɶɧɨ ɫɥɟɞɭɟɬ ɩɟɪɟɜɟɫɬɢ ɜ ɫɢɫɬɟɦɭ ɋɂ ɡɧɚɱɟɧɢɹ ɫɤɨɪɨɫɬɢ ɢɡ ɨɛ/ɦɢɧ ɜ ɪɚɞ/ɫ (Ȧ = n / 9,55) ɢ ɦɨɦɟɧɬɚ ɢɡ ɤȽɦ ɜ ɇɦ (Ɇ = ɆɄȺɌ ǜ9,81).

			ȿɫɬɟɫɬɜɟɧɧɚɹ				ɷɥɟɤ-
			ɬɪɨɦɟɯɚɧɢɱɟɫɤɚɹ				ɯɚɪɚɤ-
			ɬɟɪɢɫɬɢɤɚ ɩɪɟɞɫɬɚɜɥɟɧɚ
Ȧ Ɇ
			ɤɚɬɚɥɨɠɧɨɣ		ɯɚɪɚɤɬɟɪɢ-
	ɆɌ		ɫɬɢɤɨɣ n (I).		ɋ ɩɨɦɨɳɶɸ
		ɆɗɆ						ɯɚ-
			ɞɪɭɝɨɣ	ɤɚɬɚɥɨɠɧɨɣ
			ɪɚɤɬɟɪɢɫɬɢɤɢ ɆɄȺɌ = f (I)
ȦɄȺɌ							ɦɟɯɚɧɢ-
			ɪɚɫɫɱɢɬɵɜɚɟɬɫɹ
			ɱɟɫɤɚɹ	ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ
		ɆɄȺɌ	Ȧ = f(Ɇ). Ɂɚɞɚɸɬɫɹ ɬɨɤɨɦ
	ǻɆ
ȦȿɋɌ			IɁȺȾ, ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢ-
Ȧ1			ɜɨɣ Ȧ(I)	ɝɪɚɮɢɱɟɫɤɢ ɨɩ-
								(ɪɢɫ.
			ɪɟɞɟɥɹɸɬ		ȦȿɋɌ
Ɇȼ			3.38), ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɡɚ-
		I	ɜɢɫɢɦɨɫɬɢ		ɆɄȺɌ(I)			–
Ɇȼ			ɡɧɚɱɟɧɢɟ Ɇȼ.
IɁȺȾ	IɁȺȾ1		Ɇɟɯɚɧɢɱɟɫɤɢɟ				ɯɚɪɚɤ-
			ɬɟɪɢɫɬɢɤɢ		ɞɜɢɝɚɬɟɥɟɣ
			ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ Ȧ = f(M)
Ɋɢɫ. 3.38. Ʉɚɬɚɥɨɠɧɵɟ ɤɪɢɜɵɟ ȦɄȺɌ(I), ɆɄȺɌ(I)			ɫɬɪɨɹɬɫɹ	ɞɥɹ		ɷɥɟɤɬɪɨ-
			ɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ ɆɗɆ.
ɢ ɪɚɫɱɟɬ ɆɗɆ(I) ɢ ɆɌ(I)						ɯɚɪɚɤɬɟ-
			ɇɚ ɤɚɬɚɥɨɠɧɵɯ
			ɪɢɫɬɢɤɚɯ		ɩɪɢɜɨɞɢɬɫɹ
			ɡɧɚɱɟɧɢɟ ɦɨɦɟɧɬɚ ɧɚ ɜɚ-

ɥɭ ɆɄȺɌ = Ɇȼ = f (I).

ɋɯɟɦɚ ɪɚɫɱɟɬɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ Ȧ = f (MɗɆ ):

–ɡɚɞɚɸɬɫɹ ɬɨɤɨɦ IɁȺȾ1;

–ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢɜɨɣ Ȧ (I) ɨɩɪɟɞɟɥɹɸɬ Ȧ1;

–ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɤɪɢɜɨɣ Ɇȼ (I) – ɡɧɚɱɟɧɢɟ Ɇȼ;

–ɨɩɪɟɞɟɥɹɸɬ ɜɟɥɢɱɢɧɭ

kɎɁȺȾ	UH IɁȺȾ1 rə rOB	;
	Ȧ1

88

– ɪɚɫɫɱɢɬɵɜɚɸɬ ɡɧɚɱɟɧɢɟ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɝɨ ɦɨɦɟɧɬɚ

MɗɆ kɎɁȺȾ IɁȺȾ1;

– ɩɨɥɭɱɚɸɬ ɤɨɨɪɞɢɧɚɬɵ ɨɞɧɨɣ ɬɨɱɤɢ ɆɗɆ, Ȧ1.

Ⱦɚɥɟɟ ɪɚɫɫɱɢɬɵɜɚɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɧɟɫɤɨɥɶɤɢɯ ɬɨɱɟɤ ɢ ɫɬɪɨɢɬɫɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ.

Ⱦɥɹ ɞɚɥɶɧɟɣɲɢɯ ɪɚɫɱɟɬɨɜ ɩɨɥɟɡɧɨ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɆɗɆ(I). Ɋɚɡɧɨɫɬɶ ǻɆ = ɆɗɆ – Ɇȼ ɩɪɟɞɫɬɚɜɥɹɟɬ ɩɨɬɟɪɢ ɦɨɦɟɧɬɚ ɜ ɞɜɢɝɚɬɟɥɟ.

ȼ ɬɨɪɦɨɡɧɨɦ ɪɟɠɢɦɟ ɪɚɛɨɬɵ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ɩɨɤɪɵɜɚɸɬɫɹ ɫɨ ɫɬɨɪɨɧɵ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ. Ɇɨɠɧɨ ɩɨɫɬɪɨɢɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ

ɆɌ I MɗɆ ǻM,

ɩɨɡɜɨɥɹɸɳɭɸ ɪɚɫɫɱɢɬɵɜɚɬɶ ɬɨɤɢ ɹɤɨɪɹ ɜ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɵɯ ɬɨɱɤɚɯ.

Ɋɚɫɱɟɬ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ. Ⱦɥɹ ɪɚɫɱɟɬɚ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤ-

ɬɟɪɢɫɬɢɤ ɬɚɤɠɟ ɢɫɩɨɥɶɡɭɟɬɫɹ ɝɪɚɮɨɚɧɚɥɢɬɢɱɟɫɤɢɣ ɦɟɬɨɞ ɪɚɫɱɟɬɚ, ɬɚɤ ɤɚɤ ɨɬɫɭɬɫɬɜɭɟɬ ɚɧɚɥɢɬɢɱɟɫɤɨɟ ɜɵɪɚɠɟɧɢɟ ɤɪɢɜɨɣ ɧɚɦɚɝɧɢɱɢɜɚɧɢɹ.

Ȧ U M R .

kɎ I kɎ I 2

Ɂɚɞɚɜɚɹɫɶ ɩɨɫɬɨɹɧɧɵɦ ɡɧɚɱɟɧɢɟɦ ɬɨɤɚ IɁȺȾ =const, ɩɨɥɭɱɚɟɦ ɢ ɩɨɫɬɨɹɧɧɨɟ ɡɧɚɱɟɧɢɟ ɩɨɬɨɤɚ kɎɁȺȾ = const. ɉɪɢ ɩɨɫɬɨɹɧɧɨɦ ɩɨɬɨɤɟ ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɗȾɋ

	ȿȿɋɌ		Uɇ IɁȺȾ	rə		;
ȦȿɋɌ	kɎɁȺȾ		kɎɁȺȾ
	ȿɂɋɄ		U IɁȺȾ R
ȦɂɋɄ					,
	kɎɁȺȾ		kɎɁȺȾ

ɬɨɝɞɚ ɫɤɨɪɨɫɬɶ ɧɚ ɢɫɤɭɫɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɪɢ ɡɚɞɚɧɧɵɯ ɡɧɚɱɟɧɢɹɯ U ɢ R ɦɨɠɧɨ ɪɚɫɫɱɢɬɚɬɶ ɩɨ ɮɨɪɦɭɥɟ

			U IɁȺȾ R	.	(3.50)
ȦɂɋɄ	ȦȿɋɌ
			Uɇ IɁȺȾ rə

ɉɨ ɞɚɧɧɵɦ ɫɨɨɬɧɨɲɟɧɢɹɦ ɦɨɠɧɨ ɪɚɫɫɱɢɬɵɜɚɬɶ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɥɸɛɵɯ ɪɟɠɢɦɚɯ ɪɚɛɨɬɵ (ɞɜɢɝɚɬɟɥɶɧɨɦ, ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ).

Ɋɚɫɱɟɬ ɫɯɟɦ ɜɤɥɸɱɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ. Ɋɟɲɟɧɢɟ ɨɫɧɨɜɧɨɣ ɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɡɚɞɚɱɢ – ɨɛɟɫɩɟɱɢɬɶ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ – ɜɵɩɨɥɧɹɟɬɫɹ ɫ ɩɨɦɨɳɶɸ ɮɨɪɦɭɥɵ (3.50). ɋɨ ɫɬɨɪɨɧɵ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɜɵɫɬɚɜɥɹɸɬɫɹ ɤɨɨɪɞɢɧɚɬɵ ɡɚɞɚɧɧɨɣ ɬɨɱɤɢ: ɆɁȺȾ, ȦɁȺȾ.

ȼ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɩɨ ɪɚɫɫɱɢɬɚɧɧɵɦ ɪɚɧɟɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦ Ɇȼ(I) – ɞɥɹ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɢɥɢ ɆɌ(I) – ɞɥɹ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ ɩɨ ɆɁȺȾ ɨɩɪɟɞɟɥɹɸɬ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɹɤɨɪɹ IɁȺȾ. ɉɨ ɟɫɬɟɫɬɜɟɧɧɨɣ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢ-

ɫɬɢɤɟ Ȧ(I) ɩɨ ɬɨɤɭ IɁȺȾ ɧɚɯɨɞɹɬ ȦȿɋɌ. ɉɨɞɫɬɚɜɥɹɹ ɜ 3.50 ȦȿɋɌ, IɁȺȾ, ȦɂɋɄ = ȦɁȺȾ, ɨɩɪɟɞɟɥɹɸɬ ɬɪɟɛɭɟɦɨɟ ɡɧɚɱɟɧɢɟ U ɢɥɢ R ɜ ɡɚɜɢɫɢɦɨɫɬɢ ɨɬ ɫɯɟɦɵ ɜɤɥɸɱɟɧɢɹ. ɉɪɢ

ɪɟɲɟɧɢɢ ɡɚɞɚɱɢ ɫɥɟɞɭɟɬ ɨɛɪɚɬɢɬɶ ɨɫɨɛɨɟ ɜɧɢɦɚɧɢɟ ɧɚ ɡɧɚɤɢ ɦɨɦɟɧɬɚ, ɫɤɨɪɨɫɬɢ,

89

ɧɚɩɪɹɠɟɧɢɹ ɞɥɹ ɪɚɛɨɬɵ ɜ ɪɚɡɥɢɱɧɵɯ ɪɟɠɢɦɚɯ ɢ ɪɚɡɥɢɱɧɵɯ ɤɜɚɞɪɚɧɬɚɯ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.

ɉɪɢɦɟɪ 3.6. Ɋɚɫɫɱɢɬɚɬɶ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɩɨɫɥɟɞɨɜɚɬɟɥɶɧɨɝɨ ɜɨɡɛɭɠɞɟɧɢɹ ɬɢɩɚ Ⱦ32 (Ɋɇ = 9,5 ɤȼɬ,

Iɇ= 53 Ⱥ, Uɇ = 220 ȼ, nɇ = 760 ɨɛ/ɦɢɧ, ɆɆȺɄɋ = 677 ɇɦ, rɈə = 0,2 Ɉɦ, rȾɉ = 0,08 Ɉɦ, rɈȼ = 0,0972 Ɉɦ) ɜ ɬɨɱɤɚɯ ɆɁȺȾ = 0,8; ȦɁȺȾ= +/- 0,4.

ȼɨɫɩɨɥɶɡɭɟɦɫɹ ɤɚɬɚɥɨɠɧɵɦɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɦɢ Ɇ(I) ɢ n(I) ɞɜɢɝɚɬɟɥɹ ɢ ɫɜɟɞɟɦ ɢɯ ɜ ɬɚɛɥɢɰɭ 3.2.1.

ɉɟɪɟɜɟɞɟɦ ɱɢɫɥɨɜɵɟ ɡɧɚɱɟɧɢɹ ɜ ɫɢɫɬɟɦɭ ɋɂ:

Ɇɇ ɦ 9,81 Ɇ ɤȽɦ ; Ȧ ɪɚɞ ɫ n ɨɛɦɢɧ . 9,55

Ɋɚɫɫɱɢɬɚɟɦ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɵɟ ɦɨɦɟɧɬɵ ɆɗɆ = k Ɏ I. ȼɵɩɨɥɧɢɦ ɪɚɫɱɟɬ ɞɥɹ ɨɞɧɨɣ ɬɨɱɤɢ. Ɂɚɞɚɟɦɫɹ ɬɨɤɨɦ I = Iɇ = 53 Ⱥ, ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ Ȧ(I) ɨɩɪɟɞɟɥɹɟɦ

		ȦȿɋɌ		Ȧɇ 79,6ɪɚɞ ɫ,
ɨɩɪɟɞɟɥɹɟɦ ɤɎ ɩɨ ɮɨɪɦɭɥɟ:
kɎ		UH I rə			220 53 0,377		2,5 ȼɫ ,
		ȦȿɋɌ		79,6
ɝɞɟ
rə rɈȼ rȾɉ rɈə				0,0972 0,08 0,2			0,377 Ɉɦ.
ɗɥɟɤɬɪɨɦɚɝɧɢɬɧɵɣ ɦɨɦɟɧɬ ɩɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ
	ɆɗɆ kɎ I				2,5 53 132,5 ɇ ɦ.
Ɇɨɦɟɧɬ ɩɨɫɬɨɹɧɧɵɯ ɩɨɬɟɪɶ
ǻɆ		ɆɗɆ Ɇȼ			132,5 120 12,5 ɇ ɦ,

ɝɞɟ Ɇȼ ɜɡɹɬ ɩɨ ɤɚɬɚɥɨɠɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ Ɇȼ(I) ɩɪɢ IɁȺȾ= 53 Ⱥ. Ɍɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɧɚ ɜɚɥɭ ɩɪɢ ɡɚɞɚɧɧɨɦ ɬɨɤɟ ɹɤɨɪɹ

ɆɌ ɆɗɆ ǻɆ 132,5 12,5 145 ɇ ɦ.

ɉɨ ɬɚɤɨɣ ɫɯɟɦɟ ɪɚɫɫɱɢɬɵɜɚɸɬ ɞɪɭɝɢɟ ɬɨɱɤɢ (ɫɦ. ɬɚɛɥ. 3.2) ɢ ɫɬɪɨɢɬɫɹ ɡɚɜɢɫɢɦɨɫɬɶ ɆɌ(I).

ɉɨ ɡɚɞɚɧɧɨɣ ɜɟɥɢɱɢɧɟ ɦɨɦɟɧɬɚ ɆɁȺȾ ɝɪɚɮɢɱɟɫɤɢ ɩɨ Ɇȼ (I) ɢɥɢ ɆɌ (I) ɨɩɪɟɞɟɥɹɸɬ ɬɨɤ ɹɤɨɪɹ IɁȺȾ, ɩɪɢ ɷɬɨɦ ɡɧɚɱɟɧɢɢ ɬɨɤɚ ɩɨɬɨɤ ɧɚ ɜɫɟɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ ɩɨɫɬɨɹɧɟɧ, ɚ ɨɬɧɨɲɟɧɢɟ ɫɤɨɪɨɫɬɟɣ ɪɚɜɧɨ ɨɬɧɨɲɟɧɢɸ ɗȾɋ. Ɋɟɲɚɹ ɭɪɚɜɧɟɧɢɟ (3.50) ɨɬɧɨɫɢɬɟɥɶɧɨ U ɢɥɢ R, ɩɨɥɭɱɚɟɦ ɧɟɨɛɯɨɞɢɦɵɣ ɩɚɪɚɦɟɬɪ.

Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɆɁȺȾ 0,8 ɢ ȦɁȺȾ 0,4 ɜɜɟɞɟɧɢɟɦ

ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɜ ɰɟɩɶ ɹɤɨɪɹ RȾɈȻ ɨɩɪɟɞɟɥɢɦ ɡɧɚɱɟɧɢɹ ɩɚɪɚɦɟɬɪɨɜ ɜ ɚɛɫɨɥɸɬɧɵɯ ɟɞɢɧɢɰɚɯ.

Ɇɨɦɟɧɬ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɨɛɵɱɧɨ ɹɜɥɹɟɬɫɹ ɦɨɦɟɧɬɨɦ ɧɚ ɜɚɥɭ.

			ɁȺȾ Ɇȼɇ	0,8 Ɋɇ		0,8 9500	0,8 119,35 95,5 ɇɦ.
	ɆɁȺȾ	Ɇ
					79,6
				Ȧɇ

90