EP / Теория ЭП Драчев

ɉɪɢ ɧɨɪɦɚɥɶɧɨɦ ɩɭɫɤɟ ɡɚɞɚɸɬɫɹ ɦɨɦɟɧɬɨɦ ɩɟɪɟɤɥɸɱɟɧɢɹ Ɇ2 ~ 1,2 Ɇɋ ɢ ɪɚɫɱɟɬ ɜɵɩɨɥɧɹɸɬ ɩɨ ɮɨɪɦɭɥɟ

	M1	m 1	1	,	(3.30)
Ȝ	M2		I2 rə

ɚ ɞɚɥɶɧɟɣɲɢɣ ɪɚɫɱɟɬ ɚɧɚɥɨɝɢɱɟɧ ɩɪɟɞɵɞɭɳɟɦɭ ɚɧɚɥɢɬɢɱɟɫɤɨɦɭ. ɇɟɨɛɯɨɞɢɦɨ ɥɢɲɶ ɩɪɨɜɟɪɢɬɶ ɜɟɥɢɱɢɧɭ Ɇ1 d ɆɆȺɄɋ ȾɈɉ, ɱɬɨɛɵ ɦɚɤɫɢɦɚɥɶɧɨɟ ɡɧɚɱɟɧɢɟ ɬɨɤɚ ɧɟ ɩɪɟɜɨɫɯɨɞɢɥɨ ɞɨɩɭɫɬɢɦɨɟ ɡɧɚɱɟɧɢɟ ɩɨ ɭɫɥɨɜɢɹɦ ɤɨɦɦɭɬɚɰɢɢ.

3.1.7. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ Ⱦɇȼ

ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɩɪɢɡɜɚɧɚ ɧɚɝɥɹɞɧɨ ɩɨɤɚɡɚɬɶ ɩɨɬɪɟɛɥɹɟɦɭɸ ɢɡ ɫɟɬɢ ɢ ɩɨɥɟɡɧɭɸ ɧɚ ɜɚɥɭ ɦɨɳɧɨɫɬɢ ɢ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɩɪɨɰɟɫɫɟ ɷɥɟɤɬɪɨɦɟɯɚɧɢɱɟɫɤɨɝɨ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɢ ɩɨɤɚɡɚɬɶ ɢɯ ɫɨɨɬɧɨɲɟɧɢɟ.

Ɋɚɫɫɦɨɬɪɢɦ ɞɜɢɝɚɬɟɥɶɧɵɣ ɪɟɠɢɦ ɪɚɛɨɬɵ (Ɇ > 0, Ȧ > 0).

ɇɚɩɪɹɠɟɧɢɟ, ɩɪɢɥɨɠɟɧɧɨɟ ɤ ɹɤɨɪɸ ɞɜɢɝɚɬɟɥɹ, ɭɪɚɜɧɨɜɟɲɢɜɚɟɬɫɹ ɗȾɋ ɢ ɩɚɞɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɚɤɬɢɜɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ.

U	E I rə RȾɈȻ .
ɍɦɧɨɠɢɦ ɨɛɟ ɱɚɫɬɢ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɧɚ ɬɨɤ ɹɤɨɪɹ I
U I	E I I2 rə I2 RȾɈȻ,	(3.31)

ɝɞɟ U I = Ɋɋ – ɦɨɳɧɨɫɬɶ, ɩɨɬɪɟɛɥɹɟɦɚɹ ɢɡ ɫɟɬɢ;

I2 rə = 'Ɋə – ɩɨɬɟɪɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ ɜ ɧɟɜɵɤɥɸɱɚɟɦɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɹɤɨɪɹ;

I2 RȾɈȻ = ǻɊȾɈȻ – ɩɨɬɟɪɢ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ ɜ ɞɨɛɚɜɨɱɧɨɦ ɫɨɩɪɨɬɢɜɥɟɧɢɢ ɹɤɨɪɹ;

E I = (kɎɇ Ȧ) (M / kɎɇ) = Ɇ Ȧ = ɊɆ – ɦɟɯɚɧɢɱɟɫɤɚɹ (ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɚɹ) ɦɨɳɧɨɫɬɶ;

Ɋȼ – ɩɨɥɟɡɧɚɹ ɦɨɳɧɨɫɬɶ (ɧɚ ɜɚɥɭ ɞɜɢɝɚɬɟɥɹ); ǻɊɆȿɏ – ɩɨɬɟɪɢ ɦɟɯɚɧɢɱɟɫɤɨɣ ɦɨɳɧɨɫɬɢ (ɜɧɭɬɪɢ ɞɜɢɝɚɬɟɥɹ – ɧɚ ɬɪɟɧɢɟ ɜ

ɩɨɞɲɢɩɧɢɤɚɯ, ɧɚ ɜɟɧɬɢɥɹɰɢɸ, ɧɚ ɩɟɪɟɦɚɝɧɢɱɢɜɚɧɢɟ ɜ ɫɬɚɥɢ ɹɤɨɪɹ).

Ɉɛɵɱɧɨ ɫɱɢɬɚɸɬ ǻɊɆȿɏ § const, ɧɟ ɡɚɜɢɫɹɳɢɦɢ ɨɬ ɧɚɝɪɭɡɤɢ. Ɉɰɟɧɤɭ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɩɪɟɨɛɪɚɡɨɜɚɧɢɹ ɷɧɟɪɝɢɢ ɜɵɩɨɥɧɹɸɬ ɫ ɩɨɦɨɳɶɸ ɤɨɷɮɮɢɰɢɟɧɬɚ ɩɨɥɟɡɧɨɝɨ ɞɟɣɫɬɜɢɹ ɄɉȾ Ș =

ȘɊɉɈɅ / ɊɁȺɌɊ, ɱɢɫɥɟɧɧɨ ɪɚɜ-

						ɧɨɝɨ	ɨɬɧɨɲɟɧɢɸ			ɦɨɳɧɨ-
				Șɇ		ɫɬɢ ɩɨɥɟɡɧɨɣ ɊɉɈɅ ɤ ɦɨɳ-
	Ɋȼ
ɊɆ
						ɧɨɫɬɢ ɡɚɬɪɚɱɟɧɧɨɣ ɊɁȺɌɊ.
Ɋɋ
						ɇɚ ɪɢɫ. 3.15 ɩɪɢɜɟɞɟɧɚ
		ǻPɆȿɏ				ɡɚɜɢɫɢɦɨɫɬɶ			Ș =	f(PɉɈɅ),
ǻPȾɈȻ						ɩɨɫɬɪɨɟɧɧɚɹ			ɩɪɢ	ɪɚɛɨɬɟ
								ɧɚ ɟɫɬɟɫɬɜɟɧ-
ǻPə					Ɋ	ɞɜɢɝɚɬɟɥɹ
						ɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ.
					Ɋɇ
						ɉɪɢ			ɧɨɦɢɧɚɥɶɧɨɣ
Ɋɢɫ. 3.15. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ						ɦɨɳɧɨɫɬɢ Șɇ = 0.75…0.95,
ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ Ⱦɇȼ						ɩɪɢ	ɭɜɟɥɢɱɟɧɢɢ			ɧɨɦɢ-
						ɧɚɥɶɧɨɣ		ɦɨɳɧɨɫɬɢ Ɋɇ

61

ɞɜɢɝɚɬɟɥɹ ɄɉȾ ɪɚɫɬɟɬ. ɉɪɢ ɧɚɪɚɫɬɚɧɢɢ ɧɚɝɪɭɡɤɢ ɊɉɈɅ ɧɚ ɜɚɥɭ ɄɉȾ ɪɚɫɬɟɬ ɜ ɫɜɹɡɢ ɫ ɪɨɫɬɨɦ ɩɨɥɟɡɧɨɣ ɦɨɳɧɨɫɬɢ, ɩɪɢ ɊɉɈɅ § Ɋɇ ɄɉȾ ɞɨɫɬɢɝɚɟɬ ɦɚɤɫɢɦɭɦɚ, ɩɪɢ ɞɚɥɶɧɟɣɲɟɦ ɪɨɫɬɟ ɊɉɈɅ ɄɉȾ ɫɧɢɠɚɟɬɫɹ ɜ ɫɜɹɡɢ ɫ ɭɜɟɥɢɱɟɧɢɟɦ ɩɨɬɟɪɶ ɦɨɳɧɨɫɬɢ ɜɧɭɬɪɢ ɦɚɲɢɧɵ.

3.1.8. Ɍɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ Ⱦɇȼ

Ɍɨɪɦɨɡɧɵɦ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ ɪɚɛɨɬɵ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɪɟɜɪɚɳɚɟɬ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɩɟɪɟɜɨɞɢɬɫɹ ɜ ɝɟɧɟɪɚɬɨɪɧɵɣ ɪɟɠɢɦ. ɂɫɬɨɱɧɢɤɚɦɢ ɢɡɛɵɬɨɱɧɨɣ ɦɟɯɚɧɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɹɜɥɹɸɬɫɹ ɩɨɬɟɧɰɢɚɥɶɧɚɹ ɷɧɟɪɝɢɹ, ɡɚɩɚɫɟɧɧɚɹ ɩɨɞɧɹɬɵɦ ɝɪɭɡɨɦ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ ɢɥɢ ɞɜɢɠɭɳɢɦɫɹ ɩɨɞ ɭɤɥɨɧ ɬɪɚɧɫɩɨɪɬɧɵɦ ɦɟɯɚɧɢɡɦɨɦ, ɢ ɢɡɛɵɬɨɱɧɚɹ ɤɢɧɟɬɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ, ɫɨɡɞɚɜɚɟɦɚɹ ɩɪɢ ɫɧɢɠɟɧɢɢ ɫɤɨɪɨɫɬɢ ɞɜɢɠɭɳɢɦɢɫɹ ɢɧɟɪɰɢɨɧɧɵɦɢ ɦɚɫɫɚɦɢ.

ɋɬɟɯɧɨɥɨɝɢɱɟɫɤɨɣ ɬɨɱɤɢ ɡɪɟɧɢɹ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ:

–ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɫɩɭɫɤɟ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɩɨɞɞɟɪɠɚɧɢɟ ɫɤɨɪɨɫɬɢ ɞɜɢɝɚɬɟɥɹ

ɢɦɟɯɚɧɢɡɦɚ ɩɪɢ ɞɜɢɠɟɧɢɢ ɧɚ ɫɩɭɫɤɟ (ɞɟɣɫɬɜɢɬɟɥɶɧɨ ɞɥɹ ɚɤɬɢɜɧɨɝɨ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ);

–ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ ɩɪɢɜɨɞɚ, ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɡɚɞɚɧɧɨɟ ɜɪɟɦɹ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ (Ɍȼ).

ɋɬɨɱɤɢ ɡɪɟɧɢɹ ɩɨɬɪɟɛɥɟɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɪɚɫɫɦɚɬɪɢɜɚɸɬ ɬɨɪɦɨɡɧɵɟ ɪɟɠɢɦɵ:

–ɪɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ), ɩɪɢ ɤɨɬɨɪɨɦ ɢɡɛɵɬɨɱɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ ɜ ɫɟɬɶ;

–ɬɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ), ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɩɨɥɭɱɚɟɬ ɫ ɜɚɥɚ, ɩɪɟɨɛɪɚɡɭɟɬ ɟɟ ɜ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ. Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɠɢɦɚ ɉȼ ɩɨɬɪɟɛɥɹɟɬɫɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ. ɗɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ ɢ ɢɡ ɫɟɬɢ ɪɚɫɫɟɢɜɚɟɬɫɹ ɧɚ ɞɨɛɚɜɨɱɧɵɯ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ;

–ɞɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ), ɩɪɢ ɤɨɬɨɪɨɦ ɞɜɢɝɚɬɟɥɶ ɢɡɛɵɬɨɱɧɭɸ ɷɥɟɤɬɪɢɱɟɫɤɭɸ ɷɧɟɪɝɢɸ ɪɚɫɫɟɢɜɚɟɬ ɧɚ ɨɬɞɟɥɶɧɨ ɜɤɥɸɱɺɧɧɵɣ ɪɟɡɢɫɬɨɪ.

Ɋɟɤɭɩɟɪɚɬɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ (ɊɌ). Ɋɟɤɭɩɟɪɚɬɢɜɧɵɦ ɬɨɪɦɨɠɟɧɢɟɦ, ɢɥɢ ɩɪɨɫɬɨ ɪɟɤɭɩɟɪɚɰɢɟɣ, ɩɪɢɧɹɬɨ ɧɚɡɵɜɚɬɶ ɝɟɧɟɪɚɬɨɪɧɨɟ ɬɨɪɦɨɠɟɧɢɟ ɫ ɨɬɞɚɱɟɣ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ. ɉɪɢ ɪɚɛɨɬɟ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ɞɜɢɝɚɬɟɥɶ ɩɨɬɪɟɛɥɹɟɬ ɬɨɤ I ɢɡ ɫɟɬɢ (ɫɩɥɨɲɧɵɟ ɫɬɪɟɥɤɢ ɧɚ ɪɢɫ. 3.16). Ⱦɥɹ ɨɬɞɚɱɢ ɷɧɟɪɝɢɢ ɜ ɫɟɬɶ ɬɨɤ ɹɤɨɪɹ ɞɨɥɠɟɧ

I

			ȿ=kɎ Ȧ
	rə

E>U

Ɋɢɫ. 3.16. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ Ⱦɇȼ

–––– ɞɜɢɝɚɬɟɥɶ; – – – ɝɟɧɟɪɚɬɨɪ

ɢɡɦɟɧɢɬɶ ɧɚɩɪɚɜɥɟɧɢɟ (ɩɭɧɤɬɢɪɧɵɟ ɫɬɪɟɥɤɢ I < 0).

I U E .

R

Ʉɪɨɦɟ ɬɨɝɨ, ɧɟɨɛɯɨɞɢɦɨ ɢɦɟɬɶ ɜ ɫɟɬɢ ɩɨɬɪɟɛɢɬɟɥɹ ɷɬɨɣ ɷɧɟɪɝɢɢ, ɩɪɢ ɷɬɨɦ ɧɚɩɪɹɠɟɧɢɟ ɩɨɬɪɟɛɢɬɟɥɹ U ɞɨɥɠɧɨ ɛɵɬɶ ɧɚɩɪɚɜɥɟɧɨ ɜɫɬɪɟɱɧɨ ɗȾɋ ȿ ɞɜɢɝɚɬɟɥɹ, ɪɚɛɨɬɚɸɳɟɝɨ ɝɟɧɟɪɚɬɨɪɨɦ, ɢ ɞɨɥɠɧɨ ɛɵɬɶ ɦɟɧɶɲɟ ɩɨ ɜɟɥɢɱɢɧɟ U < ȿ..

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ ɩɪɟɞɭɫɦɚɬɪɢɜɚɟɬ ɩɚɪɚɥɥɟɥɶɧɨɟ ɜɤɥɸɱɟɧɢɟ ɫɟɬɢ ɢ ɝɟɧɟɪɚɬɨɪɚ.

62

ȼɚɪɢɚɧɬɵ ɨɛɟɫɩɟɱɟɧɢɹ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɪɢɫ. 3.17):
		1.	Ⱦɜɢɠɟɧɢɟ	ɬɪɚɧɫɩɨɪɬɧɨɝɨ
Ȧ	Ȧ0ɇ	ɫɪɟɞɫɬɜɚ ɩɨɞ ɭɤɥɨɧ – ɜ ɷɬɨɦ ɫɥɭ-
	1	ɱɚɟ ɩɪɢ ɨɞɧɨɦ ɡɧɚɤɟ ɫɤɨɪɨɫɬɢ ɢɡ-
		ɦɟɧɹɟɬ ɡɧɚɤ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɬ
4			Ɇɋ1 < 0. ɞɜɢɝɚɬɟɥɶ ɧɚ ɟɫɬɟ-
Ȧ		Ɇɋ ɧɚ
0		ɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɟ ɩɟɪɟɯɨ-
	5
		ɞɢɬ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟ-
		ɠɢɦɚ ɩɪɢ ɩɨɞɴɟɦɟ ɜ ɬɨɱɤɭ 2 ɪɟɠɢ-
	Ɇ	ɦɚ ɪɟɤɭɩɟɪɚɰɢɢ (ɪɟɠɢɦ ɬɨɪɦɨɠɟ-
		ɧɢɹ ɧɚ ɫɩɭɫɤɟ).
Ɇɋ1	Ɇɋ	2. ɋɩɭɫɤ ɝɪɭɡɚ – ɩɪɢ ɧɟɢɡɦɟɧ-
		ɧɨɦ ɡɧɚɤɟ Ɇɋ ɞɜɢɝɚɬɟɥɶ ɪɟɜɟɪɫɢ-
		ɪɭɟɬɫɹ ɢ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɝɪɭɡɚ ɜɪɚ-
		ɳɚɟɬɫɹ ɫ ɭɫɬɚɧɨɜɢɜɲɟɣɫɹ ɫɤɨɪɨ-
		ɫɬɶɸ (ɜ ɬɨɱɤɟ 3) ɜɵɲɟ ɫɤɨɪɨɫɬɢ
	3	ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ (Ȧ >
-Ȧ0ɇ		Ȧ0ɇ). Ɍɚɤɨɣ ɪɟɠɢɦ ɜɨɡɦɨɠɟɧ ɜ ɫɯɟ-
		ɦɟ ɪɢɫ. 3.21.
		3. ɉɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ
Ɋɢɫ. 3.17. ȼɚɪɢɚɧɬɵ ɩɪɢɦɟɧɟɧɢɹ		ɹɤɨɪɟ (ɜɚɪɢɚɧɬ ɩɢɬɚɧɢɹ ɞɜɢɝɚɬɟɥɹ
				ɩɪɟɨɛɪɚɡɨɜɚ-
		ɨɬ ɢɧɞɢɜɢɞɭɚɥɶɧɨɝɨ
ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ
		ɬɟɥɹ) ɫɧɢɠɚɟɬɫɹ ɫɤɨɪɨɫɬɶ ɢɞɟɚɥɶ-
		ɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ Ȧ0 < Ȧ0ɇ. Ⱦɜɢ-
ɝɚɬɟɥɶ ɢɡ-ɡɚ ɦɟɯɚɧɢɱɟɫɤɨɣ ɢɧɟɪɰɢɢ ɧɟ ɦɨɠɟɬ ɦɝɧɨɜɟɧɧɨ ɢɡɦɟɧɢɬɶ ɫɤɨɪɨɫɬɶ ɢ
ɨɫɭɳɟɫɬɜɥɹɟɬɫɹ ɩɟɪɟɯɨɞ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɪɚɛɨɬɵ ɜ ɬɨɱɤɭ 4 ɪɟ-
ɠɢɦɚ ɪɟɤɭɩɟɪɚɰɢɢ. ɉɪɢ ɬɚɤɨɦ ɩɟɪɟɯɨɞɟ ɫɨɡɞɚɟɬɫɹ ɨɬɪɢɰɚɬɟɥɶɧɵɣ ɦɨɦɟɧɬ ɞɜɢ-
ɝɚɬɟɥɹ, ɞɢɧɚɦɢɱɟɫɤɢɣ ɦɨɦɟɧɬ

	Ɇ Ɇɋ	J	dȦ
			dt

Ɋɋ

Ɋȼ

ǻɊɆȿɏ

ǻɊə

Ɋɢɫ. 3.18. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ

ɬɚɤ ɠɟ ɨɬɪɢɰɚɬɟɥɶɧɵɣ, ɩɨɷɬɨɦɭ ɫɤɨɪɨɫɬɶ ɞɜɢɝɚɬɟɥɹ ɧɚɱɢɧɚɟɬ ɫɧɢɠɚɬɶɫɹ, ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ ɭɦɟɧɶɲɚɟɬɫɹ ɢ ɫɬɪɟɦɢɬɫɹ ɤ Ɇɋ ɜ ɬɨɱɤɭ 5. ɇɚ ɭɱɚɫɬɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ – ɨɬ ɬɨɱɤɢ 4 ɞɨ Ȧ0 – ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɪɟɠɢɦɟ ɪɟɤɭɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɨɛɟɫɩɟɱɢɜɚɹ ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ – ɬɨɪɦɨɠɟɧɢɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ.

ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ ɧɟ ɢɡɦɟɧɹɟɬɫɹ (3.10), ɥɢɲɶ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɤ ɬɨɤɚ ɹɤɨɪɹ I.

ɇɚ ɪɢɫ. 3.18 ɩɪɢɜɟɞɟɧɚ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɪɟɤɭ-

63

ɩɟɪɚɬɢɜɧɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ɇɚɩɪɚɜɥɟɧɢɟ ɩɨɬɨɤɚ ɦɨɳɧɨɫɬɢ ɩɨ ɫɪɚɜɧɟɧɢɸ ɫ ɞɜɢɝɚɬɟɥɶɧɵɦ ɪɟɠɢɦɨɦ – ɨɛɪɚɬɧɨɟ, ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɜ ɫɟɬɶ.

Ⱦɨɫɬɨɢɧɫɬɜɚ ɪɟɠɢɦɚ ɊɌ:

–ɠɺɫɬɤɢɟ ɦɟɯɚɧɢɱɟɫɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɨɛɟɫɩɟɱɢɜɚɸɬ ɜɨɡɦɨɠɧɨɫɬɶ ɩɨɥɭɱɟɧɢɹ ɭɫɬɨɣɱɢɜɨɣ ɫɤɨɪɨɫɬɢ ɫɩɭɫɤɚ ɩɪɢ ɡɧɚɱɢɬɟɥɶɧɵɯ ɢɡɦɟɧɟɧɢɹɯ ɦɨɦɟɧɬɚ ɧɚ ɜɚɥɭ;

–ɜɵɫɨɤɚɹ ɷɤɨɧɨɦɢɱɧɨɫɬɶ, ɢɡɛɵɬɨɱɧɚɹ ɷɥɟɤɬɪɢɱɟɫɤɚɹ ɷɧɟɪɝɢɹ ɜɨɡɜɪɚɳɚɟɬɫɹ

ɜɫɟɬɶ ɢ ɦɨɠɟɬ ɛɵɬɶ ɢɫɩɨɥɶɡɨɜɚɧɚ ɞɪɭɝɢɦ ɦɟɯɚɧɢɡɦɨɦ, ɱɟɦ ɫɧɢɠɚɟɬɫɹ ɩɨɬɪɟɛɥɟɧɢɟ ɷɧɟɪɝɢɢ ɢɡ ɫɟɬɢ.

ɇɟɞɨɫɬɚɬɤɢ ɪɟɠɢɦɚ ɊɌ:

–ɫɥɨɠɧɨɫɬɶ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɞɚɧɧɨɝɨ ɪɟɠɢɦɚ ɩɪɢ ɩɢɬɚɧɢɹ Ⱦɇȼ ɨɬ ɫɟɬɢ ɩɨɫɬɨɹɧɧɨɝɨ ɧɚɩɪɹɠɟɧɢɹ;

–ɧɟɨɛɯɨɞɢɦ ɩɨɬɪɟɛɢɬɟɥɶ ɷɧɟɪɝɢɢ ɪɟɤɭɩɟɪɚɰɢɢ. ɉɪɢ ɪɚɫɩɪɟɞɟɥɟɧɢɢ ɷɥɟɤɬɪɨɷɧɟɪɝɢɢ ɧɚ ɩɟɪɟɦɟɧɧɨɦ ɬɨɤɟ ɢɫɬɨɱɧɢɤɢ ɷɧɟɪɝɢɢ ɩɨɫɬɨɹɧɧɨɝɨ ɬɨɤɚ ɱɚɫɬɨ ɫɨɡɞɚɸɬɫɹ ɧɚ ɛɚɡɟ ɧɟɭɩɪɚɜɥɹɟɦɵɯ ɜɵɩɪɹɦɢɬɟɥɟɣ, ɤɨɬɨɪɵɟ ɧɟ ɦɨɝɭɬ ɩɪɢɧɢɦɚɬɶ ɷɧɟɪɝɢɸ ɪɟɤɭɩɟɪɚɰɢɢ. ȿɫɥɢ ɩɨɬɪɟɛɢɬɟɥɶ ɷɧɟɪɝɢɢ ɪɟɤɭɩɟɪɚɰɢɢ ɨɬɫɭɬɫɬɜɭɟɬ, ɩɨ ɰɟɩɢ ɹɤɨɪɹ ɬɨɤ ɧɟ ɩɪɨɬɟɤɚɟɬ, ɧɟ ɫɨɡɞɚɟɬɫɹ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ, ɝɪɭɡ ɩɚɞɚɟɬ (!?).

Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɊɌ:

–ɝɪɭɡɨɩɨɞɴɟɦɧɵɟ ɦɟɯɚɧɢɡɦɵ (ɤɪɚɧɵ, ɥɢɮɬɵ ɢ ɬ.ɩ.);

–ɷɥɟɤɬɪɢɱɟɫɤɢɣ ɬɪɚɧɫɩɨɪɬ;

–ɫɢɫɬɟɦɵ ɫ ɢɧɞɢɜɢɞɭɚɥɶɧɵɦ ɩɪɟɨɛɪɚɡɨɜɚɬɟɥɟɦ (Ɍɉ – Ⱦ, Ƚ – Ⱦ).

Ɍɨɪɦɨɠɟɧɢɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ (ɉȼ). Ɋɟɠɢɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ – ɬɨɪ-

ɦɨɡɧɨɣ ɪɟɠɢɦ, ɤɨɝɞɚ ɞɜɢɝɚɬɟɥɶ ɜɤɥɸɱɺɧ ɞɥɹ ɨɞɧɨɝɨ ɧɚɩɪɚɜɥɟɧɢɹ ɜɪɚɳɟɧɢɹ, ɧɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɜɧɟɲɧɢɯ ɫɢɥ ɜɪɚɳɚɟɬɫɹ ɜ ɩɪɨɬɢɜɨɩɨɥɨɠɧɭɸ ɫɬɨɪɨɧɭ. ɋɦɵɫɥ ɪɟɠɢɦɚ ɉȼ ɦɨɠɧɨ ɩɨɹɫɧɢɬɶ ɧɚ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚɯ (ɪɢɫ. 3.19).

ɉɭɫɬɶ ɞɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 ɫ ɚɤɬɢɜɧɵɦ ɫɬɚɬɢɱɟɫɤɢɦ ɦɨɦɟɧɬɨɦ Ɇɋ. ɉɪɢ ɜɜɟɞɟɧɢɢ ɜ ɰɟɩɶ ɹɤɨɪɹ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1 ɫɤɨɪɨɫɬɶ ɞɜɢɠɟɧɢɹ ɫɧɢɡɢɬɫɹ, ɧɨ ɟɫɥɢ ɭɜɟɥɢɱɢɬɶ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɞɨ (R1 + R2), ɬɨ Ɇɋ > ɆɄɁ, ɢ ɚɤɬɢɜɧɵɣ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ Ɇɋ ɡɚɫɬɚɜɢɬ ɞɜɢɝɚɬɟɥɶ ɜɪɚɳɚɬɶɫɹ ɜ ɩɪɨɬɢɜɨɩɨ-

ɥɨɠɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɜ ɬɨɱɤɟ 2. ɋɯɟɦɚ ɡɚ-

Ȧɦɟɳɟɧɢɹ ɬɚɤɨɝɨ ɪɟɠɢɦɚ ɩɪɢɜɟɞɟɧɚ ɧɚ ɪɢɫ. 3.20. ȿɫɥɢ ɜ ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ ȿ ɧɚ-

	1		ɩɪɚɜɥɟɧɚ ɧɚɜɫɬɪɟɱɭ ɧɚɩɪɹɠɟɧɢɸ ɫɟɬɢ U
3		ɟɫɬ	(ɫɩɥɨɲɧɵɟ ɫɬɪɟɥɤɢ), ɬɨ ɜ ɬɨɱɤɟ 2 ɩɪɢ ɧɟɢɡ-
ɉȼ	R1		ɦɟɧɧɨɦ ɧɚɩɪɚɜɥɟɧɢɢ ɬɨɤɚ ɢɡɦɟɧɢɥɨɫɶ ɧɚ-

Ɇɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɟ ɞɜɢɝɚɬɟɥɹ, ɡɧɚɤ ȿ ɩɨɦɟɧɹɥɫɹ ɧɚ ɨɛɪɚɬɧɵɣ (ɩɭɧɤɬɢɪɧɚɹ ɫɬɪɟɥɤɚ)

	4	ɆC	ɢ ɫɬɚɥ ɫɨɜɩɚɞɚɸɳɢɦ ɫ ɧɚɩɪɹɠɟɧɢɟɦ ɫɟɬɢ.
			Ɍɟɩɟɪɶ ɝɟɧɟɪɚɬɨɪ ɪɚɛɨɬɚɟɬ ɩɨɫɥɟɞɨɜɚ-
		R1+R2	ɬɟɥɶɧɨ ɫ ɫɟɬɶɸ, ɫɭɦɦɚ ɧɚɩɪɹɠɟɧɢɣ U + ȿ
		ɉȼ	ɩɪɢɥɨɠɟɧɚ ɤ ɫɨɩɪɨɬɢɜɥɟɧɢɹɦ ɰɟɩɢ ɹɤɨɪɹ, ɢ
			ɞɥɹ ɨɝɪɚɧɢɱɟɧɢɹ ɬɨɤɚ ɹɤɨɪɹ ɜɟɥɢɱɢɧɚ ɷɬɢɯ
		-Ȧ0ɇ	ɗɬɨ ɢ ɟɫɬɶ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɉȼ.
			ɇɚ ɪɢɫ.	3.21 ɢɡɨɛɪɚɠɺɧɚ ɫɯɟɦɚ	ɷɥɟɤ-
	Ɋɢɫ. 3.19. Ɇɟɯɚɧɢɱɟɫɤɢɟ
				ɩɨɞɴɺɦɧɨɝɨ ɦɟɯɚɧɢɡɦɚ.	Ʉɨɧ-
	ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɪɟɠɢɦɟ		ɬɪɨɩɪɢɜɨɞɚ
		2	ɫɨɩɪɨɬɢɜɥɟɧɢɣ ɞɨɥɠɧɚ ɛɵɬɶ ɭɜɟɥɢɱɟɧɚ.
			ɬɚɤɬɨɪɵ Ʉȼ	ɜɤɥɸɱɚɸɬɫɹ ɞɥɹ ɞɜɢɠɟɧɢɹ
	ɬɨɪɦɨɠɟɧɢɹ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ		ɜɜɟɪɯ, ɨɫɭɳɟɫɬɜɥɹɹ ɩɨɞɴɟɦ ɝɪɭɡɚ. Ɋɟɡɢ-

64

	Rɉȼ			rə		ɫɬɨɪ R1 ɨɝɪɚɧɢɱɢɜɚɟɬ ɩɭɫɤɨɜɵɟ ɬɨɤɢ.
						ɨɛɟɫɩɟɱɢɜɚɹ ɩɪɚɜɢɥɶɧɭɸ ɩɭɫɤɨɜɭɸ ɞɢɚ-
+
						ɝɪɚɦɦɭ. Ʉɨɧɬɚɤɬɨɪ Ʉɉȼ ɨɬɤɥɸɱɚɟɬɫɹ
	I					ɬɨɥɶɤɨ ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɜ
			E=kɎ Ȧ
UC						ɞɜɢɝɚɬɟɥɶɧɨɦ ɪɟɠɢɦɟ Ʉɉ ɜɫɟɝɞɚ ɜɤɥɸ-
–						ɱɟɧ.
						Ⱦɜɢɝɚɬɟɥɶ ɪɚɡɝɨɧɹɟɬɫɹ ɩɨ ɯɚɪɚɤɬɟ
						-

	Ɋɢɫ. 3.20. ɋɯɟɦɚ ɡɚɦɟɳɟɧɢɹ	ɪɢɫɬɢɤɟ ɫ R1, ɩɨɫɥɟ ɜɤɥɸɱɟɧɢɹ Ʉɍ1 ɩɟ-
		ɪɟɯɨɞɢɬ ɧɚ ɟɫɬɟɫɬɜɟɧɧɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢ-
	Ⱦɇȼ ɜ ɪɟɠɢɦɟ ɬɨɪɦɨɠɟɧɢɹ	ɤɭ ɢ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 (ɫɦ. ɪɢɫ. 3.19).
	ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ	Ⱦɥɹ ɨɫɬɚɧɨɜɤɢ ɞɜɢɝɚɬɟɥɹ ɩɨ ɨɤɨɧɱɚ-
		ɧɢɢ ɩɨɞɴɟɦɚ ɨɬɤɥɸɱɚɸɬ ɤɨɧɬɚɤɬɨɪɵ Ʉȼ,

Ʉɍ1 ɢ Ʉɉ, ɜ ɰɟɩɶ ɹɤɨɪɹ ɜɜɨɞɹɬɫɹ ɞɨɛɚɜɨɱɧɵɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R1 + R2, ɡɚɬɟɦ ɜɤɥɸɱɚɸɬɫɹ ɤɨɧɬɚɤɬɨɪɵ Ʉɇ. Ʉɨɧɬɚɤɬɨɪɵ Ʉɇ ɨɛɟɫɩɟɱɢɜɚɸɬ ɢɡɦɟɧɟɧɢɟ ɩɨɥɹɪɧɨɫɬɢ ɧɚɩɪɹɠɟɧɢɹ ɧɚ ɹɤɨɪɟ ɞɜɢɝɚɬɟɥɹ (ɪɟɜɟɪɫ ɞɜɢɝɚɬɟɥɹ) ɢ ɜɤɥɸɱɚɸɬɫɹ ɞɥɹ ɉȼ ɧɚ ɜɵɛɟɝɟ ɫ ɰɟɥɶɸ ɨɫɬɚɧɨɜɤɢ ɢ ɞɥɹ ɞɜɢɠɟɧɢɹ ɜɧɢɡ ɞɥɹ ɫɩɭɫɤɚ ɝɪɭɡɚ. ȼ ɪɟɡɭɥɶɬɚɬɟ ɷɬɢɯ ɩɟɪɟɤɥɸɱɟɧɢɣ ɞɜɢɝɚɬɟɥɶ ɢɡ ɬɨɱɤɢ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ ɩɟɪɟɯɨɞɢɬ ɜ ɬɨɱɤɭ 3 ɪɟɠɢɦɚ ɉȼ ɢ ɫɧɢɠɚɟɬ ɫɤɨɪɨɫɬɶ ɞɨ ɨɫɬɚɧɨɜɤɢ ɜ ɬɨɱɤɟ 4. ȿɫɥɢ ɜ ɬɨɱɤɟ 4 ɧɟ ɨɬɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪɵ Ʉɇ ɢ ɨɫɬɚɜɢɬɶ ɹɤɨɪɶ ɩɨɞɤɥɸɱɟɧɧɵɦ ɤ ɫɟɬɢ, ɞɜɢɝɚɬɟɥɶ ɧɚɱɧɟɬ ɪɚɡɝɨɧ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ, ɱɬɨ ɱɚɫɬɨ ɩɪɨɫɬɨ ɨɩɚɫɧɨ.

Ⱦɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɫɩɭɫɤɚ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɉȼ ɞɨɫɬɚɬɨɱɧɨ ɩɪɢ ɜɤɥɸɱɟɧɧɨɦ Ʉȼ ɜɜɟɫɬɢ ɜ ɰɟɩɶ ɹɤɨɪɹ ɪɟɡɢɫɬɨɪɵ R1 + R2, ɢ ɞɜɢɝɚɬɟɥɶ ɡɚ ɫɱɟɬ ɦɚɫɫɵ ɝɪɭɡɚ ɢɡɦɟɧɢɬ ɧɚɩɪɚɜɥɟɧɢɟ ɜɪɚɳɟɧɢɹ ɢ ɨɛɟɫɩɟɱɢɬ ɫɩɭɫɤ ɝɪɭɡɚ ɜ ɪɟɠɢɦɟ ɉȼ.

ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɉȼ ɧɟ ɢɡɦɟɧɹɟɬɫɹ (3.10), ɥɢɲɶ ɢɡɦɟɧɹɟɬɫɹ ɡɧɚɤ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ ɪɟɜɟɪɫɟ.

ȼ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ɞɟɣɫɬɜɭɟɬ ɫɨɝɥɚɫɧɨ ɫ ɧɚɩɪɹɠɟ-

	ɧɢɟɦ ɫɟɬɢ (ɫɦ. ɪɢɫ. 3.19), ɢ ɬɨɤ ɹɤɨɪɹ ɛɭɞɟɬ ɪɚɜɟɧ
	I	U E		(3.32)
		R

ɢ ɧɟɨɛɯɨɞɢɦɨ ɫɭɳɟɫɬɜɟɧɧɨ ɭɜɟɥɢɱɢɬɶ ɚɤɬɢɜɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɹɤɨɪɹ, ɱɬɨɛɵ ɬɨɤ ɧɟ ɜɵɲɟɥ ɡɚ ɩɪɟɞɟɥɵ ɞɨɩɭɫɬɢɦɨɝɨ.

			LM
Ʉȼ		Ʉɇ	Ʉɍ1	Ʉɉȼ
RȾɌ
	Ɇ		R1	R2
ɄȾ
Ʉɇ		Ʉȼ

Ɋɢɫ. 3.21. ɋɯɟɦɚ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɦɟɯɚɧɢɡɦɚ ɩɨɞɴɟɦɚ

65

ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɪɟɠɢɦɚ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.22, ɢɡ ɤɨɬɨɪɨɝɨ ɫɥɟɞɭɟɬ, ɱɬɨ ɦɨɳɧɨɫɬɶ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢɡ ɫɟɬɢ ɢ ɫ ɜɚɥɚ ɢ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɬɟɪɢ ɦɨɳɧɨɫɬɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ.

		UC E	I RȾɈȻ I rə,				uI
		PC PM	'PȾɈȻ 'Ɋə.
Ⱦɨɫɬɨɢɧɫɬɜɚ ɬɨɪɦɨɠɟɧɢɹ ɉȼ:
–	ɢɧɬɟɧɫɢɜɧɨɟ ɬɨɪɦɨɠɟɧɢɟ			ɞɨ
ɩɨɥɧɨɣ ɨɫɬɚɧɨɜɤɢ;
					PC				PɆ	PB
–				–
	ɩɪɨɫɬɨɬɚ	ɨɫɭɳɟɫɬɜɥɟɧɢɹ
ɜɤɥɸɱɟɧɢɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜ-							ǻPə	ǻPȾɈȻ
ɥɟɧɢɹ.									ǻPɆȿɏ
ɇɟɞɨɫɬɚɬɤɢ ɪɟɠɢɦɚ:
– ɨɱɟɧɶ ɦɹɝɤɢɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ –							Ɋɢɫ. 3.22. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ
ɫɭɳɟɫɬɜɟɧɧɨɟ		ɢɡɦɟɧɟɧɢɟ ɫɤɨɪɨɫɬɢ
								ɞɢɚɝɪɚɦɦɚ ɉȼ

ɫɩɭɫɤɚ ɩɪɢ ɢɡɦɟɧɟɧɢɢ ɦɚɫɫɵ ɝɪɭɡɚ;

–ɷɧɟɪɝɢɹ ɢɡ ɫɟɬɢ ɢ ɷɧɟɪɝɢɹ ɫ ɜɚɥɚ ɞɜɢɝɚɬɟɥɹ ɢɞɟɬ ɧɚ ɩɨɬɟɪɢ – ɧɟɭɞɨɜɥɟɬɜɨɪɢɬɟɥɶɧɚɹ ɷɧɟɪɝɟɬɢɤɚ;

–ɧɟɨɛɯɨɞɢɦɨɫɬɶ ɨɬɤɥɸɱɟɧɢɹ ɩɪɢɜɨɞɚ ɩɪɢ ɫɤɨɪɨɫɬɢ, ɛɥɢɡɤɨɣ ɤ ɧɭɥɸ ɢɡ-ɡɚ ɨɩɚɫɧɨɫɬɢ ɪɚɡɜɨɪɨɬɚ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ.

Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ ɪɟɠɢɦɚ ɪɚɫɩɪɨɫɬɪɚɧɹɟɬɫɹ ɧɚ ɞɜɢɝɚɬɟɥɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟɛɨɥɶɲɨɣ ɦɨɳɧɨɫɬɢ (ɞɨ 100 ɤȼɬ), ɝɞɟ ɩɨɬɟɪɢ ɨɬɧɨɫɢɬɟɥɶɧɨ ɧɟ ɜɟɥɢɤɢ, ɚ ɩɪɨɫɬɨɬɚ ɨɫɭɳɟɫɬɜɥɟɧɢɹ ɪɟɠɢɦɚ ɢɦɟɟɬ ɫɭɳɟɫɬɜɟɧɧɨɟ ɡɧɚɱɟɧɢɟ (ɤɪɚɧɨɜɨɟ ɯɨɡɹɣɫɬɜɨ ɢ ɩɪɨɫɬɟɣɲɢɟ ɦɟɯɚɧɢɡɦɵ ɫ ɧɢɡɤɢɦɢ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɦɢ ɬɪɟɛɨɜɚɧɢɹɦɢ).

Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ (ȾɌ). Ɋɟɠɢɦɨɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɧɚɡɵɜɚɸɬ ɪɟɠɢɦ ɬɨɪɦɨɠɟɧɢɹ ɞɜɢɝɚɬɟɥɹ, ɩɪɢ ɤɨɬɨɪɨɦ ɨɛɦɨɬɤɚ ɜɨɡɛɭɠɞɟɧɢɹ ɨɫɬɚɺɬɫɹ ɩɨɞɤɥɸɱɟɧɧɨɣ ɤ ɫɟɬɢ, ɚ ɹɤɨɪɶ ɞɜɢɝɚɬɟɥɹ ɨɬɤɥɸɱɚɟɬɫɹ ɨɬ ɫɟɬɢ ɢ ɡɚɦɵɤɚɟɬɫɹ

ɧɚ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ (RȾɌ), ɚ ɜ ɧɟɤɨɬɨɪɵɯ ɫɥɭɱɚɹɯ ɞɥɹ ɨɛɟɫɩɟɱɟɧɢɹ ɧɢɡɤɢɯ ɫɤɨɪɨɫɬɟɣ ɫɩɭɫɤɚ – ɩɪɨɫɬɨ ɡɚɤɨɪɚɱɢɜɚɟɬɫɹ (RȾɌ = 0).

Ⱦɜɢɝɚɬɟɥɶ ɪɚɛɨɬɚɟɬ ɜ ɬɨɱɤɟ 1 ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ. Ⱦɥɹ ɩɨɥɭɱɟɧɢɹ ɪɟɠɢɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɫɦ. ɪɢɫ. 3.21) ɧɟɨɛɯɨɞɢɦɨ ɨɬɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪɵ ɧɚɩɪɚɜɥɟɧɢɹ Ʉȼ, Ʉɇ ɢ ɜɤɥɸɱɢɬɶ ɤɨɧɬɚɤɬɨɪ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ ɄȾ. ɉɪɢ ɷɬɨɦ ɫɯɟɦɚ ɛɭɞɟɬ ɫɨɨɬɜɟɬɫɬɜɨɜɚɬɶ ɪɢɫ. 3.23.

UC
	Ȧ
LM	1	ɟɫɬ
	2		ɊɆȿɏ
		ǻɊȾɌ		Ɋ
				ȼ
		Ɇ
Ɇ		ǻPə
	MC
	RȾɌ		ǻPɆȿɏ
RȾɌ	3

Ɋɢɫ. 3.23. ɋɯɟɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ, ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɢ ɷɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ

66

ɉɨɬɨɤ ɞɜɢɝɚɬɟɥɹ ɨɫɬɚɟɬɫɹ ɧɟɢɡɦɟɧɧɵɦ, ɗȾɋ ɫɨɨɬɜɟɬɫɬɜɭɟɬ ɫɤɨɪɨɫɬɢ ɜɪɚɳɟɧɢɹ, ɩɪɢ ɡɚɦɵɤɚɧɢɢ ɹɤɨɪɹ ɧɚ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɗȾɋ ɫɨɡɞɚɟɬ ɬɨɤ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ, ɜɨɡɧɢɤɚɟɬ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɜ ɬɨɱɤɟ 2. ɉɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɝɨ ɦɨɦɟɧɬɚ ɢ ɫɬɚɬɢɱɟɫɤɨɝɨ ɦɨɦɟɧɬɚ ɫɤɨɪɨɫɬɶ ɫɧɢɠɚɟɬɫɹ, ɭɦɟɧɶɲɚɟɬɫɹ ɗȾɋ, ɚ ɜɦɟɫɬɟ ɫ ɧɟɣ – ɬɨɤ ɢ ɦɨɦɟɧɬ ɞɜɢɝɚɬɟɥɹ. Ɍɚɤ ɜɵɩɨɥɧɹɟɬɫɹ ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɜɵɛɟɝɟ. ɉɪɢ Ȧ = 0 ɗȾɋ, ɬɨɤ ɢ ɦɨɦɟɧɬ ɨɬɫɭɬɫɬɜɭɸɬ.

ȿɫɥɢ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ – ɚɤɬɢɜɧɵɣ, ɬɨ ɩɨɞ ɞɟɣɫɬɜɢɟɦ ɷɬɨɝɨ ɦɨɦɟɧɬɚ ɞɜɢɝɚɬɟɥɶ ɛɭɞɟɬ ɪɚɡɝɨɧɹɬɶɫɹ ɜ ɨɛɪɚɬɧɭɸ ɫɬɨɪɨɧɭ, ɢ ɜɧɨɜɶ ɜɨɡɧɢɤɚɟɬ ɪɟɠɢɦ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ. ȼ ɬɨɱɤɟ 3 ɫɨɡɞɚɟɬɫɹ ɭɫɬɨɣɱɢɜɵɣ ɪɟɠɢɦ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ – ɬɨɪɦɨɠɟɧɢɟ ɧɚ ɫɩɭɫɤɟ (ɫɦ. ɪɢɫ. 3.23).

ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ ɞɢɧɚɦɢɱɟɫɤɨɦ ɬɨɪɦɨɠɟɧɢɢ ɫɨɨɬɜɟɬɫɬɜɭɟɬ (3.10), ɧɨ ɧɚɩɪɹɠɟɧɢɟ, ɩɪɢɤɥɚɞɵɜɚɟɦɨɟ ɤ ɹɤɨɪɸ, ɪɚɜɧɨ ɧɭɥɸ, ɫɥɟɞɨɜɚɬɟɥɶɧɨ

	U		R	M		R	M	-I	R
					-					.	(3.33)
Ȧ	kɎɇ		kɎɇ 2			kɎɇ 2			kɎɇ

ɂɡ ɷɬɨɝɨ ɭɪɚɜɧɟɧɢɹ ɫɥɟɞɭɟɬ, ɱɬɨ ɜɫɟ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɨɯɨɞɹɬ ɱɟɪɟɡ ɧɭɥɶ. Ɇɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɩɨɤɚɡɚɧɚ ɧɚ ɪɢɫ. 3.23. ɗɧɟɪɝɟɬɢɱɟɫɤɚɹ ɞɢɚɝɪɚɦɦɚ ɞɢɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ (ɫɦ. ɪɢɫ.3.23) ɨɬɪɚɠɚɟɬ ɷɧɟɪɝɟɬɢɱɟɫɤɨɟ ɩɨɥɨɠɟɧɢɟ ɪɟɠɢɦɚ. ɗɧɟɪɝɢɹ ɫ ɜɚɥɚ ɪɚɫɯɨɞɭɟɬɫɹ ɧɚ ɩɨɬɟɪɢ ɜ ɫɨɩɪɨɬɢɜɥɟɧɢɹɯ ɹɤɨɪɧɨɣ ɰɟɩɢ. ɂɡ ɫɟɬɢ ɩɨɬɪɟɛɥɹɟɬɫɹ ɬɨɥɶɤɨ ɷɧɟɪɝɢɹ ɧɚ ɜɨɡɛɭɠɞɟɧɢɟ ɞɜɢɝɚɬɟɥɹ, ɧɨ ɨɧɚ ɫɨɫɬɚɜɥɹɟɬ ɥɢɲɶ 2…5% ɨɬ ɧɨɦɢɧɚɥɶɧɨɣ ɦɨɳɧɨɫɬɢ ɞɜɢɝɚɬɟɥɹ.

Ⱦɢɧɚɦɢɱɟɫɤɨɟ ɬɨɪɦɨɠɟɧɢɟ ȾɌ ɡɚɧɢɦɚɟɬ ɩɪɨɦɟɠɭɬɨɱɧɨɟ ɩɨɥɨɠɟɧɢɟ ɦɟɠɞɭ ɪɟɤɭɩɟɪɚɬɢɜɧɵɦ ɬɨɪɦɨɠɟɧɢɟɦ ɊɌ ɢ ɬɨɪɦɨɠɟɧɢɟɦ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɟɦ ɉȼ ɩɨɱɬɢ ɩɨ ɜɫɟɦ ɩɨɤɚɡɚɬɟɥɹɦ:

–ɜ ɷɧɟɪɝɟɬɢɤɟ – ɢɡɛɵɬɨɱɧɚɹ ɷɧɟɪɝɢɹ ɜ ɫɟɬɶ ɧɟ ɨɬɞɚɺɬɫɹ (ɤɚɤ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ), ɧɨ ɢ ɧɟ ɩɨɬɪɟɛɥɹɟɬɫɹ ɢɡ ɫɟɬɢ (ɤɚɤ ɩɪɢ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɢ);

–ɬɨɱɧɨɫɬɶ ɩɨɞɞɟɪɠɚɧɢɹ ɫɤɨɪɨɫɬɢ ɧɚ ɫɩɭɫɤɟ – ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɠɺɫɬɱɟ, ɱɟɦ ɜ ɪɟɠɢɦɟ ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ, ɧɨ ɦɹɝɱɟ, ɱɟɦ ɩɪɢ ɪɟɤɭɩɟɪɚɬɢɜɧɨɦ ɬɨɪɦɨɠɟɧɢɢ;

–ɢɧɬɟɧɫɢɜɧɨɫɬɶ ɬɨɪɦɨɠɟɧɢɹ ɧɢɠɟ, ɱɟɦ ɩɪɢ ɩɪɨɬɢɜɨɜɥɸɱɟɧɢɢ, ɩɨ ɦɟɪɟ ɫɧɢɠɟɧɢɹ ɫɤɨɪɨɫɬɢ ɬɨɪɦɨɡɧɨɣ ɦɨɦɟɧɬ ɩɚɞɚɟɬ;

ȼɚɠɧɨɟ ɞɨɫɬɨɢɧɫɬɜɨ – ɜɨɡɦɨɠɧɨɫɬɶ ɬɨɱɧɨɣ ɨɫɬɚɧɨɜɤɢ ɩɪɢ ɪɟɚɤɬɢɜɧɨɦ ɫɬɚɬɢɱɟɫɤɨɦ ɦɨɦɟɧɬɟ.

Ɉɛɥɚɫɬɶ ɩɪɢɦɟɧɟɧɢɹ – ɧɟɪɟɜɟɪɫɢɜɧɵɣ ɩɪɢɜɨɞ, ɜ ɪɟɜɟɪɫɢɜɧɨɦ – ɩɪɢ ɧɟɨɛɯɨɞɢɦɨɫɬɢ ɬɨɱɧɨɣ ɨɫɬɚɧɨɜɤɢ.

Ɍɚɤɢɦ ɨɛɪɚɡɨɦ, ɪɚɫɫɦɨɬɪɟɜ ɩɪɟɞɥɨɠɟɧɧɵɟ ɜɚɪɢɚɧɬɵ ɢɫɩɨɥɶɡɨɜɚɧɢɹ ɢɡɛɵɬɨɱɧɨɣ ɷɥɟɤɬɪɢɱɟɫɤɨɣ ɷɧɟɪɝɢɢ ɤɚɤ ɫ ɬɨɱɤɢ ɡɪɟɧɢɹ ɭɞɨɜɥɟɬɜɨɪɟɧɢɹ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨɜɚɧɢɣ, ɬɚɤ ɢ ɷɮɮɟɤɬɢɜɧɨɫɬɢ ɟɟ ɢɫɩɨɥɶɡɨɜɚɧɢɹ, ɜɚɠɧɨ ɧɚɭɱɢɬɶɫɹ ɪɚɡɛɢɪɚɬɶɫɹ ɜ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ ɢ ɩɪɢɦɟɧɹɬɶ ɢɯ ɜ ɫɨɨɬɜɟɬɫɬɜɢɢ ɫ ɭɫɥɨɜɢɹɦɢ ɪɚɛɨɬɵ ɦɟɯɚɧɢɡɦɚ.

ɇɚ ɩɥɨɫɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ ɨɩɪɟɞɟɥɟɧɢɸ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ ɩɨɦɨɝɭɬ ɬɚɤɢɟ ɢɯ ɨɫɨɛɟɧɧɨɫɬɢ (ɪɢɫ. 3.24):

–ɡɧɚɤ Ȧ0ɇ ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɹɪɧɨɫɬɶ ɧɚɩɪɹɠɟɧɢɹ U ɧɚ ɹɤɨɪɟ;

–ɡɧɚɤ Ȧ ɨɩɪɟɞɟɥɹɟɬ ɩɨɥɹɪɧɨɫɬɶ ɗȾɋ ɞɜɢɝɚɬɟɥɹ ȿ;

–ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ ɫɨɜɩɚɞɚɸɬ ɢ |Ȧ0ɇ| > |Ȧ| – ɪɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɶ-

ɧɵɣ;

–ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ ɫɨɜɩɚɞɚɸɬ ɢ Ȧ > Ȧ0ɇ > 0 ɢɥɢ – Ȧ < – Ȧ0ɇ < 0 – ɪɟɠɢɦ ɪɟɤɭɩɟɪɚɰɢɢ;

67

			– ɟɫɥɢ ɡɧɚɤɢ ɫɤɨɪɨɫɬɟɣ Ȧ ɢ
	ɊɌ		Ȧ0ɇ ɧɟ			–
				ɫɨɜɩɚɞɚɸɬ			ɪɟɠɢɦ
		Ȧ	ɩɪɨɬɢɜɨɜɤɥɸɱɟɧɢɹ;
	ȾɌ	Ȧ0ɇ	– ɩɪɢ Ȧ0ɇ = 0 – ɪɟɠɢɦ ɞɢ-
			ɧɚɦɢɱɟɫɤɨɝɨ ɬɨɪɦɨɠɟɧɢɹ.
	ɉȼ	ȾɊ
			3.1.9. Ɋɚɫɱɟɬ ɫɯɟɦ
				ɜɤɥɸɱɟɧɢɹ,
		Ɇ
			ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ
			ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ
		ɉȼ
	ȾɊ						ɷɥɟɤ-
			Ɉɫɧɨɜɧɨɣ		ɡɚɞɚɱɟɣ
		ȾɌ					ɜɵɩɨɥ-
			ɬɪɨɩɪɢɜɨɞɚ		ɹɜɥɹɟɬɫɹ
	- Ȧ0ɇ		ɧɟɧɢɟ ɬɟɯɧɨɥɨɝɢɱɟɫɤɢɯ ɬɪɟɛɨ-
		ɊɌ	ɜɚɧɢɣ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ – ɨɛɟɫ-
			ɩɟɱɟɧɢɟ	ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ ɫ
	Ɋɢɫ. 3.24. Ʉ ɨɩɪɟɞɟɥɟɧɢɸ ɪɟɠɢɦɨɜ		ɡɚɞɚɧɧɨɣ ɬɟɯɧɨɥɨɝɚɦɢ				ɫɤɨɪɨ-
			ɫɬɶɸ ȦɁȺȾ ɩɪɢ ɡɚɞɚɧɧɨɣ ɜɟɥɢ-
	ɪɚɛɨɬɵ ɧɚ ɩɥɨɫɤɨɫɬɢ ɦɟɯɚɧɢɱɟɫɤɢɯ
			ɱɢɧɟ ɦɨɦɟɧɬɚ ɆɁȺȾ.
	ɯɚɪɚɤɬɟɪɢɫɬɢɤ
			ɉɨ	ɡɚɞɚɧɧɨɦɭ		ɦɨɦɟɧɬɭ

ɆɁȺȾ ɢ ɡɚɞɚɧɧɨɣ ɫɤɨɪɨɫɬɢ ȦɁȺȾ ɬɪɟɛɭɟɬɫɹ ɜɵɛɪɚɬɶ ɫɯɟɦɭ ɜɤɥɸɱɟɧɢɹ, ɩɪɟɞɩɨɱɬɢɬɟɥɶɧɭɸ ɞɥɹ ɡɚɞɚɧɧɨɝɨ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ ɢ ɪɚɫɫɱɢɬɚɬɶ ɢɥɢ ɧɚɩɪɹɠɟɧɢɟ U, ɢɥɢ ɩɨɬɨɤ Ɏ, ɢɥɢ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ R, ɨɛɟɫɩɟ-

ɱɢɜɚɸɳɢɟ ɪɚɛɨɬɭ ɷɥɟɤɬɪɨɩɪɢɜɨɞɚ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.

Ⱦɥɹ ɪɟɲɟɧɢɹ ɡɚɞɚɱɢ ɧɟɨɛɯɨɞɢɦɨ ɩɟɪɟɣɬɢ ɨɬ ɦɨɦɟɧɬɚ, ɨɛɵɱɧɨ ɡɚɞɚɧɧɨɝɨ ɧɚ ɜɚɥɭ, ɤ ɷɥɟɤɬɪɨɦɚɝɧɢɬɧɨɦɭ ɦɨɦɟɧɬɭ ɞɜɢɝɚɬɟɥɹ, ɞɥɹ ɱɟɝɨ ɧɭɠɧɨ ɭɱɟɫɬɶ ɩɨɬɟɪɢ ɦɨɦɟɧɬɚ ɧɚ ɯɨɥɨɫɬɨɦ ɯɨɞɭ ɞɜɢɝɚɬɟɥɹ ǻɆɏɏ ɢ ɪɚɫɫɱɢɬɚɬɶ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ:

Ɇɋ ɆɁȺȾ r 'Ɇɏɏ ɆɗɆɁȺȾ ,

(3.34)

ɩɪɢ ɷɬɨɦ ɡɧɚɤ «+» – ɞɥɹ ɞɜɢɝɚɬɟɥɶɧɨɝɨ ɪɟɠɢɦɚ, ɤɨɝɞɚ ɩɨɬɟɪɢ ɩɨɤɪɵɜɚɸɬɫɹ ɞɜɢɝɚɬɟɥɟɦ, ɢ «-» – ɞɥɹ ɬɨɪɦɨɡɧɨɝɨ ɪɟɠɢɦɚ, ɜ ɤɨɬɨɪɨɦ ɩɨɬɟɪɢ ɩɨɤɪɵɜɚɸɬɫɹ ɡɚ ɫɱɟɬ ɦɨɳɧɨɫɬɢ, ɢɞɭɳɟɣ ɫ ɜɚɥɚ ɪɚɛɨɱɟɝɨ ɨɪɝɚɧɚ.

Ɋɚɫɱɟɬ ɜɵɩɨɥɧɹɟɬɫɹ ɩɨ ɮɨɪɦɭɥɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ, ɡɚɩɢɫɚɧɧɨɣ ɜ ɨɛɳɟɦ ɜɢɞɟ (3.10):

		U		R	M ,	(3.35)
Ȧ				kɎ 2
	ɁȺȾ	kɎ			C

ɤɨɬɨɪɚɹ ɪɟɲɚɟɬɫɹ ɨɬɧɨɫɢɬɟɥɶɧɨ ɢɫɤɨɦɨɝɨ ɩɚɪɚɦɟɬɪɚ. Ⱦɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢɧɢɦɚɸɬ ɫɨɨɬɜɟɬɫɬɜɭɸɳɢɦɢ ɟɫɬɟɫɬɜɟɧɧɨɣ ɫɯɟɦɟ ɜɤɥɸɱɟɧɢɹ:

–ɩɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ UɁȺȾ ɩɪɢɧɢɦɚɸɬ kɎ = kɎɇ ɢ R = rə;

–ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RɁȺȾ – kɎ = kɎɇ ɢ U = Uɇ;

–ɩɪɢ ɪɚɫɱɟɬɟ ɩɨɬɨɤɚ kɎɁȺȾ – U = Uɇ ɢ R = rə.

ɉɪɢ ɪɚɫɱɟɬɟ ɜ ɨ.ɟ. ɪɟɲɟɧɢɟ ɩɨɫɬɚɜɥɟɧɧɨɣ ɡɚɞɚɱɢ ɭɩɪɨɳɚɟɬɫɹ. ȼ ɷɬɨɦ ɫɥɭɱɚɟ ɭɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɡɚɩɢɫɵɜɚɟɬɫɹ ɫ ɭɱɟɬɨɦ ɨɩɪɟɞɟɥɹɟɦɨɝɨ ɩɚɪɚɦɟɬɪɚ, ɤɨɝɞɚ ɞɪɭɝɢɟ ɩɚɪɚɦɟɬɪɵ ɩɪɢɧɢɦɚɸɬ ɛɚɡɨɜɵɟ ɡɧɚɱɟɧɢɹ.

68

U

R

.

M

(3.36)

ȦɁȺȾ

C

Ɏ

Ɏ2

ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ ɩɪɢ k Ɏ = k Ɏɇ ɢ R = rə ɭɪɚɜɧɟɧɢɟ ɩɪɢɧɢɦɚɟɬ ɜɢɞ

ə

C ,

U

M

ȦɁȺȾ

r

(3.37)

ɩɪɢ ɪɚɫɱɟɬɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ

1

C ,

R

M

ȦɁȺȾ

ɩɪɢ ɪɚɫɱɟɬɟ ɩɨɬɨɤɚ

1

r

.

ə

M

Ȧ

ɁȺȾ

Ɏ

Ɏ2

C

ɉɪɢ ɝɪɚɮɢɱɟɫɤɨɦ ɦɟɬɨɞɟ ɪɚɫɱɟɬɚ (ɪɢɫ. 3.25):

–ɫɬɪɨɢɬɫɹ ɟɫɬɟɫɬɜɟɧɧɚɹ ɦɟɯɚɧɢɱɟɫɤɚɹ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ ɜ ɨ.ɟ.;

–ɧɚɧɨɫɢɬɫɹ ɡɚɞɚɧɧɚɹ ɬɨɱɤɚ ȦɁȺȾ, Ɇɋ;

–ɩɚɪɚɥɥɟɥɶɧɵɦ ɩɟɪɟɧɨɫɨɦ ɟɫɬɟɫɬɜɟɧɧɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɫɬɪɨɢɦ ɢɫɤɭɫɫɬɜɟɧɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ ɩɪɢ ɫɧɢɠɟɧɢɢ ɧɚɩɪɹɠɟɧɢɹ U, ɨɩɪɟɞɟɥɹɟɦ Ȧ0ɁȺȾ, ɤɨɬɨɪɚɹ ɜ ɨ.ɟ. ɪɚɜɧɚ UɁȺȾ;

–ɫɨɟɞɢɧɹɹ ɬɨɱɤɭ ɫɤɨɪɨɫɬɢ Ȧ0ɇ ɫ ɡɚɞɚɧɧɨɣ ɬɨɱɤɨɣ, ɫɬɪɨɢɦ ɢɫɤɭɫɫɬɜɟɧɧɭɸ ɪɟɨɫɬɚɬɧɭɸ ɦɟɯɚɧɢɱɟɫɤɭɸ ɯɚɪɚɤɬɟɪɢɫɬɢɤɭ, ɩɪɢ Ɇ=1 (ɫɦ. ɪɢɫ.3.25) ɨɩɪɟɞɟɥɹɟɦ RȾɈȻ.

Ȧ

1	rə
Ȧɇ	ɟɫɬ
Ȧ0ɁȺȾ	RȾɈȻ
ȦɁȺȾ	UəĻ

RĹ

Ɇɋ 1

Ɇ

Ɋɢɫ. 3.25. Ɉɛɟɫɩɟɱɟɧɢɟ ɪɚɛɨɬɵ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ ɫɧɢɠɟɧɢɟɦ ɧɚɩɪɹɠɟɧɢɹ U, ɜɜɟɞɟɧɢɟɦ ɫɨɩɪɨɬɢɜɥɟɧɢɹ R

ȼ ɪɟɡɭɥɶɬɚɬɟ ɨɩɪɟɞɟɥɟɧɵ ɧɟɨɛɯɨɞɢɦɵɟ ɩɚɪɚɦɟɬɪɵ ɢ ɩɨɫɬɪɨɟɧɵ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ.

ɇɚ ɪɢɫ.3.26 ɩɪɢɜɟɞɟɧ ɩɪɢɦɟɪ ɝɪɚɮɢɱɟɫɤɨɝɨ ɪɚɫɱɟɬɚ ɩɚɪɚɦɟɬɪɨɜ ɢ ɢɫɤɭɫɫɬɜɟɧɧɵɯ ɯɚɪɚɤɬɟɪɢɫɬɢɤ, ɨɛɟɫɩɟɱɢɜɚɸɳɢɯ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɪɚɡɥɢɱɧɵɯ ɬɨɪɦɨɡɧɵɯ ɪɟɠɢɦɚɯ. ɗɬɢ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɨɫɬɪɨɟɧɵ ɩɨ ɜɵɲɟ ɩɪɢɜɟɞɟɧɧɨɣ ɦɟɬɨɞɢɤɟ.

69

0,5, ȦɁȺȾ

ɉɪɢɦɟɪ 3.2. Ɋɚɫɫɱɢɬɚɬɶ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɟ ɜ ɰɟɩɢ ɹɤɨɪɹ RȾɈȻ (ɢ ɧɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ Uə) ɞɜɢɝɚɬɟɥɹ Ⱦ32 (ɫɦ. ɩɪɢɦɟɪ 3.1), ɨɛɟɫɩɟɱɢɜɚɸɳɟɟ ɪɚɛɨɬɭ ɞɜɢɝɚɬɟɥɹ ɜ ɡɚɞɚɧɧɨɣ ɬɨɱɤɟ: ɆɁȺȾ 0,5.

Ɋɚɫɱɟɬ ɜɵɩɨɥɧɢɦ ɜ ɨ.ɟ. ɍɪɚɜɧɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɜ ɨɛɳɟɦ ɜɢɞɟ (3.36) ɜ ɨ.ɟ.

			U				R				.
										M
Ȧ
ɁȺȾ			Ɏ			Ɏ2				C

Ɋɟɠɢɦ ɪɚɛɨɬɵ ɞɜɢɝɚɬɟɥɹ – ɞɜɢɝɚɬɟɥɶɧɵɣ.

ɉɪɢ ɪɚɫɱɟɬɟ ɞɨɛɚɜɨɱɧɨɝɨ ɫɨɩɪɨɬɢɜɥɟɧɢɹ RȾɈȻ ɩɪɢɧɢɦɚɟɦ kɎ = kɎɇ ɢ U = Uɇ. ȼɵɪɚɠɟɧɢɟ ɦɟɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ Ɏ 1, U 1 ɩɪɢɧɢɦɚɟɬ ɜɢɞ:

ɍɱɢɬɵɜɚɟɦ ɦɟɯɚɧɢɱɟɫɤɢɟ ɩɨɬɟɪɢ ɜ ɞɜɢɝɚɬɟɥɟ ǻɆXX = 17,7 ɇ ɦ

			ȦɁȺȾ			1 R MC .
				ǻɆɏɏ			10,2					0,0825 .
ǻɆɏɏ Ɇɇ						123,6

Ɍɨɝɞɚ ɫɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ

Ɇɋ ɆɁȺȾ ǻɆɏɏ 0,5 0,0825 0,5825.

ɉɨɥɧɨɟ ɢ ɞɨɛɚɜɨɱɧɨɟ ɫɨɩɪɨɬɢɜɥɟɧɢɹ ɰɟɩɢ ɹɤɨɪɹ

1

Ȧ

ɁȺȾ

1 0,5

R

0,858,

0,5825

Ɇɋ

ə

0,858 0,12 0,738,

RȾɈȻ

R

r

ȾɈȻ RH 0,738 4,31 3,18 Ɉɦ.

RȾɈȻ

R

ɇɚ ɪɢɫ.3.25 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ R Ĺ, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɩɪɢ ɜɜɟɞɟɧɢɢ RȾɈȻ = 3,18 Ɉɦ. ɋɨɩɪɨɬɢɜɥɟɧɢɟ RȾɈȻ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢ-

ɱɟɫɤɢ ɩɪɢ M 1 (ɫɦ. ɪɢɫ.3.25).

ɉɪɢ ɪɚɫɱɟɬɟ ɧɚɩɪɹɠɟɧɢɹ UɁȺȾ ɩɪɢɧɢɦɚɸɬ k Ɏ = k Ɏɇ ɢ R = rə. ȼɵɪɚɠɟɧɢɟ ɦɟ-

ɯɚɧɢɱɟɫɤɨɣ ɯɚɪɚɤɬɟɪɢɫɬɢɤɢ ɩɪɢ Ɏ

1, R

r

ə ɩɪɢɧɢɦɚɟɬ ɜɢɞ

ə

C .

U

M

ȦɁȺȾ

r

ɋɬɚɬɢɱɟɫɤɢɣ ɦɨɦɟɧɬ ɨɫɬɚɥɫɹ ɩɪɟɠɧɢɦ

ɋ

ɁȺȾ '

ɏɏ

0,5 0,0825 0,5825.

Ɇ

Ɇ

Ɇ

ɇɚɩɪɹɠɟɧɢɟ ɧɚ ɹɤɨɪɟ ɜ ɨ.ɟ. ɪɚɜɧɨ ɫɤɨɪɨɫɬɢ ɢɞɟɚɥɶɧɨɝɨ ɯɨɥɨɫɬɨɝɨ ɯɨɞɚ ɜ ɨ.ɟ.

UɁȺȾ	Ȧ0ɁȺȾ ȦɁȺȾ rə Ɇɋ	0,5 0,12 0,5825 0,57.
UɁȺȾ	UɁȺȾ UH 0,57 220	125,4 B.
Ȧ0ɁȺȾ	Ȧ0ɁȺȾ Ȧ0H 0,57 90,76 51,73 1 c.

ɇɚ ɪɢɫ.3.25 ɩɪɢɜɟɞɟɧɚ ɯɚɪɚɤɬɟɪɢɫɬɢɤɚ UI, ɩɪɨɯɨɞɹɳɚɹ ɱɟɪɟɡ ɡɚɞɚɧɧɭɸ ɬɨɱɤɭ ɩɪɢ ɧɚɩɪɹɠɟɧɢɢ Uə = 125,4 ȼ. ȼɟɥɢɱɢɧɭ ɧɚɩɪɹɠɟɧɢɹ ɦɨɠɧɨ ɨɩɪɟɞɟɥɢɬɶ ɝɪɚɮɢ-

70