БЕЗОПАСНОСТЬ ЖИЗНЕДЕЯТЕЛЬНОСТИ лекции

*A ? : U”a=Ua – Uo, ? – U”b=Ub-Uo, ? ! – U”c=Uc-Uo, Uo>O.

" ( ? C>: Ia+Ib+Ic+Ih=0, (E:

(Ua-Uo)/Ra + (Ub-Uo)/Rb + (UcUo)/Rc+ (Ua-Uo)/Rh = 0 (1)

) A : Ra=Rb=Rc=R, ) (* @ ) :

(Ua+Ub+Uc)/R – 3Uo/R + Ua/Rh – Uo/Rh =0.	(2)
/ * =: Ua+Ub+Uc=0, >
-3Uo/R + Ua/Rh – Uo/Rh = 0.	(3 )

(E ) A@ * + = ( = ) L E ? *:

Uo=( Ua*R)/(3Rh + R).	(4)
# > = ? * = *:
Ih = (Ua – Uo)/Rh = 3Ua/(3Rh + R).	(5)

A , = Ua – ? ) A@ E C (A ? (

Uo ) C A > ? = E ) * =:
Ih= 3U / (3Rh + R).			(6)
U		U
U*	C		U*	C
0	B			B
RA RB	A		R R R	A
	RC
Rh		Rh	I
//////////			r?
	/////////////////////////////////////////////////////////////////////////
/ (.8			/ (. 9

? ) (* > @ A, = ? * = *, (* =, )-

*A (A ( ) * ? *A. < C ( F ( *A B ) ( A- + *B ? ( ( A ? *A ( ( ? * + + *BE.

2. (* = (* ( ) * A ? *A – Ra, Rb, Rc , = ? * =- * ) *A (A ( ( ( (1):

Ih=( 3*U *Ra* (Rb2 + Rb*Rc + Rc2)/ Rh*(Ra*Rb+Rb*Rc+Rc*Ra) + Ra*Rb*Rc …(7). 3. (* ) A@ ( B ( * 1 , = ? * = * ) *A (A - * = ( + ( ( *AEF + ? ( ( ) * A ? *A )-

, @ (* ) A B C ? = A ( = (. Ih=3U * *C/ (1 + (3Rh* *C)2) 1/2 (8)

#. . = ? * = * ) *A (A * = + ( (!a, Cb, Cc = C). - < A ( B () *B? (A * *B, = ? @ B ) A * A ( + (-

21

( *AEF +. !, * EF *BL + ( BE, = B ) ( ) (* C - *E= A ( = . ( ) C ( + ( *B

) ( E * ? A@ > (. 8( A ) ( ( )- @ A ( ) (* ( A A ) A@ A @ ? ? * ) (.

! ( ? * + + *BE, * EF *BL + ( BE, <-

L ? ) ( (, = ( ( ? ? * + + *BE.

U

*E C ? = AC ( ) * +

? *A C) *E( ) (

U*

C ? + C) + (

C

) , = = *

B

( L L + C) *E(

A

) ( ( ): -

".

) ) ) ) * + ) A@-

r0

RA RB RC

((.8) = ? >

Rh

Ih

) *A B(A: Ih=U*/ Rh.

( 9).

? (*, )

//////////////////////////////////////////////////////////////

<* C = ( C ( ( ? F

/ (.10

(<* = ( ) =) ? =-

*B ( ? > ( B ? +( A.

+ + ( ((.9) C-

B ) *E= A = * (, = F )- C AF + = ? * = *, (* = C) *E( > ) ( A, )- *A (A * + ) A@ ( ) * * = *Ih=U*/ Rh.

# ) B (( C ? E = C) E ( B ( >* C ? ? * + +-

*BE, A@ 1000 ((.10).

U

U*

UA

C

UAB

B

UAC

A

"

UB

r0

RA RB RC

UC

Rh

UCB

r?

////////////////////////////////////////////////////////////

/ (.11

/ (.12

# A ( B (380/ 220 ) ) A (A )- L* ( .

! ) * ? ? * + + * C ( AC (4 ) ? = *B @ (- ) * + =. " (. 10, 11 ) ? (C A >-, ) *B @ . ) *E( ) ( = * ?

? E ? + <* = ( + ): ? (-

– ) – = * – ? *A, ( ) * Ro. # ?, ( )- * A = > . % = ? * = * )- *A B(A ? @ A:

22

		UA
	UAC				UAB		Ih=U / (Rh + Ro)	(10)
							" ) ( *B Ro<<Rh, >:	Ih=U / Rh
				Uh			% + > ((.11 ) ? +
							. #. . ) ) *E( ) ( (
UC						UB	) ( ( B ) @ A ( * ) *A B(A
				UCB
	/ (. 13						) A@ ( <* = ( ( ) *

* = *. " ) ( *B

) (* *B + (Ih=const), *B C (* AC ? @ *E= ( ( )-

* * = * ( ) * A > , ) * ) F A . . #. .

Ih=U / ( Rh+r + r ))

(11)

C) *E( ) (, (* = ( ( ? * + + *BE:

Ih=U*/ Rh

(12)

+ @ (, ), = * ) ( *(A ? , ? ? * (B ? *E, ((. 12), ) A@ ? () *A (A ) )-

*B ( ) * E ( A ( ? A R? ( ) *- E ? ? * + + * Ro. < ) A@ ( *B ? * = ? A ? *E: U?=I?*R?, * + = ( –

Uo = I?*Ro

(13)

%? + >, ((. 13), (*, = +( *B ( ) A@

	) * @ * = * ( *B
	*BL ? > :
	Uh= ( Uo2+ U 2 – 2UoU *cos 120o)1/2
	(14)
	" = A, = Ua=Ub=Uc=U , . .
	Ro = B *, (= C )
	Uo=I?*Ro=0; # > Uh=U .
	!* *B, ) + @
	( ( >* C ? ? * +
	+ *BE = ? * = *
	) *A (A, ) ) *E(
	) (, ? ) A@
	( ) * * = *:
/ (. 14	Ih=Uh/ Rh	(15)
	$% > B

C) ? * ? * * ( ? ? * )

), > *B > ) > ? *A, *B( . . C)-

? * ? * ( ( (A (A ( ( () * A <*-

= ( + < > ) ( A ? ) C.

" ((.14) ) ? (C ) ( A = * ? ) C- ) + (, ? * + ? *. (B U – ) * ) A@, ) A@-

@ ); Uh – ) A@ ) ) ) = * (* = ) ( A F ): Rh – ( ) * * = *; r1 r2

– ( ) * A ) ) L E ? *. ? *B ) *E( >

) ( A = * ? (A ) *E= ) ** *B ( ) * E

23

r1 ) (* *B r2. < ) ? + ) () * ) A@ + ) ) L E ? *. *A >*A ( ( < * E (C, ((. 14 ). %? , = U= U) + I2*r2 = Uh + (Ih+I1)*r2 (16) = A, =

) * =:	Ih = Uh/Rh		I1=Uh/r1				(17)
		U = Uh+{ ( Uh/Rh+Uh/r1) } * r2,					(18)
(E @ Uh:
	Uh= U*R1*Rh/ ( R1*R2+R1*Rh+R2*Rh)						(19)
# = ? * = * ) * (A ? @ A:
	Ih=Uh/ Rh = U *r1/ ( r1*r2+r1*Rh+r2*Rh),						(20)
(* ) A B , = r1=r2=r, ) * =: Uh=U / (2Rh+r), >
		Ih=U / (2Rh+r)		(21)
%? ) * = C ? *B ( * :
		%? @ A (21) (*, = = *BL
		( ) * ? *A ) ) L E ? *,
		BL = ? * = *.
		%? @ A (20) (*, = = *BL ( ) *
		? *A ) ) ( (A = *,
		*BL + ) = = ? = *, (* = , > r1 |
		r2.
		C) *E( ) ( = ? * = *
		) *A (A ( ) * *				= * ) *
		) A@:		Ih=U / Rh.			(22)
		+ @ @ ) C) *E(
		) ( –
		Ih=U / Rh., ) ( *B R?<< r1, r2, Rh, ((.14 ).
			" &
		" ((.15) ) ( * (C C) + ( (
		? ? * ).
/ (.15		( ? ? * ) ) ,
	= ) A (A = ) ( A ( = ?
= * ) = . > * = :
	Ih=U / (Rh+Ro),			(23)
(* ) =B * = + Ro, > Ih=U/Rh.
(* @ ) A B ( ) * ) *,
	Ih=U / (Rh+R)+R )			(24)

( ? ? * ) = ( (= (A ? ) (, ) ( *B - ) A@ > ( *B ? * ? = *B. ( *, = * ) (-

L +(A ? ? * ) , (. 15, ? (A ) ) A@:

Uh=I>* R

(25)

> I>- > ?, R – ( ) * ) = ( - , .

*B C (* AC (, +( *B, < ) A@ *,

) ? ? ? ( ) A ) A@ A ( >

24

) = 100% U. ( = ) ) A@ = d * ? ) * ) A@ A (. #. . ) + C ( AC ) A@ @ (- > B ) ( C *A = * ? = +.

# '%0 1 " '% !" !#% / "%& 2 ' # , / '%2"17

' #/%2 ! %7 ! #&7

N	7 ) (-		/ @ + *	/ (= A *
)/)	A
1.	) *E(		%."	Ih= 3U / (3Rh + R)
	) (		Ra=Rb=Rc=R
	C ? + (		R>0,5 ,, L<1
	. @ .
2.	) *E(		%"	Ih= •3*U *Ra* Rb2+Rb*Rc+Rc2/
	) (		Ra> Rb> Rc€R
	C ? + (		R>0,5 ,, L<1	Rh(RaRb+RbRc+RcRa)+RaRbRc
	. @
3.	) *E(		%."	Ih=3*U *( *C)/ 1+( 3*Rh* *C)2
	) (		Ra=Rb=Rc=R
	C ? + (		R>0,5 ,, L>1
4.	C) *E(-		.", %."	Ih = U*./ Rh
	) (
	C ? + (
5.	) *E(		."..	Ih = U / (Rh+Ro)
	) (
	C ? + (
	. @
6.	) *E(		%."	Ih = U*./ Rh
	) (
	C ? + (
	+ + @		."..	Ih = U / Rh
7.	) *E(		? ? ? *AEF >	Ih = U*R1 / (R1R2+R1Rh+R2Rh)
	) (,		); R1>R2
	C) A		R1 = R2
	( B. "/			Ih = U / (2Rh+R)
8.	) *E(		! ? ? *AEF	Ih = U / Rh
	) (,		)
	C) A
	( B. "/

1 / !7 ,1 ! #% #/ 7N " . #

) A@ 1000 , = * (B , () ( ) * = *

(C (: C ? A C) A ( ? * + + *BE C ? A

25

= C) A ( ? ? * + + *BE. (C ( ( F ( *A (A

) C * > = ( A, ) (* A <* ? ) ( (.

C * > = ( A ) ) = (A = C) + (, ) ( *B ) ? *A () *B? B = C ) A@ A – * + ?-

. #. . @ ) B ( * E > ?, ) A@ 380 , (- *B E ( B, ) A@ 220 .

(* A ? ) ( ( ) ) = (* B C) + C ?- + ( ( ? * + + *BE, ( ( ( ) (- ( ( +. < ( *@ B ( *B , )-

@ ? +( E > (( C ( C AF C(A ) ) ( A ?

<* C = ( > ) ( *. 8 ) < C ( + ) )- L C AC ? ) ( (, ), *A ) @ C (.

! ( >* C ? ? * + (* ) A B , > ? @ () = B

* @ F E ? *A E F C ), > *B?A ( ( B )-

@ ? *A * > ( ? A ? *E ( > E *BL C ? = +.

) A@ L 1000 ) AE (A C) C ? ( ( ? * + ? ? * + + *BE.

C * > = ( A ( ( ( ) ) ( A 8, *A - ) A@ + 110 L ) ) = (A ( ( < ? ? * + * ( ) ) ( ( > ) ( A ? ? * *E – >* C). *A ( + ) A@ 1000 35 8 ( * @ ( ? *-

+ + *BE, ) ( + ? ? *AEF ( +( * ) (-

+ = ? ) ( > * ?, ? A, ? F

. .

(* A ? ) ( ( ( AC ) A@ L 1000 ) ) = - (A ( ( ? * + + *BE, . . ? F A *B ? *A = (A ?- ? *BL + ( ) ( *B ? * *A = * ) ( ) ( ) ( ( ? * + ? ? * + + *BE. ( A? ( ,= ) ) A@ AC L 1000 , ( AC ( ? * + + *BE ? @ > ? A ? ? *E, > ( ? A > ?-

B *> ( F ( B ( ) *, . . *BL ) A@ A )- ( A L >. A ( ( ? ? * + + *BE ) ? + - ( *E= ) @ > = ( * + + ? F + ( ) ? @ A ) ( ( B *A = *.

/ !1 '& ! , / / %

1.# C ? A C) A ( B ( ? * + + *BE:

) *B + @ (, ) *E( C) *E( );) + + @ (.

2.# C ? A = C) A ( B ( ? ? * + + *BE:) *B + @ (;

) + + @ (.

3.? A C) A ( B.

26

3.3 ! / #% ' "% / !# "%3 # ,'3

" ) A@ ) ( A L > ) A@

? F C ) ? *E @ ) ( <*-

A ? * +, @ @ *B = >, > ? @ C @-

*E +, ? E ) A@ A, (B, ) ( *A = *. *A < + ) ( ( C (( B ? () * A ) * ) C- ( > ) ( . / (( (C ( A ? *, (= A, = ? *E ( = ? ) * ( = ( + ? ? * *B ( –C, ) > @ + + > ( *B ( ) * - ((.16 ).

/ (.16

? * *B – ) ) ( ( C AF +(A ( ) ( ( ?- * +. = + ), C AF +(A ( ? * +, ? (A =-

? ? * * * ? ? *AEF <*, ? ? * *B, ( ( AF + ? - ( *B C ) ** *B ( C <* ? (A > )) ? ? *- *. < (* = ? A I? ( B ( ) C ( ? ? * *A ) ) * E ( ? ? * *A (. (

? *E > ? ? * *A ? (A ? ( A , + ( * =-

(( A A ? ? * *A )* ( B BL (A (* ( ? ( A ( = A ? *, = ? ) .

=	3	(A 2 )	(1)
	2 2

# = ( ) * ( A ) ( (A ( = (. , *B C

(* AC (( A 1 ( ( A ) * BL (A 68%,

(( A 20 ( ? A ? *E ) = ( 0 ( 20 – -

( ? ( A ).

# = ) =, * @ F ? ( A , ? E (A “? * +” <*- C = ( ( (* (*.

* (( A C (= ) ? ? * *A <* + (* + *F + dx,

) * = ) ) A@ A < (*
dU=Edx	(2)

> – ) A@ ( B <* = ( > ) *A + @ = ( ), A ( >* ( ?-

:

E =

(3)

> – *B ( ) * >.

27

) A@ A <* L (* *F + dC :

dU =	I3	2	dx	(4)
	2

/ ? ( B ) * @ A = ) C ( ? * := + (-

= * + = + , :

	I dx				I3	(5)
= dU =	3		x2	=
	2				2 x
1		x			1
		1

, ( *B + ) * ) BL ? = - C , . . ) x r ( ? ? * *):

	3 =	I3	(6)
		2 r

" ) A@ @ +-* ? ? * + = ( BE <* ( = ? *, C AF (A ? ( A , ? (A ) A@ (- *B ? * U3 .L < > ) A@ A U? I3 , ) EF = ? ?-

? * *B ? *E, ? (A ( ) * ? ? * *A:.

R	=	U3	=		(7)
3		I3		2 x

( ( *AEF: ( ) * ( > ? ? * *A, ( ) * @ ? ? * * > ( ) * >.

" ) A@ ) ( A

(* <* ( ) ? L * ) + ? *A ) (, ) ( + ? ? * *E, ( ( EF ** = ( E ( A?B ( < ) (, ) E ) * ( *B ? * , + ) * ? ? * *A (6). / () * ) * * ? ? * *A *E + <* ( ) (- *A (A + ( (. 17) .

( = * + ** = ( + = (, ( + ( ? ? *- * +, , = ) ) * ? ? *A A .

= * @ ( B(A > = ) = ( > ) * . ? *B

@ + > = * ? ? ( B ) *.

" ) A@ ) ( A (U ) - < ? ( B ) * C = <* =- ( + ), C ( (A = *:

	U = R I h			(8)
	U = 3 = 3 (1	3	) = 3d1	(9)
	d 1= 1
				(10)
	3

*A = * ) ( EF > (A ) + ( , + ( ) ( (

? ? * * ? ( B ) * @ + > U = 0 - ?- ) ( + (* = +.

28

" ) A@ ) ( A. U = 3 - * = (A ) * A ? ?-

* *A ( > ( *B > ? = A, > = * ( (A <* (-

C A(B ? ( A.

" ) A@ L > (L > ) A@)

2 *, F + ) ) C ( ? * ? ( A , ? (A ) ) A@, ( A(B C-* = ( + <* (. ) (C )-

, = * ? (( A A ? ? * *A = ) =, C

( E (A > = *, E ? ) *.

" ) A@ L > ? (A ? ( B ) * C = ) C ( ? *? ( A , C ( = * ((.17).

U = x x+a

> x- (( A ? ? * *A + >; – L > = *, ) (=

=0,8

U = x x+a

(11)

#. . x x+a A *AE (A = ( A ) * ? ? * *A 3 , ? ( B C – = ( <-

	> ) *. (* x =	I	: x+a =	I	; U = x x+a =	I a	(12)
		2 x		2 (x + a)		2 x(x + a)

%? * U – ) ) * A ? ? * *A (( ? A ?- *E). * 20 U = 0 ;

/ (. 17

? ) * = > @ A ? ((. 17), ) A@ L > ? ( * L > (( A A ( ? A ? *E. " ) A@ L >

( *B ? = * ? ( ? A BL (A ) * A

>. " (( A 10—20 ( ? A ) A@ L > ) = ( (= ?.

) ( ( B ? +( A ) A@ + L > ? *E= (A , = , ) A ) ) «> — >», ? ( ( > L, = ) )- E = * ? *E, ? *B = > @ ( B(A ? * ?-

) B « — >», ) ( *AEF + *BL E ) ( ( B *A = *-

29

. < * = (A @ (( A @ = ? *, C -

( B(A. %? @ B ) @ A <* = ( ? +( A ) A@ + L > @ ) <* = ( C , > * L, . *A ? F ) ( > ? +( A ) A@ A ) ( A ) ? C ( ( ? F-(* ) A B <* = ( ) =, ? * EF L >, ( ( ? * = . ).

3.4 I%#"1 , /1 /% / # ! ' #/ 8!# " ,%

%( *E= *B @ ? = *A ) F A <* ?

) *B A > ? A (* @ A +( EF C <* ( , )-

C @ C ) * = ( C . < ) ) *B + > ? + ) (A ( > ) * A > ? C C = ( C

) A + ( (, ( * C +( EF « * C = ( + < ()* <* ( ) * + ) * C ? ) ( ( ) < ()* <* ( ) * +» ( # # ) * +) « - * ( +( <* (» ( 8).

+( EF ? E <* (, C A (A ) ) A@ * C ) A@ A, @ B ) *E= *E=- *A, > > ) ( *A * > + + )).

@ EF A ( ) F A, C (A , ? +(<* = ( E ? *A E ), ( +(, <* = ( ( ) * - * = * @ ( ? B (* A *A ) @ A (* @ EF > ) ( * <* = ( . < L ?* = E ) ? ( ) F A ( ) L + ) ( ( BE, ( ) ( ? ) L + ) ( (.

, I "%& !# "% !" !#% % !#8 " !#%

*BL ( (* = ? ) ( (* @ ( ? ( (* + ( ) F A. " * = * > (100%), C ), > ?, ) AF A ) *B, - ( A ) - ( @ E ( ) * ? *A ? L E . >

A (A <* = ( ( ) * * = * ) ? +( L )- = (* C ) . < + ( A? * ) ?

' :

-( ( B (( *B A * @ ( B * 75%) * * = ) AF + )- *;

-) AF ) *;

-) L A ) ? C (* 35 !);

-? @ ( B > ) ( A ) AF = ( A ? ?- * ) (;

( A *AE (A :

-* = ( ( ( 100%);

-C = ( A (.

#. . ) F A ) ( ) ) ( ( ) ? *AE (A :

30