.
Copyright 41 . (010) 3608065 (010) 3608197 Fax (010) 3608197
.: (010) 3606826 (010) 3606760
ISBN: 978-960-381-393-4
, , . , , , . , . . . . email:[email protected].
, .
3.1 3.1.1. Coulomb . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .11 3.1.2. . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .13 3.1.3. . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .19 3.1.4. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .22 3.1.5. . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . .28 . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .34 . . . . . . . . . . . . . . . . . . . . . . . .43 . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .48 . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . .50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . .51 . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . .63 . . . . . . . . . . . . . . . . . . .
. . . .72 . . . . . . . . . . . . . . .90
3.2 3.2.1. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .123 3.2.2. . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .124 3.2.3. Kirchhoff . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .127
3.2.4. () . . . . . . . . . . . . . . . . . . . . . . . . . . .
.129 3.2.5. () . . . . . . . . . . . . . . . . . . . .136 3.2.6. ()
. . . . . . . . . . . . . . . . . . . . . . . . .139 3.2.7. . . . .
. . . . . . . . . . . . .141 3.2.8. & 3.2.9. Ohm . . . . . . .
. . . . . . . . . . . . . . . . .150 3.2.10. . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.154
3.2.11. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .155 . . . . . . . . . . . . . .
. . . . . . . . . . . . . .156 . . . . . . . . . . . . . . . . . .
. . . . .169 . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .178 . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . .179 . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .180 . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . .191 . . . . . .
. . . . . . . . . . . . . . . .203 . . . . . . . . . . . . . .219 .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .267
3 3.3.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . .279 3.3.2. . . . . . . . . . . . . . . . . . .
. .286 3.3.3. . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . .292 3.3.4. . . . . . . . . . . . . . . . . . . . . . . . . .
. .296 3.3.5. . . . . . . . . . . . . . . . . . . .298 3.3.6. . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . .298 . . . . .
. . . . . . . . . . . . . . . . . . . . . . .313 . . . . . . . . .
. . . . . . . . . . . . . .326 . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .339 . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . .341 . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .342 . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
.355 . . . . . . . . . . . . . . . . . . . . . .373 . . . . . . . .
. . . . . . . . . .394
4 4.1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .461 4.1.1. - . . . . . . . . . . . . . . . . . . . . . . . .461
4.1.2. . . . . . . . . . . . .461 4.1.3. ( ) . . . . . . . . . . .
. . . . . . . . . . . . . . . . .476
. . . . . . . . . . . . . . . . . . . . . . . . . . . .479 . . .
. . . . . . . . . . . . . . . . . . . .488 . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .495 . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .497 . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .498 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . .504 . . . . . . . . . . . . . . . . . . . . . .510 . .
. . . . . . . . . . . . . . . .524 . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . .551 . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. .560
1
3.1
3.1.1.
COULOMB
, Coulomb 1784 Coulomb . Coulomb : F q1 q2 r, : , . : F=k q1 q2
r2 (1),
k Coulomb, , , , ( ) ( ), , q1 q2. k . , k (S.I.) : m2 1 k= = 9
109 . 40 c2
12
To 0 (S.I.) : c2 N m2 A , , k : 0 = 8,85 1012 1 40 , ( ) > 1,
.. 81. ( = 1). q1 q2. O k= Coulomb F1, F2 - (F1 = F 2). T Coulomb:
q1 q2 F 1 = F2 = k r2 (1) Coulomb , 1 C , 1 m . q1 q2 , F = k r2 F=
= k q1q2 = > 0. F r , . r2
13
F=k
q1 q2 r2 : x2 F, x r, kq1q2
=
. q1 q2 F=k . r2 , , r . , r . (1 C) S.I. : q1 q2 r2 1 C (1 ) 1
m F=k 9 109 .
3.1.2 , , . : , . , . , :
14
, F , q , , : F = q
(2)
To , F , q . : = F q (3)
H , , q , , q . Q, . Q Q. Q Q.
H S.I. (3) 1 1 . C
Q. Q , Q r q. , (3):
15
= F = k Qq . r2 O (3) : k = Qq r2 q
F , q
E=
Q kQq kQq = E=k 2 2 2 r q r q r Q : r2 = r2
(4)
E = k
= k Q = > 0. r , . Q . r2 E = 2 : x , x r, (Q) = H . 3 ( ) q
, Q. (4) q Q r . : . , , .
16
Q1 Q2. Q1 Q2 . 1 Q1 2 Q2. : Q1 Q2 2 = k , 2 2 r1 r2 r1, r2 E1 =
k Q1 Q2 . 1, 2 , Q1 Q2 . : = 1 + 2
(5) ( )
( 4) : =2 1 + 2 + 212 2
(6),
1, 2. 1, 2. ( 5) : = 2 1 + 2 (7)
, .
17
, , , : . (6) .
) .
) .
) .
) .
6.
: . . . , , , . . .
18
( ) . , : . , . . , . ( 7). . , . . 6 .
(1/C) S.I. 1/C , 1C 1 .
19
3.1.3
: , Newton : F m1 m2 r, : , . , F=G m1 m2 r2 (8),
G , , , , , , m1 m2. G Nm2 G = 6,67 1011 kg2 m1 m2. F1, F2 - (F1
= F2). : mm F1 = F2 = G 12 2 r , m. m Mm F F = G 2 . r
20
UA, m , WA F , m . , UA = WA A WA = G : U() = G Mm r (11)
(9)
Mm r
(10)
WA F m , . F . , , , , . : WA : WA = U = (U UA) = UA U (12),
U (U = U U = U U) U, U . , Coulomb, -
21
, ( , ), . , , , S.I. 1 Joule (1J).
Q < 0 , q > 0. q Q F r2 UA, q , WA F , q , . , UA = WA A
WA = k : UA = k Qq r (15) Qq r (14) (13)
F=k
Qq
Q, q (15) . : Q, q UA < 0, Q, q UA > 0. UA < 0 WA <
0. , F q . , q , q .
22
. UA > 0 WA < 0. F q . , q F () . . : U q1 q2 ( m1 m2) (
). : U=k q1q2 r (16) U=G m1m2 r (17)
3.1.4 ,
, , : VA , , UA, q , . : UA q
VA =
(18)
S.I. 1 Volt (1V) (18): 1V = 1J C
, VA = 5 V UA q = 1C ( ) UA = 5 J. , VA = 5V UA q = 1 C UA =
5J.
23
, , . : VA , , WA q , . : WA q
VA =
(19)
(1 V) S.I.To 1 V , 1C 1 J.
Y Q. Q , r Q, q. , VA , VA = UA q , UA = k k , VA = Qq r q Q r
VA = k Qq qr Qq r q
VA = k
(20)
(20) , , . (18), (19), (20) , .
24
: r Q (Q < 0) V < 0. r V . Q (Q > 0) V > 0. r V . Q
V = k r V= = kQ = > 0, Q > 0 = kQ = < 0, Q < 0 V r , .
V=k = : V xr kQ x Q r r ,
V = k
Q
.
25
VA Q1, Q2, Q3 ..., Qv. Q1, Q2, Q3 ..., Qv VA Q1, Q2, Q3 ..., Qv
r1, r2, r3 ..., rv . V1, V2, V3 ..., Vv Q1, Q2, Q3 ..., Qv : , r1
r2 r3 rv VA V1, V2, V3 ..., Vv , Q1, Q2, Q3 ..., Qv . V = V1 + V2 +
V3 + ... + Vv (21) ( ) V1 = k Q1 , V2 = k Q2 , V3 = k Q3 , ..., Vv
= k Qv
, , V . , . , F U .
() : V = V V , WA q , . : WA q (22)
V = V V =
26
S.I. 1 Volt (1 V). , , WA = U U, : V = V V U U q , . : U U q
V = V V =
(23)
q>0 ( ) ( ). , q , WA > 0. : V = WA q == = V > 0 VA V
> 0 ==> q>0WA>0
VA > V
, WA > 0 WA = UA U UA U > 0 UA > U : (q>0) , . q
< 0, WA > 0 V = WA qA == = V < 0 VA V < 0 VA < V
==> q0
WA > 0 U U > 0 UA > U : (q0 , . q>0 F : WA > 0 F
q . , V = WA q == = V > 0 ==> q>0WA>0
V A V > 0 V A > V q 0 VA V > 0 VA > V ==> q 0 :
C= = 0 S = . > 0
S = C= 0 S
32
C = f(S) C = f( )
C=
0
S.
C= =
0 S
.
= x : C xS 0 17.
: C x x 0S
C = 0 S, S
= : C= 0S C = , = 0S = . > 0.
C = f () S C= 0 . = x : c x S 0
33
C =
Q 1 Q = C V V = Q V C
Q = CV Q = V , = C = > 0 1 1 Q V = Q, = = > 0. C C Q =
f(V) V = f(Q) V=
Q = C V. E = x Q xV C 19.
1 Q. E C = x V xQ 1 C V=
34
1.
: Coulomb: . . . . k: . . . . m2/C2 S.I. 3. , , , : . . . . . r
, F. r/2 : F . 2F . 8F . F . 4 H Coulomb : . . . . . , , = = r, q1,
q2, q3 , q2 q1 :
2.
4.
5.
6.
35
. k
q 1q 2 r2
. k
. 7.
q1q 2 qq + k 32 2 2 r r q1 q3 . k 2 r
Coulomb : . . , . . . q1 q2 = 2q1: . q2 q1 . q2 q1 . q2 q1. . q2
q1
8.
9.
q q1 q2: . . . q1, q2 . q1, q2
10. : . . . . . 11. : . . . . o ,
36
12. . . . () . . 13. :
. . B . . . 14. :
. . . . . 15. :
. .
37
. . . 16. :
. . . . . 17. Q. : . Q, . . . . 18. : . . . . 19. : . . ,
Coulomb . . . 20. q : . . . .
38
21. : . . . . . 22. : . . . . . 23. q : . q . q . . q , q .
Joule S.I. 24. . . . . 25. . . . . 26. . Joule S.I. . . . Volt.
39
27. A VAB 20 V VA = 4 V : . VB = 16 V . VB = 16 V . VB = 24 V .
VB = 24 V
28. q VA = 3 V VB = 8 V. : . q . q . q . q . 29. WA q : . . . .
30. :
. () Coulomb r . . () . () . . () -
40
, r . 31. : VA = 20 V VB = 8 V. : . VA V = 12 V . VA V = 12 V .
VA V = 0 V . V V = 12 V 32. , VA = 8 V VB = 4 V. :
. . . 5 V . 9 V. 33. , V = 2 V V = 22 V. :
. VM = 12 V . VM = 12 V . , . . 34. VA 14 V, , WA q = 1 C : . WA
= 14 J . WA = 14 J
41
. WA = 14 J q ( ) . WA = 14 J q ( ) 35. r q , : . , . , q . 4k ,
r q . 4k r . k, . 36. . . . . . 37. H : . . . . C (Coulomb) S.I.
38. A, V , : . . . . . 39. ( = 8) C. V , , . : . 4C . . .
42
40. A Q , ( = 5) : . . . . . 41. Q . : . . . . . 42. =
VA V
VA V , : . . . . . 43. : . 1 . QV2, Q V 2 1 . CV, C V 2 . . 44.
:
43
U V, : . () . () . () . () 45. :
. () Q V . () C . () 1 V o Q = , C C . () C Q . 46. H : . . . C
= 0 . C = 0 S
S
, , , . 1. . F = k q1q2 r Coulomb
44
. Coulomb () . . . Coulomb. 2. . Coulomb . = 81. , , , , Coulomb
81 . . Coulomb . . Coulomb S.I. Joule. . Coulomb . . , , . . , . .
. . . . . . . . O . . .
3.
4.
5.
45
. . . , . . . 6. . o . . . . Q = k 2 , Q r , r . . Q V = k , r Q
, r k . . , . . . . . . . . . . 20 V. 1 C 20 .
7.
8.
46
. , . . , , , . 9. . Q. , . . Q. , . . Q. , WK . . W q W = (VA
V)q .
10. . , , . . . . . . . 11. . . . q q2 3k , k Coulomb.
47
. . . . 12. . Q. , . . , , , Q, Q, Q, Q. , . . , . . , () . 13.
. , . . . . . . . 14. . . . . . . . Wimshurst .
48
15. . . . . . . . , . 16. . . . V J . m C . 6,5 4,5. , . . .
. . 1. . Coulomb . . . . . . . . . . V/m . Joule . J/C . . C .
/m . () .
2.
49
3.
. k . . . E. 0
. . . . . C2/Nm2 . m2/C2
4.
. B. . . E. Coulomb
. C = 0 . = S
F q U . V = q q1q2 . F = k r2 1 . U = QV 2 .
5.
. (Q) (V)
. (C) (Q) .
.
. (F) Coulomb r
.
.
50
: 1. .......................... ................... .
................ .................... .............
..................... ..................................... .
................... S.I. 1 V. S.I. .....................,
..................... S.I. .....................
................................. , .......................
................. . ................................
............................ . .....................
................................................
....................... ........................... .
.............................
2.
3.
4.
51
** . 1 3 109 C 2 cm q. ; , 27 105 . N m2 . q. : k = 9 109 C2 :
Q=3 109 C r = 2 cm = 2 102 m F = 27 105 N k = 9 109 Nm2\C2. q=;
F Q q () Q>0 q0
1 1 = 2 2 4r r2
r 2 = 4r2 r2 = 2 7.
4 r2
r2 = 2r
, , . ; q , , q FB F . : FB = k qq qq q2 q2 FB = k 2 (1) F = k F
= k 2 F B = F
(2)
(1) (2)
(3)
F q : F = FB + F F : 3(3) F F 6 0 = = = FB + F =60 F+F60
F
3 = 2 3 2
2
=
3 3
1 F 1 + 2
= 30
F . F .
76
8.
. , () ; Q>0 q>0 . = . FA F q : FA = k Qq KA2 F = k Qq 2
FA = F . FK
=
FA, F, : FK = FA F
FK = 0
O FA F, , , . q ( ) : Qq Qq F = k 2 AB 2 = ( FA = k )
FA = F . A F B
FA, F , , : FB = FB = FA2 2 FA + F FB= FA = F 2 2 FA + F = 2
2FA
2 FB = k
Qq AB 2
2 > 0. FB > FK F = 0.
77
9.
T , . . ; . , . . , , , , () . . 10. ; . 3.1.2 : ..., q . 11. :
) C, ) /m, ) /c, ) J/c A ) /c 12. : Q, Q . Q. 13. X () , () . , :
() () () , () () () 14. (), , () . q -
78
Q. q: () q . () () . () () , () , Q. () () . () 15. Q1, Q2 Q1 =
2Q2, () () .
(I) To : () () () () r1 r2 , Q1 Q2 , 1 1 2 , () , () , () 2 1 2
() 2 r1 : r2
() () 1 2 ( 1 = 2).
() (), 1 2, , : 1 = 2 k Q1 Q2 =k 2 2 r1 r2 r1 r2 2
2Q 2 Q = 22 2 r1 r2r1 >0 r2
2
2 1 = 2 2 r1 r2
2 r1 =2 2 r2
=2
r1 = r2
79
16. . . . . . 17. (), , () . () : () () () () () () 18. : () .
() . 6 , () ) () ). 19. () , () . q , . q: () . () () q. () () . ()
() . () () . () 20. , , . 7 .
80
21. . () . () . () F . F (F = ), . () F (q0 ( F ). : (VA V)q
> 0 VA V > 0 VA > V VA V . . 36. () () . () : () , . () .
() () , () . () () . () ) . () () ) . () () . () () () . () . () ,
, () () . , .q>0
86
() , , . 37. (), , . +q ) () (. ) ) () ) . () ) . () 38. . 3.14.
( ) : VA = VA V .......... WA q . VA = VA V = 39. : 1 Volt. 1 Volt
, +1 C , 1 Joule. 41. (), , () . VAB = 10 V. : ) +q ()
87
(.. ) ) VA VB 10 V. () ) VB > VA () ) q = 1 C 10 Joule. ()
42. ; 3.1.5 ( ) Q : C ......................... C = V 43. Q , ; C (
C = ) V , : Q Q C= V= (1) V C Q 2Q Q (1) =2 V1 = 2V. Q1 = 2Q V1 = 1
V1 = C C C , . 44. : . 1 Farad 1 C 1 Volt. C, Q ( ) 1 Q2 . 2 C 45.
; : ) . ) . ) . ().
88
46. (), , () . : ) . () ) , . () ) Q V . () 47. (), , () . : )
() ) () ) () 48. ) . ) , ; ) +q , , Q 2Q; ) q ; , ; ) . ) Q , C , V
Q , C = V Q V V= (1) = (2) C Q 2Q (1) Q1 = 2Q V1 = 1 = V1 = 2 V, C
C V 2V (2) 1 = 1 = E1 = 2E
89
, . ) Q V : W = V q (3) Q1 = 2Q V1 V1 = 2V : W1 = V1 q = 2V q
(3)
W1 = 2W
. ) , , : VA > VM > V, . : VA q > VM q > V q UA >
UM > U. (U) q , . 49. , , VQ . , ; Q Q 1 C = V= V= Q (1) V C C
(1) = x : 1 = > 0 C (1) . : V, x Q, = 1 C (2)
( = x = ). (2) , , C. : Q .
90
) , , : m2 k = 9 109 2 , qp = qe = 1,6 1019 C, me = 9 1031 kg, C
C2 mp = mn = 1,6 1027 kg 0 = 8,85 1012 , g = 9,81 m/s2. N m2 ) ( ).
1. : ) 1 C, ) 1mC, ) 1C, ) 1nC, ) 1pC Q : ( Q0 F = K 2 r2 = K r = q
2 r r F 9 109 m r = 2 108 103 m 9 103 K FS.I.
S.I.
r = 2 108
r = 2 105 m
4.
4 1. 3 109 C 2 cm q. q , 27 105 . q.
4.
5.
+2C Q1 = +6 C Q2 = +4 C,
10 cm. . q = 2 C = 2 106 , r = 10 cm = 101 m Q1, Q 2, x = r = 5
102 m 2 q Q1, Q2 F1, F2 Q1q S.I. 6 106 2 106 F1 = 9 109 x2 2 5 1 0
4
q Q1, Q2 . : F1 = K F1 = 43,2 N
92
F2 = K
Q2q S.I. 4 106 2 106 F2 = 9 109 2 x 25 104
F2 = 28,8 N
F = F1 + F2 F1, F2 : F = F1 F2 F = (43,2 28,8)N S.I.
F = 14,4 N
F F1 (F F1) 6. +2C, 3C 5C , , . () = 0,4 m () = 1,2 m, 3C. FA, F
Q2 Q1, Q3 . : = = 0,8 m FA = k Q1Q2 S.I. 2 106(3) 106 FA = 9 109 N
FA = 337,5 103 N (AB)2 0,16
F = k
Q3Q2 (5) 106(3) 106 F = 9 109 F = 210,9375 103 ()2 0,64
F = FA + F FA, F : F = FA + F F = (337,5 103 + 210,9375 103)N
S.I.
F = 548,4375 103 N
F (F FA, F) 7. N , Q = 2C, 3 cm . r = 3 cm = 3 102 m r Q. : =k Q
S.I. 2 106 N E = 9 109 2 r 9 1 04 C E = 2 107 N C
93
8.
+4 109 C, 3,6 103 /C r . r. Q = 4 109 C = 3,5 103 C r Q. : =k Q
kQ r>0 Er2 = kQ r2 = r= r2 E 6 36 104 kQ S.I. E
S.I.
r=
9 109 4 109 mr= 3,6 103
mr=
6 m r = 102 m 6 102
9.
1 cm -
, 36 109 /C. . Q - , r = 1 cm = 102 m = 36 109 , C r. :
=kS.I.
Q E r2 S.I. E r2 = kQ Q = 2 r k 36 109 104 C Q = 4 1022 C 9
109
Q =
10. +9C 30 cm +4C. . Q1 = 9 C = 9 106 C, Q2 = 4 C = 4 106 C, , r
= 30 cm = 3 101 m r x = = 15 102 m 2 r, . 1, 2 Q1, Q2 , :
94
1 =
Q1 S.I. 9 106 N E1 = 9 109 2 x 225 104 C Q2 S.I. 4 106 N E2 = 9
109 2 x 225 104 C
E1 = 3,6 106
N C N C
2 =
E2 = 1,6 106
H = 1 + 2 = 1 2 = (3,6 106 1,6 106) S.I.
C
E = 2 106
N C
1 ( 1), . 11. q1 = 2C, () 2 10 , x. : ) (). ) q2 = 4 C (). ) F1
= 2 103 q1 (), () . q1 > 0 F1 = F1 S.I. 2 1 0 3 N E= q1 2 1 0 6
C
E = 103
N = C
) F2 q2 () F2 q2 < 0 : =S.I. F2 F2 = Eq2 q2
F2 = 103 4 106 N
F2 = 4 103 N
95
12. (), d = 0,3 m, +2 C +8 C . ) ; ) +8 C 8 C. ) q1 = 2 C q2 = 8
C . , ( , ) : = 1 + 2, 1, 2 q1, q2 . , , = 0 1+ 2 =0 1 = 2 = 0 1, 2
. : 1. , 2. , 3. (1 = 2), 1, 2. 1., (). : 1 : . 2. 2 : . 2. 3 : .
2, 3. 1 = 2. x dx. q1 q2 (dx)2 q dx 2 q : 1 = 2 K 2 = K = 2 = 2 2 2
x (dx) x q1 x q1 == =>dx >0 x
dx = x
q2 S.I. dx = q1 x
8 1 0 6 dx = 2 dx = 2x 6 2 10 x
96
d = 3x x =
d S.I. 3 101 x= m x = 101 m = 0,1 m 3 3 ) () ( q2 = 8 C = 8 106
C): 1 : . 2. , 3. 1 = 2
K q1 q2 q1 q 2 (d+x)2 q2 =K 2 = = 2 2 2 2 x (d+x) x (d+x) x
q12
d+x x
=
q2 x >0 d+x == => = q1 x 4
d+x
q2 S.I. d+x 8 1 0 6 = q1 x 2 1 0 6 x = 3 101 m
d+x = x
S.I. d+x = 2 d+x = 2x d = x x
2 : . 2. , 3. 1 = 2 q1 q2 q1 q2 x2 q2 =K = = (d+x)2 x2 (d+x)2 x2
(d+x)2 q1 x d+x2
=
q2 x = 2 x = 2(d+x) x = 2d + 2x q1 d+x
x = 2d x = 2d x = 6 101 m x > 0. 3 : . h 2. (.. () . , -
97
() , , = 0, (), ). 13. d = 6 m. : ) +4 C, ) 4C. , () d, 3 m d. )
q = 4 C = 4 106 C d, M r = M = 3 m. , = = d\2 = 3 m. , = = = r = 3
m. , ( = 90) . : 2 = r2 + r2 A2 = 2r2 = 2 , , , : q q S.I. = k =k 2
2 A 2r = 9 109 = k 4 106 N N = 2 103 2 9 C C
q q N = k 2 = = 2 103 = 2 B 2r C
= 45, B. H = + B , : N C = 45 ( =2 2 + = = = => = 2 2 =
2 =2
S.I.
2 103
), , .
98
) q = 4 C = 4 106 C, , .
14. 32 103 , . , = 100 /C, . . = 32 103 , F . , F = B + F . F =
0 B + F = 0 F = B (1) F B . B . F , . q . , (1) F = B ==
=>F=Eq
E q= B q=q
15. , 0,45 , , . 0,20 m. , , , .
99
q , r , = 0,2 m = 0,45 . Coulomb F . x , x . , . = 45. F . F = 0
Fx = 0 (1) F = 0 (2) qq = T r2
(1) Fx = 0 F Tx = 0 F = Tx k k
q2 = T (3) r2 (2) F = 0 = 0 = = (4) (4) (3) : (4 ) (3 )
Br T r2 B 2 = = kq2 = r2 g = 2 2 k kq q k 2 r r2 = 2 + 2 r2 = 2
2. : q2 = 2B 2 q= k 2B S.I. q= k 0,2 2 0 ,4 5 C 9 1 09 1
2
q=
0,2
1010 C q =
0,2 105 C
q=
0,2 106 C
16. To 16 2. 17. 1,0 105 kg +1C 12 /C. : ) 1 s. ) .
100
) ; ) m = 105 kg q = 1 C = 106 C , , (0 = 0) , C . F : ( ) = 12
F=E q S.I.
F = 12 106 N
. , F , , , . : = F S.I. 12 106 m = m 105 s2
= 1,2
m s2
F . , , . x t = 1 s : x= 1 2 S.I. 1 1,2 12 m t x = 2 2 x = 0,6
m
) t = 1 s = t = 1,2 1S.I.
m s
= 1,2
m s
, =S.I. 1 1 m2 = 105 1,22 J K = 0,72 105 J 2 2
K = 7,2 105 J
) F ( ) . : ,() = ,() () + UA = K + U UA U = (1)
101
= = 0 U, UA . UA > U ( , , ), , (1) , (UA U), ( ) . ( F ).
18. M 1 s , . , 1 s. , , t = 1 s , , = + 1 : = 1 (1)
1> t1 = 1 s 1 = 0. 1 (1 < 0) , 17, 1 = + 1 t1 1 = 1 t 1 1
=
1 S.I. 0 1,2 m 1 = t1 1 s2 m s2
1 = 1,2
F F = m F = 1,2 105 .S.I.
102
=
F S.I. 1,2 105 N = q 106 CS.I.
E = 12
C
(1) 1 = + 1 = (12 + 12)
1 = 24 1 C C
19. +4 C 6C, 0,4 m. . q1 = 4 C = 4 106 C q2 = 6 C = 6 106 C , r
= 0,4 m = 4 101 m U . : U=K q1q2 S.I. 4 106 (6) 106 U = 9 109 J r 4
101 U = 54 102 J
20. +3 C +4 C 0,27 Joule. N . q1 = 3 C = 3 106 C q2 = 4 C = 4
106 C , U = 0,27 Joule r . : U=k q1 q 2 kq q S.I. 9 109 3 106 4 109
U r = kq1q2 r = 1 2 r = m r U 0,27
r = 0,4 m 21. - +6 C . 0,3 m 6nC. ; (1nC = 109 C). Q = 6 C = 6
106 C , r = 0,3 m = 3 101 m , q = 6nC = 6 109 C U q. : U=k Qq S.I.
6 106 (6) 109 U = 9 109 J U = 108 105 J r 3 10 1 U = 1,08 103 J
103
22. 0,9 m +6 C. Q = 2 C = 2 106 C, , V = 4 104 Volt r . : V=K Q
S.I. 6 1 0 6 V = 9 109 Volt V = 6 104 Volt r 9 1 0 1
23. +2 C 4 104 Volt; V=k Q KQ S.I. 9 109 2 106 V r = kQ r = m r
V 4 1 04 r = 0,45 m
24. +2 C () . () 10 V : ) . ) ; ) q = 2 C = 2 106 C , V = 10 V U
q. : U = V q U = 10 2 106 J S.I.
U = 2 105 J
) W () q, . : == U + W = U + K = = > U + W = 0 W = U K=0
U=0
W = 2 105 J
25. +2 C +18 C 16 cm. : ) r1 = 2 m r2 = 4 m (). ) q = 1 C r1, ;
) q = 2 C r1 r2, ; q;
104
) q1 = 2 C = 2 106 C q2 = 18 C = 18 106 C r = 16 cm = 16 102 m .
12 , , . q1 , q2 rx. : q1 q2 1 = 2 k 2 = k x (rx)2rx
q1 q2 (rx)2 q = 2 2 = 2 2 x (rx) r q1 rx = r 18 106 rx = 2 1 0 6
r
rx r
2
r q rx = 2 == => = q1 r
>0
q2 q1
9
rx = 3 rx = 3x r x = 4 102 m
r = 4x x =
r S.I. 16 102 x= m 4 4
r x = 12 102 m ) V1, V2 q1, q2 . , V : q q S.I. 2 1 0 6 1 8 1 0
6 V = V1 + V2 V = k 1 + k 2 V = 9 109 + 9 109 V x r x 4 1 0 2 1 2 1
0 2 V = (4,5 105 + 13,5 105)V V = 18 105 V 26. +2 C, . ) r1 = 2 m
r2 = 4 m (). ) q = 1 C r1, ; ) q = 2 C r1 r2, ; q;
105
Q = 2C = 2 106 C , V1 r1 V2 r2 . : V1 = k V2 = k Q S.I. 2 106 V1
= 9 109 V V1 = 9 103 V r1 2
Q S.I. 2 106 V2 = 9 109 V V2 = 4,5 103 V r2 4 ) U q r1 U = V1 q
U = 9 103 106 J S.I.
U = 9 103 J
) Wr1r2 , : Wr1r2 = (V1 V2)q Wr1r2 = (9 103 4,5 103) 2 106 J
Wr1r2 = 4,5 103 2 106 J Wr1r2 = 9 103 J q , ( V1 V2). . 27. Bohr ,
() () . r1 = 21 106 m, : ) ) ) r1. ) qp = 1,6 1019 C = e , qe = e =
1,6 1019 C , me , U F Coulomb . , U ( ):S.I.
106
U=k
q pq e e(e) e2 S.I. 1,62 1038 =k U = k U = 9 109 J r1 r1 r1 21 1
0 5 U=
7,68 1024 J 7 . ) Coulomb F F . qpqe m U2 e2 = e k = meU2 (1) 2
r1 r1 r1 1 E = meU2 (1) 2 F = F kS.I. 1 e2 U= r1 1 E = k = => E
= == U 2 r1 2 e2
E =
7,68 1024 J 14
, . 2U=k
) = U + = => == = U + 1 U 2 = U + 1 U 2 = 7,68 1024 J 14
e r1
. : = , = U U = 2 2
: U > U ,U < 0. 28. +30 C, 60 C, +90 C 120 C , , , , 5 : )
(). ) . 2 m.
107
) q = 109 C, . ; 5. 29. 28 , +1 C. ) ) ; 28 ( 5 ) : VM = 54000
2(1 + 0,2 q = 1 C = 106 C WM = VM q WM = 54000 2(1 + 0,2 WM = 0,054
2(1 + 0,2 S.I.
5)V V = 10800 V.
) WM 5) 106 J
5) 106 J
) W : W = V q W = 108000 106 J W = 0,108 J S.I.
q . 30. 4 e++ 2 (mp mn). , . (0 = 0), , 12.000 V, .
108
q qp . , q = 2qp q = 2 1,6 1019 C q = 3,2 1019 C. VAB = VA VB ,
: VAB = VA VB = 12000 V = 12 103 V F , . : E() = () KA + UA = KB +
UB 0 + VA q = + V q VA q V q = (VA VB)q = = 12 103 3,2 1019 J KB =
38,4 1016 JS.I. S.I.
=mp=mn S.I. 1 mU2 (1), m = 2mp + 2mn = = m = 4mp => 2S.I.
m = 6,4 1027 kg
U . 2KB >0 , (1) 2 = m2 2 = => = m = 2KB S.I. = m 2 38,4
1016 m = 6,4 1027 s 12 1011 m s
=
1,2 1012
m s
= 106
1,2
m s
6 .
109
31. , 25 C. , , . - 5 107 V, , (). ) ; ) , 103 s; ) - Q = 25 C V
= 5 107 V, , . , U . 1 1 S.I. : = U E = Q V E = 25 5 107 J 2 2 E =
62,5 107 J
) t = 103 s : P= E tS.I.
P=
6,25 107 103
Watt
P = 62,5 1010 Watt
32. 50 F. , 103 C; ; C = 50 F = 5 105 F , Q = 103 C , V U . Q
S.I. 1 03 Q V= V= = 0,2 102 V V = 20 V : C = C 5 105 V U = 1 2 Q V
U=S.I.
1 2
103 20 J
U = 102 J
33. 10 cm x 20 cm 0,5 mm. ; S = 10 cm 20 cm = 200 cm2 S = 2 102
104 m2 S = 2 102 m2
110
, = 0,5 mm = 5 104 m, C . S S.I. 2 1 0 2 F C = 3,54 1010 F : C =
0 = C = 8,85 1012 5 1 0 4 34. E 200 cm2 . 17,7 1011 F, ; S = 200
cm2 = 2 102 m2 , C = 17,7 1011 F . : C = 0 S C = 0 S = 0 S
CS.I.
=
8,85 1012 2 102 17,7 1011
m
= 103 m
35. 0,2 m2, 4 mm. : ) . ) , 200 V. ) S = 0,2 m2 = 2 101 m2 , = 4
mm = = 4 103 m C . : C = 0 SS.I.
C = 8,85 1012
2 1 0 1 4 1 0 3
F C = 4,425 1010 F
) V = 200 V = 2 102 V , Q : Q = C V Q = 4,425 1010 2 102 C Q =
8,85 108 C 36. 2 F, 2 cm 150 V. . : ) . ) .S.I.
111
) . ) . ; C = 2 F = 2 106 F , 102 = 2 cm = m V = 150 V =2 . , Q
: Q = C V Q = 2 106 150 C S.I.
Q = 3 104 C
M , , Q1, . Q1 = Q = 3 104 C ) , C 1 = 0 S1 1
1
=2
-
C 1 = 0 C1 =
S 2
1 S C 1 = 0 2
S 0 =C
C1 =
1 C 2
(S.I)
1 C1 = 106 F 2 106 F 2 ) V1 : Q Q C1 = 1 V1 = 1 V1 C1 ) = V V1 =
2 V Q Q V1 = =2 C C C C1= 2 2Q1=Q (S.I)
Q =V C
V1 = 300 V
1 2V 2 V 150 V 2 102 m
, : 1 = V11 V1=2V1=2
E1 =
1 =
=E
S.I.
E1 =
E1 = 7500
V m
) V =
1 Q V U1 2
112
Q1=Q 1 Q1 V1 = = => V1=2V 2
, : U1 = U1 =
S.I. 1 1 4 1 Q 2V U1 = = 2 2 Q V = 2U U1 = 2 2 3 10 150 J 2
U1 = 45 103 J , . ( ) . 37. 0,5 cm 80 V. . V = 120 V , V = 600 m
. : = VS.I.
=
80 V V E = 16 103 3 m 5 10 m
38. 120 V . 600 V/m, ; = V = V S.I. E = 120 m 600 = 0,2 m
39. 4,5 V. +4 C ) ; ) ; .
113
) V = 4,5 V q = 4 C = 4 106 C . : V = VB VA = 4,5 V
= . W ( W > 0) q A B, (...) : UA + KA + W = UB + KB = = UA +
W = UB W = UB UA => W = VB q VA q W = (VB VA)q W = 4,5 4 106 J W
= 18 106 J F q F . W F . (....) q :AB + W 0 = W AB + W = WF F A W =
WF B S.I. KA=KB
AB = (V V )q = (V V )q = 18 106 J WF A B B A
W = (18 106)J
S.I.
W = 18 106 J
: , , q // . . , W . .
114
) F . , 1 = mU2 2 . ...: UB + KB + W = UA + KA = = => U B + W
= U A W = U A UB W = VA q VB q W = (VA VB)q = (VB VB)q W = 18 106 J
W , W F, q . .... : + W 0 = W + W W = W = WF F F S.I. KB=KA
W = (VB VA)q
W = 18 106 J
. 40. d = 5 cm = 1 cm. , 90 V. 0 = 2 107 m/s, . , .
115
V = VBA = 90 V. : = VS.I.
=
90 V 102 m
V m , t, . A , , : 1: 0 ( ) E = 9 103 0, . 2: , , F F = = , F me
me ( )
F = Eqe F = 9 103 1,6 1019 N
S.I.
F = 14,4 1016 N
me . = F S.I. 14,4 1016 m = me 9 1 0 31 s 2 = 1,6 1015 m s2
: d = 0 t t = d S.I. 5 1 0 2 t= s 0 2 107 t = 2,5 109 s
: = t = 1,6 1015 2,5 109S.I.
m s
= 4 106
m s
116
:
x = 0 = 2 107
m m = 20 306 s s
: = =2 2 x + = S.I.
16 1012 + 400 1012 = 4 106 26
m = s m s
416 1012
m = s
16 26 1012
m s
x, , : = t, : = = 1 1,6 6,25 1018 m 2 = 5 103 m = 1 2 S.I. t 2 4
1 06 = x 2 0 1 06 = 1 = 0,2 5
2
.
. V > VZ . H -
. : V Z V M = E 0 V Z VM = 0 S.I.
VZ = VM
V > VM V VM = E V VM = 9 103 5 103 V V VM = 45 V
F . : () = () KM + UM = K U = + UM U = + VM. qe V K =S.I. 1 m 2
+ (VM V)qe 2 e 0
117
S.I.
K =
1 9 1031 4 1014 + (45) (1,6 1019) 2
K = (1800 1019 + 7,2 1019)J = 1 2 m 2 2 = = 2 e me
K = 1872 1019 2 S.I. me = 4 106 m s
S.I.
=
2 1872 1019 m = 9 1 0 31 s
416 1012
m s
26
: = 2 1 07 x = 0 = 4 106 26 = 5 26
41. , , 20.000 V. ) ; ) ; ) = 0 , , V V , V V = 20000 V = 2 105
V. ... : + U = + U = U U = V qe V qe = (V V)qe S.I. S.I.
K = (2 105) (1,6 1019) J
K = 3,2 1014 J
) , : = 1 2 >0 me 2 2 = me 2 2 = = 2 me 2 3,2 1014 m = s 9 1
0 31 64 1016 m s 9 2 meS.I.
=
=
8 m 108 3 s
118
42. 5 105 V/m. , 3,2 1013 . ; V . = 5 105 m , , F F = 0 , . . q
B ( q > 0) : F = 0 F B = 0 F = B E q = B = E 3,2 1013 S.I. q= C
q = 6,4 1019 C 5 10 5 43. , 2 104 kg +6 C, . 5 cm. , 30 ( ). m = 2
104 kg q = 6 C , =5 102 V = 5 cm = m , V = (1)
.
= mg ,
x , , F F = E q :(1)
F=
Vq
. = 30,
119
F = 0
Vq = T (2) Fx = 0 F Tx = 0 F = Tx F = 0 T = 0 = T mg = T (3)
Vq (2 ) T = (3 ) T mg S.I.
Vq = V q = mg mg 2 104 10 5 102 3/3 6 106
V = V V=
mg S.I. q 3 102 V V = 50 9 3 V
V=
18
44. . V = 100 V. 50 cm. : ) ) , +200 V. ) , = 50 cm = 5 101 m. ,
: = VS.I.
=
1000 V 5 101 mS.I.
E = 2000
V m V = 100 V
) VK = V V V = VK V V = (200 100)V 45. , 100 cm 2.000 V. +1C 20
cm (). : ) WK )W ) WK VAB = VA VB = (2000 0)V= = 2000V () =
= 1 m.
120
, : 2 + 2 = 3600 cm2 + 6400 cm2 = 10000 cm2 = 2. = 90. : =
VABS.I.
E=
2000 V V V E = 2000 = 2 103 1 m m m
) : VK V = () VK V = 12 103 6 101 V VK V = 12 102 V W q = 1 C =
106 C : W = (VK V)q W = 12 102 106 JS.I. S.I.
W = 12 104 J
) : V M VK = E 0 V M VK = 0 V :
WMK = (VM VK)q = 0 q
WMK = 0 J
) : WK = VK V q = 0 q = 0 J , , : WK = WK + W + W = = (VK V)q +
(V V)q + (VM VK)q = = (VK V + V V VK)q = 0 q=0J
2
123
3.2
3.2.1.
() ( ), . , . ( ). (+), ().
:1. , . , . : 2. , . () . :
(, , ) . : ) ( ) ) ( )
124
) )
3.2.2
: . , ( ), , , , , ), , , . . , , , , , , , , , . . . . , . , ,
, (Si) (Ge). H ( ) , . . , , , . .
125
, .. , 20. 20 ( ) ( m/s) , . . ( Km/s). . . . . . , , : . : . .
. .
126
, : 1. . ( , , , ..) 2. . (, , , ..). 3. . ( , ..)
, dq, dt (dt 0), . : dq dt
= =
(36)
dq dt dq () dt ( dt 0). A dq dt
q , q t q ( ) t . = . : t dq = . dt = dq q = dt t
, , :
127
, , q t, . :
=
q t
(37)
o S.I. 1 Ampere (1 A). 37 1 = 1C s (38)
: 1 , , 1 m, 1 kg, 1 s, , . q t 1 1 s 1 C. 1 = 1 C q = I t 1 C 1
s, 1 . 1 C = 1 A s.
3.2.3 K
KIRCHHOFF
( )
: 1. , , , . 2. , . . 3. , . , , .
128
21
21 . , , , . , , , , . . , . , V, , . . , 1
, . (, 1) . ( ) . , 1 1. , , . (V) . ( ) . , 21 VM VN ( ). . 21
3 . . irchhoff Kirchhoff : . :
=
(39)
129
, (39) 21, = 1 + 2 (40)
kirchhoff : , . -
=0
(41)
(41) , : 1 2 = 0 (42) = 1 + 2
. Kirchhoff . kirchhoff : , . V,
V = 0
(43)
kirchhoff .
3.2.4 , : R , V, , . :
130
R=
V I
(44)
S.I. 1 (1 Ohm), (44) 1= 1 1 , 1 V, 1 . , , , . . , ( ) ( ). . .
. : ; R : 1. . , . 1V A (45)
131
. . 2. S . , . , . 3. ( ) . , ( , ..) . , . 4. . , . . . : R= S
(46)
R . (46) R= S (47)
(47) S.I. 1 m 1 m = 1 m m2
R 1 m 1 m2.
132
, , : = 0(1 = ) (48),
C, 0 0C, (C), S.I. grad1 (1 grad = 1C) R0 = 0 R = S S 0C, S )
(48) : S = 0(1 + ) S = 0 S (1 + ) = R0(1 + ) (49) C, (
R =
R = R0(1 + )
(49) : R = R0(1 + ) R = R0 + R0 R = R0 + R 0 (50)
= x + R, x , R0 = . R0 = . : ) = R0 > 0 . > 0 ) = R0 <
0 . < 0 ) = R0 = 0 . = 0. : ) > 0. .
133
) (), 0. R = f(v), , 24. () , : = 1 R 1 . R
24
: Ohm (.. , , ..) ( ) . . R R= V , I . 23 ( ) . VA>VB . VAB =
IR VA VB = IR . , IR
. R R.
135
0 1 2 3 4 5 6 7 8 9 () . , ( 25) . . ( %) () . 10%, 5% 1%.
: ) , , , 1000 10%. 10 1000 R = (1000 100) R = 1000 100 ) , , ,
3300000 10%. R = 3300000 10 3300000 100 3300000)
R = (3300000
) , , , 470 10%. 10 R = 470 470 R = (470 47) 100
136
3.2.5
()
. , . 26 R1, R2, R3 . . VK : VK = V :RKA=0
26
VKA = I RKA = = VK VA = I 0 VK VA = 0 => V = I R = = V V = I
0 V V = 0 => : VK = V VK V = V == = ==>V=V VK=VA RA=0
V K = V V = V
V V = V
R , R1, R2, R3. R R1, R2, R3. 27. 26 : VA V = (VA VB) + (VB V) +
(V V) 27
137
= == = V = I R1 + I R2 + I R3 = ==> V = I(R1 + R2 + R3)
(43)
VAV=V
27 : = ==> VA V = I R = == =VAV=V
V = I R
(44)
(43) (44) : R = (R1 + R2 + R3) = = R = R1 + R2 + R3 =>I 0
(45)
R1, R2, ..., Rv R : R = R1 + R2 + ... + R (46)
( ) , . . 28 R1, R2, R3 . 28 , , .
VK :RKA=0
VK = V
: VKA = I RKA = = VK VA = I 0 => V K VA = 0 R=0
V K = V V = V
V = I R = = V V = I 0 V V = 0 =>
138
: ==> VK = V VK VA = V == =V=V VK=VA
V V = V
R , R1, R2, R3. R R1, R2, R3. 29. 1 Kirchhoff 28 : = 1 + 2 + 3 :
1 = (47)
V VA V , 2 = A 3 = A , R1 R2 R3
(47) : V V V 1 1 1 I = A + A + A I = VA + + R1 R2 R3 R1 R2
R3VA=V
29
== =>
I=V
1 1 1 + + R1 R2 R3
(48)
29 : = VA VA=V == => R I= V R (49)
(48) (49) : V 1 1 1 =V + + R R1 R2 R3 == =>V 0
1 1 1 1 = + + R R1 R2 R3
(50)
R1, R2, ... Rv R : 1 1 1 1 1 = + + + .... + R R1 R2 R3 Rv
(51)
139
: 1. , . 2. , .
3.2.6 ( )
, 0 , . 30 . 0 ( ) : () (o ) S : RAB = RA = () S 30
, ( ) : = V RA + R (52)
() RA ( 52). , . .
140
, , q ( ) , . , , , , ( ). q , , ( ) . q . (.. ) . () . UA - U q
W . ( ) , . : W = U A U = V A q V q W = (VA V)q
VA V = V q = It, : W = V I t = E (53)
(53) W t . : , , , t, ;
141
31 , , ( ) . () () ). RA (RA= S VA VK. 31
, .
3.2.7
32 . , R, . 32 . t q , : = q t q=I t
q : U A = VA q U = V q
VA, V . q ( ) : VA > V => VA q > V q =q>0
U A > U
142
. . Joule. . , , , , . : . . () . . () . , , James Prescot Joule
Joule: Q () , , R t . : Q = I2 R t (57)
143
, , t ( ), dt (dt 0). V, I dW dt. : dW1 = V1 I1dt1, dW2 = V2
I2dt2, ......., dWN = VN = INdtN dW W t, . : W = dW1 + dW2 + .....
+ dWN W = V1 I1dt + V2I2dt + ....... + VNINdt W = (Vidt) (V I dt)
(VIdt) = V1I1dt1 + V2I2dt2 + ....... + VNINdt (56) (55), (54)
: W (55) () . = . , , . ( Joule) . . , () . , , , -
144
( ) R, , . V , W 33
t Q , : W = Q VIt = I2R t V = I R I = , , Ohm. R, , . V , W t, :
34It 0
V R
. : Q R t () , ..., : W = Q + Vit = I2R t + 58 : V > IR I<
V RIt 0
V = IR +
t
(58)
Ohm. . It
145
. . ( ). : W = Q VI t = I2 Rt V = IR I= V RIt 0
35
Ohm. : Ohm . : Ohm. , , , , Joule (Q = I2Rt), ( R) t . : Ohm
Joule :=
Q = I2Rt
Q=
V R
V2 R t R2
Q=
V2 R
t
(61)
: R ; , t, (55) : Q = (2Rdt) (59) Q = R(I2dt) (60)
146
( ) dW dt (dt - 0), . : P= dW dt (62)
dW dt . , dW . = dt . W t W ( ) t P = W . t dW dW W = . = = . dt
dt t :
( ) W, , t, . W P = (63) t SI 1W (1 Watt). (63) 1W = 1 J/s : 1 W
1s 1 J.
147
dW dt - 0 dt dW = V I dt (64) V, I dt . , , V , , , , : dW VIdt
P= p= P = V I (65). dt dt (65) ( V, I ). V, I , = , (65), , . , PR
Joule : P = PR = dQ I2 Rdt PR = dt dt P R = I2 R (66)
(65) ( , ) . : Ohm :I=
P R = I2 R = = > P R = ==
V R
V2 R R2
PR =
V2 R
(67)
1 W. 1W. 1h W : P= W t W=P t (68)
W = 1 W 1 h W = 1 Wh. H 1 Wh (1 ) , SI, ( SI J) :
148
1 Wh 1 W 1h. I 1 Wh = 1W 1 h = 1 W 3600 s = 3600W s = 3600 J
1KWh (1 ) : 1 KWh 1 KW (1KW = 103W) 1h. I 1 kWh = 1kW 1 h = 103 W
3600 s = 36 105 Ws = 36 105 J
Joule) , , Joule, . : , , , , , , . ) Joule . ) Joule . .
() ( ) ( VK) ( ) . VK .
149
, 220V, 2200W. : VK = 220 V = 2200W. ; ) VK. , . ) VK , , VK . )
9 ) = V K IK IK = PK VK (68)
, VK , . ) ( ) Ohm. , R, : R = VK IK (69)
(69) (.. ) .
150
3.2.8. KAI
()
3.2.9.
OHM
.
36 R1, R2 . . R1 R2 . ( ). . . , r SI . , W, t q t () . : () , W
, q , . : E= W (70) q 36
.
151
SI 1 V. 1J . 70 : 1V = C t : W = P t q = I t. 70 : W Pt P = E =
= . q It I : E= () , . : = = (71)
r . . 71 : = = (72) , W t : W=P t W=E I t (73)
( = ). 36 : W=Et t, QR1 = I2R1t QR2 = I2R2 t Q r = I2r t R1 t,
R2 t, r
t, R = R1+R2 , R = R+r .
152
: W = QR1 + WR2 + Qr E I t = I2 R1 t + I2R2 t + I2 r t E = IR1 +
IR2 + I r E = I (R1 + R2) + I r E = I R + r . R Ohm : ( ), () R . :
E = I (R + r) E = I R = (74) R 36 : V = V K V = V A V . = VA V = R
= (R1+R2) R1, R2 . 74 : = R=VAV = R = (R + r) E = I R + r == = = =
== = => R
E = VA V + Ir === => E = V + r (75). == = = (75) V = r
(76)
VAV=V
, V I r . . . , , , 76. 75 : = 0 ( ) r = 0 ( ) = V. :
153
V ( = 0) (r = 0). , (R = 0) , 37. v . V : V = R V = 0 75 = V + r
= r 76 : V = Ir V = r I + E (78) I = E r (77) 37
V = f(I) . (78) = + : V, , -r, . 38. V = ( 78 = 0) = = ( r 78 V
= 0). , 38
: = r = r (+ = 180). : = (79) .
154
= V = + r V = - r = R
(80) (82) (83) (84) (85) (86) (87) (88)
. . Ohm . () . t. t. t.
R = R + r W = PE t W = t Q r = I2 r t
W = W + Qr (89) (79) (83) (85) (89) , (.. ).
3.2.10. , (.. ). , : . : = (90)
: . = 100% (100).
155
3.2.11. . , , . 39 , , , . . 39 . () .
156
1.
: : . . . . . . . . : . . . . . . . . : . . . , . . S.I. J. . .
: . . . . . . . . : . . . . . . . . : . , , mm/s.
2.
3.
4.
5.
6.
157
. . . . . mm/s. 7. : . . . . . . . . : . . . . . . . . : . . . .
. . . .
8.
9.
10. : . SI mA. . . . . . . 11. : q . = q t . = t V . = V R . I =
R 12. 1 : . SI. . . . SI. . .
158
13. : . . . . . . . . 14. 5 . : . min 300 C. . min 5 C. . s 10
C. . h 5 C. 15. q = f(t) , : . 1 . 2 . 3 . 1 mA 16. I = f(t) , 0 s
5 s : . 5 C . 20 C . 5 C . 0,8 C 17. : . . . . . 1 . . . 18. : .
.
159
. . . . . . 19. : . . . . . 100 . . . 20. : . . . . . . . . 21.
: . . . . . . . . 22. : . 1, 2 3 . . 1 3 . . 2 . . 2 1 . 23.
Kirchhoff: . . . . . . . : .
160
24. 1 = 2 , 2 = 3 , 3 = 5 4 = 6 . : . 1 , 3 . . 2 , 1. . 4 , 2.
. 3 , 2 . 25. VA, VB, V , , VAB = 5V V = 15V. : . V = 10V . V = 20V
. V = 10V . V = 20 V
26. Kirchhoff: . , , . . , . . . . . 27. : . . . , , . . . . ,
SI, (Ohm). 28. 2 10 : . 20 C. . 20 V. . 5 V. . 0,2 V. 29. Ohm: . .
. . . . . .
161
30. Ohm: . V R = . I . . . V R = . I . . 31. = f(V) : . 3 3 . .
3 . 3 . 30
32. V = f(I) : 3 3 . . .m 3 3 . 3 . 30 33. = f(V) : . . . . . .
. I V, , . 34. 1, 2 3 R1, R2 R3 . , :
162
. R1 = R2 = R3 . R1 < R2 < R3
. R1 < R3 < R2 . R1 > R2 > R3
35. , : . . . . . . . . 36. 0C : . . . . . ( 0C) . . . 37. . : .
. . . . . . , . 38. S , : . . . . . . . . 39. : . . . . . . . .
163
40. R, . : R . 4 R . R . 2 R . 2 41. , 50C 40C : . . . . . . . .
42. . : . (110 1,1) . (1100 11) . (11 1,1) . (110 11) 43. R1 = 1,
R2 = 2 R3 = 3 R = 1,5 : . R1, R2 R3. . . . R1, R3 R2. . R2, R3 R1.
44. : . . . . . . . . 45. : . . . . . . . .
164
46. () : . R2, VAB . . R3 R1, R2 VAB . . R2, () . . R3 R1, R2 .
47. (V) : . V . . R3 R1, R2 R1, R2 . . R3 R2, . . . 48. : . . . . .
. . . 49. : . . . Ohm. . Ohm. . Ohm. 50. W t :
165
V t, V I . . V I . . I2Rt, R . . VI t. 51. Q t : . I2Rt, I R . .
VIt, V . V2 . R . I R t 52. : . VIt, V t. . 2 R, R . . I2 R t V t .
R 53. PR : . VI, V . . I R t, R t. . I t . V I t 54. W t. :
166
. . . . . . . . 55. , : . . . . . . . . 56. P t. : . . . 10h 5
KW. . 4h 2 KWh. . 1h 500 J. 57. 1 KWh : . 1000 W . 3600 J . 36 105
W . 36 105 J
58. (110 W, 220 V). : . 440 . . 0,5 . . 110 W. . 220 V.
167
59. : . . . . . . . . 60. (1100 W, 220 V). : . 3 . . 44 . . 1100
W, . . , 1100 W. 61. : . . . . . . . , . 62. I = f(V). : . = 10 . r
= 2 . . = 5 V. . = 1 1 = . r 2
63. R 2R, : . . . . . . . .
168
64. : . Ohm . . Ohm . . . . . 65. : . W = E I t t. . PE = E I t
. . Pr = I2 r , t. . = V t. 66. () (V) : . R3 VAB . . R3 . . R3 . .
.
169
67. : . = V . = PR1 + PR2 + PR2 + Pr . = Pr . = R1 + PR2 + PR3 +
PR4+ Pr 68. 0,9 90 W, : . 20 W. . 81 W. . 1 , 100 V. . . 69. : . .
. . . . . .
, , , ). 1. . , . . . . . . .
170
. 1 , , 1 C. 6. . . . . . . . Kirchhoff , , . . , . . , . . , .
. Kirchhoff . . , Kirchhoff. . , , . . , . . . . . . , ,
7.
8.
9.
171
2.
. . . . . mm/s. . Joule . . . . . . . . . . 60 C 1 min 120 C 2
min . . . . 1 1 m. . 1 1 C s. . q = , t , t . . , , . . , .
3.
4.
5.
172
. . , . . . 10. . . . (Cu, Ni) . . grad-1 . . . 11. . , , 10C 5
, 20C, 10 . . cm. . 3,8 103 grad1 3,9 103 grad1. . . . 12. . R = V
I Ohm . . I = f(V) . . , . . Ohm.
173
13. . , , (6200 310) . . ( C) . . 5 8 8. . 3 100 3. 14. . . . ,
, . . , , . . . 15. . . . . 5V 10V 15V. . . 6V 12V . . . . 16. . :
. . . ,
174
. . , . 17. . . . , . . S.I. Watt Joule. . Joule Watt : 1J = 103
W. 18. . W = P t. . W = (V I dt). . P = V I. . P = V I . 19. . , W
= V I t, I2 W = t W = V2R t. R . W = P t P = . . . . 1 W, 1 J
s.
175
20. . , P = V I, V2 . P = I2 R P = R . ... KW. . ... KWh. . : i)
1 KWh = 103 W ii) 1 KWh = 103 Wh iii) 1 KWh = 36 105 J.
21. . 1 Wh 1 W 1 h 1 Wh = 36 J. . 1 KWh 1 KW 1 h 1 KWh = 3600000
J. . 1500 W 2 h. 0,09 /KWh ... 0,27 . . 1100 W 900 W. 22. . Q =
I2Rt ( = ) , . . P = I2 R = . . cal (). 1 cal = 4,17 J 1 J = 0,24
cal. . , , . 23. . (220 V, 100 W). 220 V 100 W. . (440 W, 220
V)
176
2 110 . . (220 V, 176 W). 0,8 275 . . . 24. . . . . . . . . 25.
. . . . . . . . 26. . , . . . . . . .
177
27. . Ohm . . . . E . r . . 28. . 30% 0,7. . 0 = = = . = 32 4 3
4S.I
: = 100% = 100% = 75%.
186
5 R1 = R2 = 40 . V = 120 V. R2 () VK = 60 V = 90 W. . . . R3 R1,
. R1 = R2 = 40 V = 120 V VK = 60 V PK = 90 W . . . R3 = ;
.
VK, PK , . : PK = VK IK IK = PK S.I 90 9 IK = A IK = A VK 60 6
IK = 3 A 2
Ohm. R : R = VK S.I 120 60 R = R = IK 3 3 2 R = 40
R R2, R :S.I 1 1 1 R R 40 40 = + R= 2 R= R R2 R R2 + R 40 +
40
R=
40 40 2 40
R = 20
1, 2.
187
R R1, R : R = R1 + R R = (40 + 20) : VA=V V V S.I 120 = = =>
= == = R R 60 1 : V = R V = 2 20V : 1 = V S.I 40 1 = R 40 1 = 1 S.I
S.I
R = 60
=2
V = 40 V
1 < . . ( V < VK). . R1 R3 . , 3, . V R2 VK. : V = 4 R VK
= I4 R2 I4 = VK S.I 60 I4 = A R2 40 I4 = 3 A 2
188
1 Kirchhoff : 3 = 4 + 3 = : V = VAB + V = => V = VAB + V =
=> VAB = V VK = => == == == I3R3 = V VK R3 = R3 = 20 V VK S.I
120 60 60 R3 = = I 3 3VA=V VB=V VA=I3R3
S.I
3 3 + 2 2
3 = 3
6 , r, R . . ,max . . ; ( ) . = r = I2 r . : = + Pr E I = P + 2r
I2 r + = 0 rI2 E I + = 0 (1)
(1) : (x2 + x + = 0) . : 0 2 4 0 ( )2 4 r 0
189
2 4r
0 2 E2 4r
4 r
2 : 4r
,max =
(2)
.
= ,max =
E2 = 0, 4r (1) : = ( ) = 2 2r I= E 2r
(3)
, Ohm =(3) R=R+r E E E 0 1 1 = => = == = = R R+r 2r R+r 2r
R+r
2r = R + r 2r r = R
R=r
(4)
R = r. ( ). ( ) . : = + Pr E I = + 2 r E I I2 r = P = r I2 + E I
(5)
(5) = x2 + x + : , x , r2, , 0. = f(I) . , , : : = E 2r = 2( r)
2
I=
190
: = 2 4r
(2 4) E2 [2 4 ( r) 0] = = = 4 4 4r 4( r)
P =
. : Pmax = 2 4r E2 = . 4r 2r
.
. = ,max = = = . : R R+r E = 2r = R + r 2r R+r
R=r
!
191
1. t1 = 3s t2 = 4s 90 C C 7 . Ampere min s t1 t2. [. 1 = 1,5 t1
2 = 7 t2]. 2. t = 320 s , , = 1022 . e = 1,6 1019 C, . [. = 5 ]. 3.
R = 10 V = 100 V. . . . R R1 R 1 = 4 . R1. [. . = 10 4. . R1 = 15
].
, 5 , 20 V. . . . . [. . R = 4 . R1 = R = 4 1 = 10 ]
192
5.
R = 2. : . . . . . . . . 24 33 20 . R = 3,5 . R = . R = ]. [. .
R = 7 14 7 R1 = 2 R2 = 4. .
6.
[. R = 2 ]. 7. R1 = 5 , 2 = 20 R4 = 3 . R = 20 , R4. [. R4 = 30
] 8. R = 7 . , . [. R = 11 ]
193
9.
1, 2 V . : R1 = 10 , R2 = 40 , R3 = 60 , R4 = 20 2 = 2 . . . . .
[. . 1 = 17 10 340 , 2 = . V] 3 3 3
10.
T , (220 W, 220 V). R1 = 90 R2 = 220 , V . [. V = 400 V]
11.
V = 20 V. A R1 = 3, R2 = 7 , C1 = 3 F C2 = 5 F : . Q1 U1 C. . Q2
U2 C2. . [. . Q1 = 0 C, U1 = 0 J . Q2 = 7 105 C, U2 = 49 105 J]
194
12.
1 6 . R1 = R2 = 10 R3 = 20 : . r. . . 5 . . = 48 V, r = 2 , . =
6
13.
. = 90 V, R1 = 5 , R2 = 10 , R3 = 14 V = 42 V, : . . r . R1 . V.
[. . = 3 . r = 1 . VR1 = VAB = 15 V . V = 30 V]
14.
O 1 2 : 1 (11W, 22V) 2 (10W, 10V). H HE = 33 V r = 1 . , ; R 1 ;
[. 1 2 . R = 44 ]
195
15.
1 2 : 1 (16V, 4W) 2 (24V, 6W). H HE = 42,5 V r = 2 . , ; R ; [.
. R = 8 ]
16.
= 12 V, r = 2 , R1 = 1 , R2 = 3 3 = 2 . , , : . . . R4 . , r .
[. . = 3 . R4 = 2 . = 1. Pr 6 .]
17.
r = 3 . , , , , : . . V . . V 1 . . R = 3 . = 2
196
18.
R = 1,1 , R5. : R1 = 1 , R2 = 2, R3 = 3 , R4 = 1 , R6 = 2,8 R7 =
2,8 . A , = 10 V r = 0,9 R1 R4. [. R5 = 4 , PR1 = 6,25 W, PR4 =
4W]
19.
2 m, 2 mm2 106 m. (10 W, 5 V) = 7 V r. , 3,5 . : . r . V1 . . (
). [. r = 1 . V1 = 3,5 V . = 6 W . = 0,6]
20.
= 50 V, r = 2 , R1 = 10 R2 = 40 , : . . . R1 R2. .
197
. 1 min. [A. . = 5 , 1 = 4 , 2 = 1 . = 250 W . R1 = 160 W PR2 =
40 W . = 200 W . Qr = 3000 J] 21. T , , . = 88 V, r = 1 , R1 = R3 =
35 , R2 = R4 = 15 . . VK = 2V . [. . = 4 . VK = 84 V, V = 42 V . VM
= 42 V] 22. R1 = 3 , R2 = R3 = 2, R4 = 2, R5 = R6 = 2, = 90 V r = 1
. , . 1, 2, 3 . 1, 3 2 . 2 1, 3 . 1, 2, 3 . [. 1 = 0 . 2 = 9 . 3 =
10 . 4 = 11,25 ] 23. 80% 160 W. H VAB = 100 V. R1 = 230 , R2 =
25
198
= 200 V : . . . . . . . . KWh, . [. . = 200 W . = 2 . Ra = 10 .
r = 2 . = 400 W . = 232 W . W = 576 103 . W = 0,6 KWh] 24. , R1 =
0,5 , R2 = 1, R3 = 2 , R4 = 4,5 , R5 = 2 R6 = 1,3 , R7 = 1,8 r =
1,3 = 60 V. ;
[. = 10 , 1 = 2 , 2 = 8 VM = 29 V] 25. R1 = R4 = 60, R2 = R3 =
40 , = 208 V = 2 . . . . . .
199
. . [. R1 = 50 , R2 = 48 . R1 = 52 , R2 = 50 . 1 = 4, 2 = 4,16 .
V1 = 200 V, V2 = 199,68 V . 1 = 832 W PE2 = 865,28 W] 26. 2 (2 L) g
103 3 . 5 m 1 min 220 V 20C 80C. () . c al c = 1 1 cal = 4,17 J. gr
grad
: Q = m c ( ) m c . [. Q = 80400 J] 27. A R = f() . . [. ]
28.
200
1 1 r = , . 2 3 R . R = 4 = 9 V, 1 2. r 1 [. . = . 1 = 9 W RE2 =
27 W] R 4 . 29. R1 = 10 V, R2 = 40 R3 = 30 . , = 80 V r = 1 . (48
V, 96 W). [A. R1, R2 R3.] 30. R = 80 , R1 = 20, R = 12 , = 282 V r
= 2 . , R1 R. R1 . [. R1, = = 362,142 W] 31.
201
A R = R = 20 , = 40 V r = 0, ; ; [. 1 , (1 = 4 > 2 = 1 ] 32.
:
: = 100 V r = 5 . R1 = R4 = 15 R2 = R3 = 30 , : . R1, R2, R 3,
R4 . . R3 . R1, R 2 , R3 , R 4 [ 2000] [. . R = 45 . V = 30 V . 3 =
1 . = 180 W] 33.
: R1 = 1 , R2 = 2 , R3 = 3 , R4 = 4 , R5 = 5 ,
202
R6 = 6 , C1 = 8 F, C2 = 6 F, = 100 V r = 4 . . [. U1 = 2,56 104
J, U2 = 1,08 102 J] 34. C = 5 mF q = 10 C. T t = 0 s R = 0,4 . t =
105 s . . . . t = 0 s t = 105 s . [. . = 1 . QR = 105 J] 35. N : =
360 V, r = 0, R1 = 20 , R2 = 80 , R3 = 100 , R4 = 60 , R5 = VB =
200 V. 20 3
[. 1 = 6 , 2 = 4 , 3 = 2, 4 = 4, 5 = 6, = 10 ]
203
1.
() . : ) ) ) )
2.
() : ) ) ) )
3.
() . , : ) ) ) )
4.
() . Ohm : ) ) ) )
204
5.
() . , : ) ) ) )
V2 = , V2 = > 0 R R P. ( ). = 2 R, I2 = > 0 R P. ( ). . 6.
() . , , : ) 100% ) 200% ) 300% ) 400% V2 t Q1 = R (2V2) V2 Q2 =
t=4 t = 4Q1 Q2 = 4Q1 R R Q = Q2 Q1 = 4Q1 Q1 Q = 3Q1. : Q1 3Q1 100
x; x = 300. = 300%
205
7.
() () . ) ( ) ) ) = q t S.I. )
8.
() () . ) ) 1 Kirchhoff . ) , ) 2 Kirchhoff .
9.
() () . ) ) ) ) 10
10.
. 1) q ) W 2) ) C 3) V ) J 4) W ) 5) ) V 6) HE
206
11.
() () . ) ) ) )
12.
, ; .
() () . ( ). : V2 V2 = R R . : V2 V2 1 1 > > > R K <
R R R RK R = . 13. . () () . I ) R = V ) = V I ) = V I t
) W = V I t 14.
M . () () . ) .
207
) ) 15.
2KW, 220V. , 1, 2, 4, 6, 8, 10, 15, 25, 35 ; . ) 1 ) 6 ) 10 )
25
= 2.000 W VK = 220 V = VK IK IK = 16. PK S.I. 2000 IK = A IK VK
220 9,09 A. ( )
: 1) ) VI 2) 3) 4) ) 2Rt )V/I ) V/R ) R
17.
; .
(220 V). 220 V . 220 V. . , -
208
( ). 18. . () () . ) R = R1 + R2 ) V = V1 V2 ) = 1 + 2 ) V = V1
+ V2 19.
. () () . R R ) R = 1 2 R1 + R2 ) V = V V1 2
) = 1 + 2 ) V = V1 + V2 20.
10 . , : ) 40 ) 2,5 ) 10 ) 25
.
R = R + R + R + R R = 4R .
S.I.
R = 40
1 1 1 1 1 1 4 R S.I. = + + + = R = R R R R R R R 4
R = 2,5
209
.
R1 = R + R R1 = 2R R2 = R + R R2 = 2R
S.I.
R1 = 20 R2 = 20
S.I.
1 1 1 R R S.I. 20 20 = + R = 1 2 R = R = 10 R R1 R2 R1 + R 2 20
+ 20 .
R1 = R + R R1 = 2R
S.I.
R1 = 20 R1 = 20
1 1 1 1 2 R S.I. = + = R2 = R2 R R R2 R 2 R = R1 + R2
21.S.I.
R = 25
() . : ) ) ) )
22.
() . 10 V 8 , 8 V. H : ) 1 ) 2
210
) 3 ) 4 V V 8 = AB = I = A R R 8 V = r I = V r= V S.I. 10 8 r= I
1 r=2
I=1
23.
() () . ) ) , ) )
24.
() () . , : ) ) ) )
25.
: (V) (I) A (R) (W) 220 0,5 ; 110 220 2 110 440 220 1 ; 220
211
(, ) Ohm. : VI 2 R . : = VI = I2R + P =>I 0
V=I R+
P I
, V > IR.
R ( VI ). 26. : P(W) 27. 3000 2000 60 100 P(KW) 3 2 0,06 0,1
t(h) 1 1 1 1 W(KWh) 3 2 0,06 0,1
: R I V W A Volt Joule V I q t W q V q
28.
() . : = 1 + 2 t(S.I.). 0-3 s : ) 7 C ) 21 C ) 3 C ) 12 C
212
= q dq = dq = I dt t dt
q 0-3 s :3s 3s
q=0
dq =0
(Idt) = = f(t). q = E (1 + 7) 3 C 2S.I.
q=
q = 12 C
29.
R1 = 60 , R2 = 20 , R3 = 20 R4 = 35 . R= 59 .
R 5 = R2 + R3 R5 = 40 S.I.
1 1 1 = + R6 R5 R1 R R S.I. R6 = 5 1 R5 + R1 R6 =S.I.
4 0 60 S.I. 40 + 60
R6 = 24 S.I.
R = R6 + R4 S.I.
R = 59
213
30.
V = f(I) . .
V = V V = E Ir V=E (1) (2)
= 0 (1)
: = 0 V = 12 V V = 12 V I= E r (3) I=2A
(2)
V = 0 (1) I r = E
: V = 0 (3) r = = 31. E 12 r= I 2 r=6
. r
= 2
. . . . . . . .
32.
214
33.
. dq . dt S.I. Ampere. . =
34.
. 1 Kirchhoff : . . 2 Kirchhoff : . . . R = V . S.I. I
35.
1 . . . . 36. . : ) = 1 = 2 = 3 ) V = V1 + V2 + V3 ) R = R1 + R2
+ R3 ) . . ) = 1 + 2 + 3 ) V = V1 = V2 = V3
215
) R =
R1 R 2 R 3 R 1 R 2 + R1 R 3 + R 2 R 3
) . 37. . A () . . H P = dW . dt S.I. 1 Watt. P = V I. ( )
38.
P = P = I2 R. 1 KWh 1 kWh 1 (1h). 39. . H E E = E = W q
P . , I , . , .
40.
. , . , . .
216
41.
, 4,5 V, 4,5 V , . 30cmxcm , , , . . . . , V1 , , . V2 , ( ) . ;
.
42.
. , , . V1 = VAB . = (V = r => V = ). I=0
V1 = E
217
0. V2 = VAB . = (V = r = > V < E) 43. V2 < V1I 0
V2 < E
. . ;
. , , , , V R = . . . 44. T : ) , , , ) , ,, ) , , ,
.
218
45.
. ) . ) ;
) . ) i) C C ii) C B C B 46. , , 1, 0, . 47. 1 1 0 0 0 2 0 0 0
1
, , (). ; ;
. .
219
1.
C = 20F V = 24 V. , t = 0,02s. , . : qe = 1,6 1019C.
: Q Q = C V 20 106 24 C Q = 4,8 104 C , Q . , : Q = N qe = Q
S.I. 4 ,8 1 0 4 N= qe 1 , 6 1 0 19 N = 3 1015S.I.
H , = Q t =S.I.
4,8 104 A 2 102
= 2,4 102 A
2.
, , f = 5,8 1015Hz. : qe = 1,6 10-19C.
220
: . t = N=v t t (1)
O , , t Q = N qe Q = vtqe(1)
(2)
E = 3. Q (2) vtqe S.I. I = I = v qe I = 5,8 1015 1,6 10 19 A t t
I = 9,28 104 A
( ), , : ) : , ) n: , ) S: , ) qe: .
: n = 16, n = 8 1023 S = 1mm2, qe = 1,6 1019C. cm3 : Q N = Q = N
qe n = t V V = S . : = Q Q=Nqe qe N=n V = == = = => = == ==>
t t nV qe V=S = => == t I= nS qe t
I=
221
= t = t
=
nStqe I = nSqe = nSqe t
: = 8 1023 16 C 1mm2 1,6 1019 3 cm . = 16 8 1023 1,6 1019 1 m2 C
106 m3
= 1,25 104
A m A m m = 1,25 104 = 1,25 104 C A s s 103 mm s = 1,25 101 mm
mm = 0,125 s s
= 1,25 104,
: 1cm3 = 106 m3, 1mm2 = 106 m2, 1C = 1A s, 1m = 103 mm 4. V 1 2,
. 1 S1 = 0,2mm2, 2. : 1 R1 = V0 0 V0 2 I0 (1) R2 = 1 V0 (1) 1 R2 =
R 2 I0 2 1
2 R2 = R1 = 2R2 (2) . A ,
S2
2, (2) S1 = 2 S2 1 2 = S2 = 2S1 S2 = 2 0,2 mm2 S1 S2
S2 = 0,4 mm2
222
5.
: ) ) ) ) . : : R= S (1)
) , S : (1) R = S R = (2) ( = > 0) S
H (2) = x : r R, x , = > 0 S .
) , (1) S
: R= S (3) ( = > 0)
: x R, x S = > 0 . H (3) =
,) R V . V, I R = .
223
6.
= 10m m = 3,6 g. ,
d = 21 g/cm3 = 9 108 m. : d = 21 Kg g 103 Kg = 21 d = 21 103 3 m
cm3 106 m3 m = 3,6 103 Kg
m = 3,6 g
S , V=S m V=S = => == V m d
d = d= m S S d=m S=
:S=
R=
S
== R = m => d d 2 S.I. 21 103 102 R = 9 108 m 3,6 103 R=5
m d
R= 7.
R=40 = 2m. , R = 160. .
224
: A d , m V = S , : d= m m V=S = => d = == S V (1)
V V = S : d = m m V=S = == d = ==> S V m S (2) S
(1) (2)
=
m S = S S
S =
(3)
: R= R = . S S R = 160 = 4R : R = 4R S=4 =2 8. S S = 4 =
4m(3)
S2
= 4
S
S 42
=
4 S
S
2
=4
=
, 0C; , ; , ; Cu = 3,9 103grad1.
: 0 0C C = 2 : = 0 (1 + Cu ) 20 = 0(1 + Cu ) 2 = 1 + Cu 1 = Cu =
1 Cu = 1 3,9 103 C
225
=
1 00 C 3,9
256,4C
1 Cu 1 0C = . , . 1 = = = 20 9. 1 = 20C , 1 = 2, 2 = 252C 2 = 1.
. : R1, R2 0 2 : R1 = R0 (1 + 1) R2 = R0 (1 + 2) R1 R (1 + 1) = 0
R2 R0(1 + 2) V R1 R ( 1 + 1 ) = 0 R2 R 0( 1 + 2 ) V I2 (1)
I1 V I 1 + 2 VI 1 + 1 (1) 1 = 2 = V V I1 1 + 2 1 + 1 I2 2 1 + 1
= I2(1 + 2) = I1(1 + 1) 1 1 + 2
A V : R1 =
R2 =
2 + I22 = 1 + I11 22 11 = 1 I2
226
(I22 11) = 1 2 =
1 2 2 2 1 1
=
1 1 21 = 2480 grad 2520 40 C
4 104 grad1
10. V = 100 V. R1 = 5 R2 = 15. , , . :
R = R1 + R2 R = (5 + 15) 2 : = V S.I. 10 0 VA B I= I = A R R 20
I=5A
S.I.
R = 20
A 1 : V = R1 V = 5 5 V V = R2 V = 5 15 V S.I. S.I.
V = 25 V V = 75 V
227
S.I. V = V + V V = V V V = (100 25) V V = 75 V
11. V = 120 V. R1 = 30 R2 = 60. , . :
R R S.I. 30 60 1 1 1 = + R = 1 2 R R1 R2 R1 + R2 30 + 60 R =
1800 R = 20 90
2 : = VAB VAB=V 120 V S.I. = == = == > = R 20 R VAB VAB=V 120
V S.I. = = = 1 = == > 1 = R1 30 R1 VAB VAB=V 120 V S.I. = = = 2
= == > 2 = R2 60 R2 =6
1 : 1 = 2 = 1 = 4 2 = 2
1 Kirchhoff,
228
1 = 1 + 2 2 = 1 2 = (6 4) 12.
S.I.
2 = 2
: ) , ) , ) , . : ()
) R4 =
R R S.I. 3 6 1 1 1 = + R4 = 1 2 R4 = R4 R1 R2 R1 + R2 3+6 18 R4
= 2 9S.I.
R = R4 + R3 R = (2 + 4) R4 = 2 ,) 3 : = V V=V V S.I. 60 = == = I
= ==> R R 6 = 10
2 :
229
VAB = I R4 VAB = 10 2V
S.I.
VAB = 20 V = VR1 = VR2
R3. A 1 : VB = I R3 VB = 10 4V 20 3S.I.
VB = 40 V = VR3
1 =
V S.I. R1
1 =
2 =
V S.I. R2
1 =
10 3
()
) R4 = R2 + R3 R4 = (40 + 50) R =S.I.
R4 = 90
10 90 1 1 R R S.I. + R = 1 4 R = R1 R4 R1 + R4 10 + 90 900 100 R
= 9 VB=V
R =
,) VR = V = = = VR = V = =>1 1
V1 = 90 V
A 2 : 1 = 2 = V V=V V S.I. 90 1 = == = I1 = ==> R1 R1 10 V
V=V V S.I. 90 2 = = = = I2 = = => R4 R4 90 1 = 9 2 = 1
230
2 R2 R3. 1 : VA = I2 R2 VA = 1 40 V V = I2 R3 V = 1 50V 13. : R1
= 3, R2 = 6, R3 = 8, R4 = 7, R5 = 3, V = 60V. : ) , ) , ) , . :S.I.
S.I.
VA = 40 V = VR2 V = 50 V = VR3
) R6 =
R R S.I. 3 6 1 1 1 = + R6 = 1 2 R6 = R6 R1 R2 R1 + R2 3+6 R6 = 2
R7 = R4 + R5 R7 = (7 + 3) S.I. S.I.
18 9
R7 = 10
R8 = R6 + R3 R8 = (2 + 8)
R8 = 10
10 10 1 1 1 R R S.I. = + R = 8 7 R = R R8 R7 R8 + R7 10 + 10 1
00 R = R = 5 20
231
,) 3 : 3 = V V=V V S.I. 60 3 = = = = I3 = = => R8 R8 10 3 =
6
3 R3. E 4 = V V=V V S.I. 60 4 = = = = I4 = = => R7 R7 10 4 =
6
4 R4 R5. 2 : V = I3 R3 V = 6 8 V V = I3 R6 V = 6 2 V A 1 : V =
I4 R4 V = 6 7 V V = I4 R5 V = 6 3 V 1 = 2 =S.I. V 12 I1 = R1 3 S.I.
S.I. S.I. S.I.
V = 48 V = VR3
V = 12 V = VR1 = VR2
V = 42 V = VR4 V = 18 V = VR5
1 = 4 2 = 2
V S.I. I2 = 1 2 R2 6
R1 1 R2 2. 14. 4V, V = 10V R1 = 2, R2 = 4, R3 = 4, R4 = 5 R5 =
11. Rx. , , .
232
: : V = 4 V
, 1 V S.I. V = 3 R2 I3 = R2 4 I3 = A 3 = 1 4 V = 4 R3 I4 = 4 = 4
A 4 V S.I. R3
4 = 1
1 1 Kirchhoff : S.I. 1 = 4 + 3 1 = (1 + 1) 1 = 2
: S.I. R6 = R4 + R5 R6 = (5 + 11) 1 1 1 = + R6 = 16 R7 R2 R3 R7
= R7 = R2 R3 R2 + R3 R7 =S.I.
4 4 4+4
16 R7 = 2 8
233S.I.
R8 = R1 + R7 R8 = (2 + 2) R8 = 4
3 : V = 1 R8 V = 2 4 V VK = 8V 2 = V S.I. 8 I2 = A R6 16 I2 =
0,5 AS.I.
H 2 . 1 1 R R S.I. 1 = + R9 = 6 8 R R6 R8 R6 + R8 R = 16 4 64 R
= 16 + 4 20
R = 3,2 VK S.I. 8 = R9 3,2 = 2,5
4 : = 5 : R =
VKM VKM=V V S.I. 10 = = = R = R = = => I I 2,5S.I.
R = 4
R = R9 + Rx Rx = R R9 Rx = (4 3,2) Rx = 0,8 15. R* = 5/cm. ,
.
234
: : 2 = 2 + 2 = 2 = = 64 cm2 + 3 cm2 = 2 = 100 cm2 B = 100 cm2 =
10 cm
: R* =
RAB AB 8 cm RAB = R* AB RAB = 5 cm
RAB = 40 , R = R* R = 5 R = R* R = 5 V = V 6 cm RA = 30 cm R =
50
10 cm cm
V = V + V V = I1 RAB + I1 R V = I1(RAB + R) 1 = V 14 14 S.I. A
I1 = A I1 = R + RA 40 + 30 70 V V S.I. 2 = R R I1 = 0,2 A
V = 2RB 2 = 2 = 14 50 I2 = 0,28 A
16. V = 30 V, R1 = 2, R2 = 1, R3 = 5 R4 = 10V. ) VAB. ) R R4,
VAB = 0.
235
: V=V ) V = V + VA = = => V = I1R1 + I1R2 V = I1(R1 + R2) I1
= I1 =S.I. V 30 I1 = A R1 + R2 2+1
30 A 3
I1 = 10 A
V = V + VB V = I2R3 + I2R4 V = I2(R3 + R4) S.I. V 30 30 I2 = I2
= A I2 = A R3 + R4 5 + 10 15
I2 = 10 A
VAB = V + V VAB = 1R2 + ( I2R4) VAB = 1R2 I2R4 VAB = (10 1 2
10)V ) R R4 VAB = 0 . : V = V + V = = V = I4R1+I4R2 => V S.I. R1
+ R2 30 30 S.I. I4 = A I4 = A 2+1 3 V = I4(R1 + R2) I4 = I4 = 10 A
V = 0 V + V = 0 I4R2 + ( I6R4) = 0 I4R2 6R4 = 0 I4R2 = I6R4 I6 = I6
= 1 AV=V V=V
VAB = 10 V
I4R2 S.I. 10 1 I6 = A R4 10
V = V + V = = V = I5R3 + I6R4 V I6R4 = 5R3 => I5 = V I6R4
S.I. 30 1 10 20 I5 = A I5 = A R3 5 5 I5 = 4 A
1 Kirchhoff :
236
5 = 6 + 7 7 = 5 6 7 = (4 1) : V = 6 R4 V = 7 R I7R = I6R 4 R
=
S.I.
I7 = 3 A
10 I6 R4 S.I. 1 10 R= R= 3 I7 3
17. , R = 30.
: () , VA = V. , , V = VB. 2 3. 1 R 1 R = = 3 R 1 R + 1 R + 1
R
R =
S.I.
30 3
R = 10
237
, , VA = V. 2, 3, 4, 5. 1 1 1 1 2 = + = R1 R1 R R R R1 = R S.I.
30 R1 = R1 = 15 2 2S.I.
R2 = R1 + R R2 = (15 + 30) R2 = 45 1 RS.I.
: R = R = R R
=
1 1 + R2 R 45 30 75
R+R
R =
3 30 3 6 5
R = 18
18. : R1 = R2 = R3 = = 10 , V1 = 20V, V2 = 10V. ,, . : . VZ = 0
V1 = V V2 = V
238
: V = V + VB V1 = IR1 + R2) V1 = I(R1 + R2) I = I= 20 10 + 10
AI= V1 R1 + R2
20 I = 1A 20 R3
A :
V = 0 R3 = 0S.I.
: V = V + V + V S.I.
V V = R1 + ( V2) + 0 S.I.
VA 0 = IR1 V2 VA = IR1 V2 VA = (1 10 10)V VA = 0 VS.I.
VAB = IR1 VA VB = IR1 0 VB = IR1 VB = IR1 VB = 1 10 V VB = 10
VS.I.
V = IR2 V V = IR2 VB IR2 = V V = ( 10 + 1 10) V V = 0 V
V = 0 V V = 0 V = V V = 0 V 19. : V = 10V, R1 = 10, R2 = 20. ,
R1. R3 = 20, . : , , , , , , () .
239
V = V = V = 0V V = V
: V = V + V + V V = R1 + 0 + 0 V = R1 = V 10 I= A R1 10 I=1A
M R3, . :
V = V + V V = 3R1 + 5R3 10 = 10I3 + 20I5 I3 + 2I5 = 1 (1)
V = V + VZ + VZE + V V = 3R1 + 4R2 + 0 + 0 10 = 103 + 204 I3 +
24 = 1
1 Kirchhoff I3 = 4 + 5 (3) I5 = 4 (4)
(1), (2) 3 + 25 = 3 + 24 25 = 24 (3) (4) 3 = 4 + 4 I3 = 24
(5)
240
(2), (5) 24 + 24 = 1 44 = 1 4 = (5) 3 = 2 0,25 I3 = 0,5 A
1 I4 = 0,25 = 5 4
(4)
B : R2 R3 . 2, 3. : R4= 1 1 1 = + R4 R2 R3
R2 R3 20 20 R4 = R2 + R3 20 + 20 400 40
R4
R4 = 10
Ro = R1 + R4 Ro = (10 + 10) R = 20
3 : V V 3 = R R 10 3 = 3 = 0,5
