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= =
C
F( )
F C/V
=
0
V V
S m2 d m
Q C Q C
2
+ 2
= p50
/m2 = ÷ m2 = ⋯
=
, = =
( )
1.0
1.00054
80
2.2
2.9
3.2 3.6
7.0
0
0
= 2.2 0 F
=
=
m
m2
+
−
m2
μ = 10−6, p = 10−12 → 1 μF = 10−6 F, 1 pF = 10−12 F
p50
2
2
2
2
0
0
= ! =
Q
V
= =π≒ × −
1 S m2
Q C ( > 0 )
0!F/m
(1) ( )
(2)
0 V/m
2 1 A
B d m +Q C Q C
(3) A 1 V/m B 2 V/m
AB E V/m 1 2 E (4) AB V V (3) E d,V
Q 0, d, S, V
(5) A B C 0, d, S
(6) (4),(5) Q C V
(7) AB !
A B F , 0,
d, S
(8) 0 0 = 1
4π! k
(1) 2.0 F 100 V Q C
(2) 10 cm 2 1.0 mm 8.0
C F
8.9 × 10−12 F/m! 2
(3) 2 1
2
=!( ) F
( )
= ( )
= ( )
( )
= ( ) F
0 = ( ) V/m
= ( )
= ( )
= ( )
1 ( ) V/m 2 ( ) V/m E ( ) V/m
1 0
0 +
2 A
B
−
+ 1
2
2
S
C1
Q C Q C
0 C
C2
Q C Q C
C1 50 C
S C1
+ 1 C, − 1 C C2
+ 2 C, − 2 C
50 C
− 1 + 2 = −50!
, ,
,
,
,
= =
V 1
2
C1
C2
= + = =
+ +
− −
1 2
C1 C2
+ 1 − 1
− 2 + 2
C1
C2
+ 2 − 2
+ 1 − 1
50 C
+ −
+ −
50 C
50 C
,
0 C Q Q 0
C2 C1
C2 C1 C2 C1
C2 C1
S
S
S
S
+50 C -50 C
C1 C2
6.0 F C1
300 V
(1) C1 Q C
Q ( ) C
C1 3.0 F
C2 C1 ,
C2 1 C, 2 C C1
V V
(2) 1 , 2,V 3 1 , 2 ,V
1 = ( ) C 2 =!( ) C V ( ) V
2.0 pF 3.0 pF
C1 , C2 C3
6.0 V S
S C1
4.0 × 10−12 C
(1) C1 , C2 , C3 1, 2, 3
1 = ( ) V 2 = ( ) V 3 = ( ) V
(2) C2 2 C
(3) C3 3
(4) C3 3 pF 3 = ( ) pF
3 = ( ) C
2 = ( ) C
C1(6.0 F)
C1(6.0 F)
C2(3.0 F)
C1(2.0 pF)
C2(3.0 pF)
C3
S 6.0 V
1
C
C1, C2 1!C 2 C
= 1 + 2 C1, C2
V
= 1 = 1 2 = 2
, , = 1 + 2
V = 1 + 2
C1, C2, C3 C
C1 C2 12 12 = 1 + 2
C12 C3 C
= 12 + 3 = 1 + 2 + 3
C1, C2,⋯ , C
C
0
Q
Q
C C1, C2
1, 2
= 1 + 2
C1, C2
Q C
= 1 1 = 2 2
C C1 C2
C Q
C =
, ,
1 =1
, 2 =2
, =
=1
+2
1
=1
1
+1
2
C1, C2, C3 C
C1 C2 C12 1
12
=1
1
+1
2
1 2
C1 C2
+ + − −
+ 2
+ 1
− 2
− 1
C2
C1
C1
C2
C3 C3
C12
C1 C2 C3
= + +⋯+
C = + +⋯+
2.0 F, 3.0 F 2 C1, C2
12 V
(1) C1, C2 C1, C2
C
(2) C1, C2 C
C1 ( ) C C2 ( ) C
2.0 F, 3.0 F 2 C1, C2
12 V
(1) C1, C2 ( ) F
(2) C1, C2 C (1)
( 2 )
C1 ( ) C C2 ( ) C
(3) C1, C2 1, 2 V
1 ( ) V 2 ( ) V
1 F 2 F
C
0
Q
C12 C3 C
1=
1
12
+1
3
=1
1
+1
2
+1
3
C1, C2,⋯ , C
C
= ( ) F
( ) F ( ) C
2.0 μF
3.0 μF
12 V
3.0 μF 2.0 μF
12 V
1
1
2
C12 C3
= + +⋯
C , ,⋯
0
30 V 2
C1 (10 F) C2 (20 F) 90 V S
S
C1, C2 C1, C2
S C1, C2 1, 2
1 = 10 μF × 30 V = 300 μC 2 = 20 μF × 30 V = 600 μC
−300 + 600 = 300 μC S C1, C2
1 C, 2 C
1 V 2 V
− 1 + 2 = 300 μC
1 + 2 = 90
=
1 = 1 1 = 10 μF × 1 V = 10 1
2 = 2 2 = 20 μF × 2 V = 20 2!
, −10 1 + 20 2 = 300!
, 1 = 50 V, 2 = 40 V! ( )
,
1 = 10 × 50 = 500 C, 2 = 20 × 40 = 800 C ( )
3.0 F 20 V C1 2.0 F
15 V C2
C1 C2
30 V
90 V
30 V
S 1=
1
1
+1
2
C1, C2
ab
Q C
C1, C2 1, 2
= 3.0 1 = 2.0 2 1 = 3
,2
= 2
1 ∶ 2 = 2 ∶ 3 C1
1 = 20 V, 2 = 30 V 2 C2
C2
1 = 10 V, 2 = 15 V! 1 C1 ab
10 + 15 = 25 V! 25 V ( )
C2 C1
1 2
a b
15 V 20 V
90 V S
C1 C2
+ 2− 2 + 1− 1
2 1
C1
90 V S
C2 +300 μC − 300 μC
+600μC − 600μC
C1 (1.0 F) C2 2.0 F) 90 V
S
(1) S a
C1 Q C
Q ( ) C (2) S b
C1, C2
1, 2 C C2 V V
1 = ( ) C 2 = ( ) C V ( ) V
(3) S a
C1
C
(4) S b
C1, C2 1, 2
C C2 V
1 = ( ) C 2 = ( ) C = ( ) V
4.0 F, 300 V C1 1.0 F, 600 V
C2
=!( ) C
′ + 1
− 1
+ 2
− 2
S a
90 V C1 C2
b
+ 1
− 1
+ 2
− 2
S a
90 V C1 C2
b
S a
90 V C1 C2
b
( ) V ( ) V
B A
A B
C F Q C
q C ( 0 < < )
V
= = ⋯
1, 2 dq 1 2
dW
( ) ( ) dW = d 1 − d 2
= d ( 1 − 2) 1 − 2 =
d = d V
d = d
q 0 Q
W
=0
=2
2 0
=2
2
2
2 J F
C =
2
2
= Q
= 1
2 2 , =
1
2
d d
q 0 Q
W=
2
1
B
A
A
B
−
d
= = =
Q CV
2.0 F 3.0 × 102 V
U J
C F Q C 1
Q/n C ( > 0, n )
n Q C 1 0 V Q/n
C 1 1 0 J
1 2 n 1 n
(1) 1 1 n, Q, C 1 = ( )
(2) 2 1 V C
2 2 n, Q, C
(3) 2 2 n, Q, C 2 = ( )
(4) 3 2 V C
3 3 n, Q, C
(5) n 1 −1 n, Q, C
(6) n −1 V C
n C n, Q, C
(7) = 1 + 2 + 3 +⋅ + 1 + 2 + 3 +⋯+ ( − 1) = ( −1)
2
W n, Q, C
(8) lim→∞
Q, C lim→∞
= ( )
W ( )
2 = ( )
3 = ( )
= ( )
−1 = ( )
( ) J
0
0 C 0 C
1 2 −1
+ C − C +2
C −2
C −( − 1)
C +( − 1)
C + C − C
k q C ( > 0 )
4π q C 4π
S m2 A Q C ( > 0 )
A
( ) A
A = ( )
A B Q A B
d m
E A,B
E ( ) E ( )
V E d V ( )
C =
E ( ) ,V ( ) C k, S, d C ( )
= ( ) C , d, S
C ( )
( ) ( ) ( ) ( ) ( )
( ) ( ) ( )
C1, C2, C3 6.0 pF
2.0 pF 3.0 pF 16 V
S
(1) ab F ( ) F
(2) S C1, C2 1, 2 V
1 = ( ) V 2 = ( ) V
(3) S C1, C2, C3 1, 2, 3
2
1 = ( ) J 2 = ( ) J 3 = ( ) J
C1
C3
C2
a b
S 16 V
m
m2
+ C − C
m2
A B
(1) C F x y
z
C
( )
(2) 100 V C 2
( ) V ( ) V
(3) F 1
20 V 2
C1 (10 F) C2 20 F) 120 V
S S
C1 C2 1 C
2 C C1, C2 1V 2V
1 = ( ) C 2 = ( ) C 1 = ( ) V 2 = ( ) V
S
120 V
C1 C2
20 V 20 V
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