I, J
V, ρ , q v E
I = ∫ J ⋅ dS
S ( V )
⎛
⎞
⎜
⎟
Q
d
−
J ⋅ dS t d = Q
d ⇒
J ⋅ dS = −
⎜
∫
⎟
∫
t
d
⎝ S V
( )
⎠
S V
( )
∫
∂
J ⋅ dS = ∫
d
divJd V = −
∫ q d = −
v
∫ q
V
v d V
d t
∂ t
S V
( )
V
V
V
∂ q
div
v
J +
= 0
∂ t
Prawo Ohma (klasyczne) J = 1 E = E
ρ
γ
∂ q ∂ t = 0 ⇒
J = 0 ⇒ J =
v
div
0
Ogólne prawo Ohma
E = E + E
k
z
B
B
B
∫ d l
I ρ
= ∫E ⋅dl +
k
∫E ⋅dl
z
S
A
A
A
Dla E ⋅ l
d = −dϕ
B
E ⋅ dl = ϕ −
=
∫
ϕ
k
A
B
U AB
A
B
E ⋅ d = E
= −
∫
l
z
AB
EBA
A
ϕ B
l
d
J
B
EAB
A
ϕ A
B
B
U *
= E + E ⋅ dl = E ⋅ dl =
+
AB
( k
z )
U
∫
∫
AB
EAB
A
A
Dla J = const., ρ = const. i S = const.
B
B
I
l
ρJ ⋅dl = ρ d l AB
= ρ
I = R
I
∫
∫
AB
S
S
A
A
l
R
AB
= ρ
AB
S
U *
=
AB
IRAB
∨
IR
=
+
AB
U AB EAB
ϕ A
I
A
UAB
RAB
U*AB
B
ϕ B
Gdy ϕ A = ϕ B, RAB = R, EAB = E
IR = E
Prawa Kirchhoffa
I
J ⋅ dS = 0
∫
S
II
E ⋅ dl = 0
∫
L
Energia, moc, ciepło. Prawo Joule’a– Lenza
d W = U d I t ⇒ W = UIt W
d
P =
= UI
t
d
W
RI 2
=
t
1 cal ↓ 4.185 J
Q ≅
RI 2
24
.
0
t
Pierwsze prawo Kirchhoffa
n
∑ I =
k
0
k =1
I 5
I 1
w
I
4
I 2
I 3
I − I − I + I − I = 0 ⇔ I + I = I + I + I 1
2
3
4
5
1
4
2
3
5
n
n
∑ R I = ∑ E
k k
k
k =1
k =1
E 1
w
R
1
1
I 1 w 2
I
R
2
1 I 1
E 2
U
R
R
R
2
2 I 2
3 I 3
I 3
w 4
w 3
R 3
U +
−
−
−
−
=
1
E
1
R 1
I
2
E
2
R I 2
3
R I 3 0
c
U +
−
=
+
+
1
E
E 2
1
R 1
I
2
R I 2
3
R I 3