Laurea Magistralis
MEDICINE
and SURGERY
Corso di in
Laurea
Specialistica
in
MEDICINA
e CHIRURGIA
“HARVEY”
corso integrato
FISICA - disciplina
FISICA
Integrated
Course/Discipline:
PHYSICS
ELECTRIC CURRENT
Ist part
- ELECTRIC CURRENT and ELECTRIC CURRENT DENSITY
- OHM’S LAWS
- DIRECT ELECTRIC CURRENT CIRCUITS
D. SCANNICCHIO 2009
01/16
ELECTRIC CURRENT
→
A
Δq
i=
Δt
dimensions
measure unit
I.S.
E
S
S
+q
dq
i=
dt
B
i
(carica
elettrica
electric
charge +q )
[Q][t]–1
fourth fundamental physics quantity
ampere (A) = coulomb s–1
1 ampere = C s–1 = C (1.6 10–19 C/electron) s–1 =
= (1.6 10–19 )–1 electrons s–1 = 6.25 1018 electrons s–1
D. SCANNICCHIO 2009
02/16
ELECTRIC CURRENT
Δq
i=
Δt
dq
i=
dt
electricelettrica
charge – q
carica
(carica
elettrica
electric
charge +q )
correnteinverso
opposto
current
opposite
direction
i = electric charge motion
constant flow: i = constant in time
direct current
variable flow: i = variable in time
i = i(t)
D. SCANNICCHIO 2009
03/16
ELECTRIC CURRENT DENSITY
B
→
A
S
S
E
+q
→
i, J
densità
di current
correntedensity
elettrica
electric
:
Δq
J=
= i
S Δt S
→
J direction
direzione
verso cariche
of epositive
charge: +q
dimensions
measure unit
D. SCANNICCHIO 2009
[Q][t]–1[L]–2
I.S.
ampere x m–2 (A m–2)
04/16
OHM’S LAWS
l
→
E
A S
S
B
+q
→
i,J
VA – VB
legge diOhm’s
Ohm law
generalizzata
general
(empirical)
→
→
J=σE
(empirica)
electric conductivity
σ = conducibilità
elettrica ∝ velectrons
elettroni
D. SCANNICCHIO 2009
05/16
OHM’S LAWS
l
→
A
S
S
E
B
→
i,J
+q
Ohm’s laws
(empirical)
VA – VB
VA – VB
i
= R
R=ρ l
S
R = electric resistance of the conductor
1
ρ = resistività
elettrica
=
f
(T)
=
electric resistivity
σ
electric conductivity
ofconduttore
the conductor
σ = conduttività
elettrica del
D. SCANNICCHIO 2009
06/16
OHM’S LAWS
VA – VB
i
= R
l
R=ρ
S
R = electric resistance of the conductor
1
electric resistivity
ρ = resistività
elettrica = f (T) = σ
σ = electric conductivity of the conductor
dimension of [R] = [M][L]2[t]–1[Q]–1 = [M][L]2[i]–1
measure unit
I.S. ohm (Ω) = volt ampere–1
dimension of [ρ] = [M][L]3[t]–1[Q]–1 = [M][L]3[i]–1
practical measure unit
D. SCANNICCHIO 2009
ohm x cm ( Ω cm)
07/16
OHM’S LAWS
legge generalizzata
≡ 2leggi
di Ohm
Ohm’s
general law ≡
Ohm’s
laws
E = – grad V =
VA – VB
l
J=σE
i=JS=σES=σ
l
R=ρ
S
VA – VB
i=
R
D. SCANNICCHIO 2009
VA – VB
l
S=
VA – VB
ρl
S =
VA – VB
R
electric di
resistance
simbolo
resistenzasymbol
elettrica
R
08/16
classe
CLASS
MATERIALS
sostanze
ρ (20°C) ohm cm
–6
argento
............................
silver
1.62
10
conduttori
metal
–5
copper
rame
................................
0.17
10
metallici
conductors
alluminio
aluminium........................0.28 10–5
iron ................................ 1.10 10–5
ferro
mercury .........................9.60 10–5
mercurio
osmoles) ................ 85.4
KCl (C=0.1 osmoli)
conduttori
electrolytic
elettrolitici
liquido
interstiziale
interstitial
liquid ....... ................ 60
conductors
serum(25°C)
(25°C) ............................. 83.33
siero
cerebrospinal
liquid (18°C)(18°C)
......... 84.03
liquido
cerebrospinale
assoplasma
di assone
axon axonplasma
.........................200
1.08
germanio ...............................
semiconduttori germanium
semiconductors
silicio
silicium..................................... 100
5
isolanti
alcool
etilico
........................
ethyl
alcohol
3
10
insulating
acquadistilled
bidistillata
twice
water ................ 5 105
membrana
di assone
axon
membrane
........................ 109
vetro
1013
glass ....................................
mica
mica .....................................
1016
D. SCANNICCHIO 2009
09/16
DIRECT CURRENT CIRCUITS
resistenzein in
serie
resistences
sequence
A
i
R1
R2
i
ΔV1
B
ΔV2
VA – VB ΔV1 + ΔV2
ΔV2
ΔV1
R=
=
=
=
+
i
i
i
i
= R1 + R2
D. SCANNICCHIO 2009
10/16
DIRECT CURRENT CIRCUITS
R1
resistenze
resistencesinin parallelo
parallel
A
i1
i
i2
B
R2
i1 + i2
i2
i1
i
1
=
=
+
=
=
VA – VB
VA – VB R
VA – VB VA – VB
1 + 1
=
R2
R1
D. SCANNICCHIO 2009
11/16
ELECTROMOTIVE FORCE
A
r
G
–
+
f
R
f = f.e.m.
e.m.f.
r = generator’s
resistenza interna
internal
del
generatore
resistance
i
B
open circuit
: : i = 00
circuito
aperto
VA – V B = f
closed circuit
circuito
chiuso: :
f = ( R + r) i
D. SCANNICCHIO 2009
f
i=
R+r
12/16
DIRECT CURRENT CIRCUITS
Kirkhoff’s principles
(solution of direct current circuits)
Ist principle of Kirkhoff
nodo :
branch
nodopoint
i1
i2
at branch point:
∑ in = 0
n
i3
i1 – i2 – i3 = 0
D. SCANNICCHIO 2009
13/16
DIRECT CURRENT CIRCUITS
II°IIprincipio
diofKirkoff
nd principle
Kirkhoff
for each mesh:
maglia :
R1
+
V
–
∑V
00
d.d.p.
i ==
R3
i3
i
i3
R4
i2
R2
{i R + i R – i R = 0
i1R1 + i2R2 = V
3
D. SCANNICCHIO 2009
3
3
4
2
2
14/16
DIRECT CURRENT CIRCUITS
voltage
generator
generatore
di d.d.p.
G
A
–
Vo
+
r
B
VA – VB = V = Vo – r i
R
i
V
D. SCANNICCHIO 2009
15/16
DIRECT CURRENT CIRCUITS
current
generator
generatore
di corrente
A
–
G
io
r
+
D. SCANNICCHIO 2009
i
R
B
V
i = io – r
16/16