Electric (conduction) current + + + + + + + + I I According to general agreement its direction is chosen to coincide with the direction in which positive charge carriers would move, even if the actual carriers have a negative charge. a) Transport of charge; The SI unit of current is 1A (ampere). (1C=1A1s.) I dQ dt b) The electric current across a surface is defined as the rate at which charge is transferred through this surface. - - - - - - - + -
Transcript
Electric (conduction) current
+
+++
+
+ +
+
I I
According to general agreement its direction is chosen to coincide with the direction in which positive charge carriers would move, even if the actual
carriers have a negative charge.
a) Transport of charge;
The SI unit of current is 1A (ampere). (1C=1A1s.)
IdQdt
b) The electric current across a surface is defined as the rate at which charge is transferred through this surface.
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drift velocity
The average velocity, , of charge carriers over a differential vicinity of a given location is called the drift velocity at this location.
v rd
v vi
id N 1
r
drift velocity
The center of charge enclosed in this volume moves with the drift velocity.
dt
d cqr
N
1iiq
Nq
1
dt
dr
i dt
d
Nq
q ir
dv
current density
The current density (associated with one type of charge carriers) is defined as a product of the drift velocity, the concentration of charge carriers and the charge of the carriers:
J
J vdnq
current density and current
Current through a surface is equal to the flux of current density over that surface.
dAvd vddt
dQ = ?
n
The charge transferred through a differential surface dA in time dt
dq dVnqc
cosdtvdAnq dc
Advd
dtnqc
AdJ
dt
The charge dQ transferred though the entire surface in time dt
surface
dqdQ
the current through the surface
surface
I AdJ
surface
dt AdJ
electric current in a conductor
In a conductor, current density is proportional to the electric field vector
J E (Ohm's law)
The constant of proportionality is called the conductivity of the conductor.
Under a steady flow of charged particles along a conductor, the current across any cross section of the conductor has the same value.
I
I
I
We assign this value to the current in the conductor.
resistor
A resistor is an electrical element with two sides for which (at any instant) the current passing through this element (any cross section) is proportional to the potential difference between its terminals.
Va Vb
R
I
Va – Vb = IR
The proportionality coefficient R is called the resistance of the resistor.
In SI 1 is the unit of resistance (1=1V/1A).
construction of a resistor
I
JA
A
1R
l
surface
AdJ
EAJA VA
l
A
l
resistivity
effect of temperature
In a relatively wide range of temperatures the resistivity of a material is a linear function of temperature:
= 0 [1 + (T-T0)]
The proportionality coefficient is called the temperature coefficient of resistivity.
temperature
resi
stiv
ity
metals
semiconductors
resistors in series
dQ dQ I I
Vz Vb Va
V az VV yzbcab VV...VVVV
n21 IR...IRIR )R...RR(I n21
Equivalent resistance of resistors connected in series is equal to the sum of the resistances of all resistors
Rs = R1 + R2 + … + Rn
resistors in parallel
V1 V2
I n21 I...II
n21 R
V...
R
V
R
V
n21 R
1...
R
1
R
1V
The inverse of the equivalent resistance of resistors connected in parallel is equal to the sum of the inverses of resistances
n21p R
1...
R
1
R
1
R
1
electric power The rate at which the electric field performs work on the charged particles is called the electric power.
The electric power delivered to an electrical element at instant t is equal to the product of the current flowing through this element and the voltage across this element at this instant.
V1
V2
I
dq
dq
tP dt
dWel dt
)VV(dq 12 tVtI
electric power dissipated in a resistor
dQ I
V1 V2
VIRI2
From Ohm's law (which is satisfied by all resistors) the electric power dissipated in a resistor can be determined also if the resistance of the resistor and either the current through or the voltage across the resistor is known.
