Electric (conduction) current

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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 dQdt

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 vii

d N 1

r

drift velocity

The center of charge enclosed in this volume moves with the drift velocity.

dt

d cqr

N

1iiq

Nq1

dtd r

i dtd

Nqq 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

surfaceI 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

IVa – 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

A1R l

surface

AdJ

EAJA VA

l

Al

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

itymetals

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...RV

RV

n21 R1...

R1

R1V

The inverse of the equivalent resistance of resistors connected in parallel is equal to the sum of the inverses of resistances

n21p R1...

R1

R1

R1

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.

tVtItP

IRV

VI

RVI

PRV2