Electric Current 2013

7/28/2019 Electric Current 2013

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04.02.2013 Asoc.prof.J.Blms 1

Electric current

A B

___

_

++

++

E FE

E* FE

*

- nonelectric forces(mechanical, chemical

etc).

*EF

Electromotive force- equal to the work done by

source to move positive unity charge around closed

curcuit:0q

A EMF


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Current: ;dt

dqI [1A]

Current density: ;dSdIj [1A/m2]

Voltage (potential difference): .12

12q

AV

Ohms law for a branch: .R

VI


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Resistance

Relectrical resistance; .11

A

V

R1 - electrical conductance; simenssS 111

For a cylindrical wire- ,S

lR

- resistivity [1m].


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Resistance as temperature function

1. Metals (conductors)

)1(0 t

).1(0 tRR

t0

0

- temperature coefficient of resistance;

- shows the normalised change of resistivitywhen the change of temperature is 1 degree.

R

R0

t


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2. Liquid electrolytes (NaCl, Cu2SO4 u.c.).


R

t


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3. Pure semiconductors and isolators


R

t

R

kTW

e 2

Wenergy gap.


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Connection of resistances

(resistors):

Connection in series:

R1 R2 R3

....321 RRRR

Connection inparallel:

R1

R2

R3

321

1111

RRRR


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Differential form ofOhms law

I = f(V, , geometry)

).,( Efj

,

R

dVdVdI .

dl

dS

;dl

dV

dS

dVj

but ,Edl

dV then

EEj

1

Ej


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Ohms law for closed circuit:

I

+ -

, r

R

rRI


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Multiloop circuits and

Kirchoffs laws.

A B

CD

R1

R2

R3

R4

I2

I1

I3

1, r1

2, r2J unctions D, B

Branches DAB, DCB, DB

Closed loops

DABD, DBCD, DABCD.

I .Kirchoffs law: i i

I 0 At any junction the algebraic sumof the currents must be zero.

D: I2 = I1+ I3

B: I1 + I3 = I2


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Multiloop circuits and Kirchoffs laws.

A B

CD

R1

R2

R3

R4

I2

I1

I3

1, r1

2, r2

II. law:

i i

iiiRI

The algebraic summ of potential

differences in closed circuit is equal tothe summ of EMFs in this curcuit.

DABCD: I1R1 + I2R2 + I2R3 + I1r1= -1

DABD: I1R1 + I1r1I3r2 I3R4 21


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Joules law

dq

dq

1, 1

2, 2 UdqdqdA 12

UdtIdA [1J = 1 AVs]

tUIA I = const; U = const :

I const; U const : t

UdtIA0

UIt

AP [1W = 1 AV]

Electric Current 2013

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