1. . ) R1 R2, . ) R1 ( 1

2. . ,

+

+

=

2

2

2

13118

3rx

bpr

r ,

+

+

=

2

2

2

31118

3rx

bpr

t

, b r , . ) r t x/r. . ) Ui=0,8mV. . =1,71011 N/m2, =0,17, r=1m, b=0,7mm. R0=100, k=50, E=6V.

: ) ( ) ( )

+++

+

+

==

22

2

2

31113118

3rx

rx

Ebpr

EE yyt

y

rr

=

=

=

22

2

22

2

2

313118

33318

3rxpC

rx

Ebpr

rx

Ebpr

yyr

, =0

pEb

rpCy

r

==

1

83

2

2

, . , (R1). ( 2) , .

pEb

rpCy

r

==

1

83

2

2

.

32

32131

22=

=

=

rx

rx

rx

. 3/2rx = ,

(R2) . ( . R3 R4 , , . , R1 R2 ).

( ) ( )

+++

+

+

==

22

2

2

3131118

3rx

rx

Ebpr

EE yyr

y

tt

=

=

=

22

2

22

2

2

1118

3118

3rxpC

rx

Ebpr

rx

Ebpr

yyt

(=0 ), . , , , . , , .

) ( )( ) ( )pKCRKRR r +=+= 101 001 , ( )( ) ( )( ) ( )pKCRKRrKRR rr ==+= 1013/21 0002 ,

,

( )( )( ) ( )

( ) ( )( ) pEbrEKpKCE

RpKCRpKCRpKCRpKCRE

RRRRRRRREU

yi

=

=

+++

=++

=

1

83

242

21111

2

2

000

20

20

4321

3241

. pEb

rEKUy

i

=

13

16 22

Pa

EbrEK

Up

y

i 4

2

21022,1

1316

=

=

3. ( ) ( )20 1 ttRtRPt ++= , ( ) ( )320 '''1' tttRtRNi +++= , R0=250, =3,9810-31/oC,

=0,58510-61/oC2, `=6,0110-31/oC, `=6,5310-61/oC2, `=1,110-81/3. , ( ). ) R0`, . ) ( ) 140. :

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) 302000000

320

20

'''''''

'''1'1

tRtRRtRRRR

tttRttRtRtRtR NiPte

++++++=

++++++=+=

) , ( `). ,

. ===+ 4,22'

'0'' 0000

RRRR .

, '00 RR + ,

( ) ( )

+

+++

++= 300

0

00

0000 '

'''

''1' t

RRR

tRRRR

RRtRe ,

CRRRR

oe11015,4

''' 3

00

00 =++

=

) ( ) ( )( )tRRtR eel ++= 1'00 .

( )( ) %16,01057,11''' 3

00

30 =

++=

=

tRRtR

RRR

eel

ele

4. . , ( ) ( )201 1 ttRtR ++= , R0=100 25, =7,6810-31/oC, =1,8810-51/oC2. ) R2 . ) ) , (U=3V, 0,5mV).

U

Ui R1

R2

: ( )

20002

20

21

1 1tRtRRR

ttRU

RRRUUi

+++

++=

+=

02 RR + ...111 322 ++++

xyxyxyx

,

1 :

( )( )

( )

+

++

+

++

++

=

+

+

++

+

+++

=

+

++

++

++=

...1

...111

1

22

02

02

02

202

02

02

02

0

02

0

22

02

02

02

0

02

02

02

0

2

02

0

02

002

20

tRR

Rt

RRR

tRR

Rtt

RRR

tRR

RU

tRR

Rt

RRR

tRR

Rtt

RRR

Ut

RRR

tRR

RRR

ttRUU i

, 10-9 , , . :

+

++

++

+=

++

++

++

+=

2

02

20

02

2

02

2

02

0

2

02

20

02

22

02

2

02

2

02

0

1

1

tRR

RRR

Rt

RRR

RRR

U

tRR

RRR

Rt

RRR

tRR

RRR

RUUi

)

, 02

20

RRR+

=

, =

= 2141

2

02 RR

) R2

+

++

= tRR

RRR

RUUi

02

2

02

0 1 ,

( ) CmV

RRRR

Udt

dUS o

i 5202

20 =+

==

SdtdUi = . , , minmin tSUi = ,

CS

Ut oi 1,0minmin =

=

5. (NTC) . . 12. ) R1 T1 T0=(T1+T2)/2 T2, ( ) ( ) ( ) ( )1002 TITITITI = . ) R1 , Ti=T0. ) ) ) E=4,5V, T1=273K, T2=313K. : 20 R20=10k, B=4000K. : ( ) ( ) === kRKRTR 10293 200 ,

00 2020TB

TB

eRAAeR

== . 1 2:

R1 R() mA

E

( ) ( ) =====

keRRAeRKRTR TTB

TB

2,27273 01111

20001

( ) ( ) =====

keRRAeRKRTR TTB

TB

18,4313 02211

2040402 ) ( ) ( ) ( ) ( )1002 TITITITI = ,

( )( ) ( )( ) ( ) ( )

( )=

++

=

+++=+++++

+=

++++

+

+

=+

+

kRRR

RRRRRR

RRRRRRRRRRRRRRRRRRRR

RRRRR

ERR

ERR

ERR

E

59,722

22222

22

20400

400400201

40040012

1400202040012

1

20140101

4001

01201201401

) ( ) ( )TRRETI+

=1

. ,

R1 . 293.

( ) ( )( )( )21 TRR

TRETI+

= .

( ) ( ) ( )( ) ( )( ) ( )( )( )( )41

122

1 2TRR

TRRTRTRRTRETI+

++= .

( ) ( )( ) ( )( ) ( )( )( )

( )TRTR

TRRTRTRRTR

==+

2

12

122 (1)

( ) TB

AeTR = , ( ) ( )22 TTRB

TBAeTR T

B

=

= . (2)

( ) ( ) ( ) ( ) ( ) ( ) ( ) 4442

2

222T

TBTBRT

TTRTBRBT

TTRTTRBT

TRBTR +==

=

= (3)

(2) (3) (1)

( )

( )( ) ( ) ( )

TBTBTR

TBTBBTRTR

TTBTBR

TTRB

R22

222

2

2

4

4

22

1 +

=+

=+

=

=293, R1=7,44k

) ( ) ( ) ( ) ( )( )

( )( ) ( )( )( )12211121

12

12TTTRRTRR

TRTRETT

TITISsr ++

=

=

) KASsr

33,6= , ) KASsr

43,6=

6. NTC R(293)=11k, B=4000K Rb(293)=10k, Bb=3800K. 50. 50 . Ra(T), . ) Rp Rr. ) 70oC.

Rp Ra(T)

Rr

Rb(T)

: R Rb 50.

: ( ) ( ) ===

keRKRRaB

aaa 10,32933232931

3231

( ) ( ) ===

keRKRRbB

bbb 00,32933232931

3231

:

brpa

pa RRRR

RR=+

+ (1)

( ) ( ) ( ) ( )

( ) ( )( )( ) aa

bb

a

b

p

ab

pa

aapaap RB

RB

TR

TR

RR

TRRR

TRTRRRTRR =

=

+=

+

+

1

12 (2)

) (2) =

= k

RBRBR

R

bb

aa

ap 2,72

1,

(1) =+

= 28pa

pabr RR

RRRR

) 70 ( ) ( ) ==

keRKRaB

aa 50,12933432931

3431

( ) ( ) ==

keRKRbB

bb 51,12933432931

3431

( ) ( )( ) %83,05,12343343

343 ==+

=ab

rpa

pab R

RRRR

RRRR

7. (NTC) . : 25 R25=5k, B=3500K, 0 50. ) R1 . ) 0, 10, 20, 30, 40 50 ( mAI 5,0= , 0,01mV).

: ( )( ) ITRR

TRRUi +=

1

1 , I, .

) 25

( ). ( ) ( )( ) ( ) ( )( )( )

( )( )( )2121

21

11 TRRTRRi

TRIRTRTRTRRTRIRU++

=

+=

( ) ( )( ) ( )( ) ( )( )

( )( )411

2212

12

TRRiTRRTRTRRTRIRU

+

++=

(1) 5.

5, R1 : ( ) =+

= kTBTBTRR 54,3

22

1

) ( ) ( )( )( )

( )( )( )21221

21

21 TRRTTRRi

TRBIRTRIRUTS++

=

== .

I

R1 R(T)

V

I

R1 R(T)

V

4. ( )TSUT i minmin

=

= kR 66,140 , = kR 32,910 .....

K

mVS 02,130 = , KmVS 43,1510 = ....

mKT 77,00min = , mKT 65,010min = .....

8. (NTC), U0=6V. : 20 R20=10k, B=3800K, 10 50. ) R1 . ) ), 0 20.

: ( )( )TRRTRUU i +

=1

0 , I, .

) 20

( ). ( ) ( )( ) ( ) ( )( )( )

( )( )( )2121 10

10 TRRTRRi

TRRUTRTRTRRTRUU++

=

+=

( ) ( )( ) ( ) ( )( )

( )( )41

1

22

1

10

2

TRR

TRRTRTRRTRRUU i

+

+

+

=

(1) 5.

5, R1 : ( ) =+

= kTBTBTRR 33,7

22

1

) ( ) ( )( )( )

( )( )( )21221 1010 TRRTTRRi

TRRBUTRRUUTS++

=

== .

= kR 86,250 = kR 1020 .

K

mVS 64,520 = KmVS 82,6420 = .

9. 0-40 (NTC) . . R20=1k ( 20) B=3500K. , . ) R2 . ) 0=273K ( ), m=313K Um=1V. R3 R4 () . ) T0 Tm ( ), t1=2s 90% Tm. : ( )

( )

+

+

=43

3

21

1RR

RRTR

TREUi (1)

E

R1 R2

R3 R4

Ui -t

U0

Ui R(T)

R1

) ( )( )( )212

12 TRRi

TRERU+

= ,

( ) ( )( ) ( )( ) ( )( )( )( )412

122

12

122

2TRRi

TRRTRTRRTRERU+

++=

( ) ( )( ) ( )( ) ( )( )( )

( ) ( ) =+

=

==+ 713

2222 11

1

21

22

1121 TBTBTRTR

TR

TRRTRTRRTR

) 273 , (1) ( )

( )( )

37,3273

273273

2

1

4

3

43

3

21

1 ==+

=+ R

RRR

RRR

RRR

( ( ) ==

keRRB

40,2273 2931

2731

201 ) , 313 VU m 1= , (1)

( )( )

( ) ===

+

+

=

keRRV

RRRR

R

UEB

i 466,031366,2

1

1313

313

2931

3131

201

3

421

1

) mi UU 9,0= (1) ( ) = kTR 542,01 , t1=2s KT 309= . ,

s

TTTT

t

m

m87,0

ln 01 =

= .