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7/31/2019 el_teh pres

1/88


2/88

1.

2.

3.

4.

5.

6.

2


3/88

1.

:

-

-

-

1.1.

..

=

.

1.1.1.

.

:

x+3=10

x =10-3

x =7

:

U+U1=U2

U =U2-U1

.

:

x-5=3

x =3+5

x =8

:

I-I1=I2

I =I2+I1

3


4/88

:

x+3=50 x-3=50 U+15=18 U-70=30 I+8=10 I-5=50

= = = = = =

= = = = = =

.

:

2x=6

x=2

6

x=3

:

RI=U

R=I

U

54

=x

x=5*4

x=20

:

UI

P=

P=UI

4


5/88

:

10x=30 3

8

=x

3R=U 2I=U UP

=

2

6=

U

P

x= x= R= I= P= P=

x= x= R= I= P= P=

U=6

:

: :

x

2

=16

x= 16

x=16 21

x=(4 12

) 21

x=4

x

3

=8

x= 3 8

x=8 31

x=(2*22) 31

x=(21+2) 31

x=2

U

2

=PR

U= 2 PR

U=(PR) 21

I2=RP

I2= 2R

P

5


6/88

: P=20 R=5

x2=4 x3=27 U2=PR I2=P/R

x= 2 x= 3 U= I=

x=( ) x=( ) U= I=

x= x= U= I=

.

72

=x

x=72

x=

53

=x

x=53

x=

IR

P=2

2I

R

P=

UPR =2

PR=U2

6


7/88

: R=2,

I=3 U=4.

62

=x 43 =x IR

P=2 UPR =

2

x= x= =R

PPR=

x= x= P= P=

P= P=

7


8/88

1.1.2.

, :

:

:

2+x+(x-1)=2+x+x-1=1+2x

:

U1+(U1-U3)=U1+U1-U3=2U1-U3

:

2+2x-(x-1)=2+2x-x+1=3+x

:

2U1-(U1-U3)=2U1-U1+U3=U1+U3

:

(+)(+)=(+) (+)(-)=(-) (-)(+)=(-) (-)(-)=(+)

:

(3+x)(2-y)=(3)(2)-3y+x2-xy=6-3y+2x-xy

:

(I1-I2)(R1+R2)=I1R1+I1R2-I2R1-I2R2

:

:

4x+4y=4(x+y)

:

IR1+IR2=I(R1+R2)

, .

8


9/88

:

x+[4-(3-y)]=x+(4-3+y)=x+(1+y)=x+1+y

:

U1+[U2-(U3-U4)]=U1+(U2-U3+U4)=U1+U2-U3+U4

:

1. (10x-5y)-(4x-3y)=

2. 2x(3y+4)=

3. (2x+3y)(4z-5s)=

4. 2x+x+4x+5x=

5. 5y+3y+6z-4z=

6. 8t+12u-t-15u=

7 9d-15e+4d+5e=

8. x-y+z+y=

9. 15x+13x-37x=

10. 10c-16e+3c+3e=

11. 30p+45k-18p-17k=

12. 170a-40b-7a-35b=

13. 66a+40b-15a+8a+24b-21b=

14. 15.5k+330.2-12.2k+23.3=

9


10/88

:

a 9a+3c-6b-6c+4a+9b=

b 30a+17b-5c+12a-31b+19c=

c 300m+434p-324n-78m+189n-137p=

d 185.2p+124.2x-289.2r-76.4x-120.3p+314.7r=

e 460m+840s+780y+550m-1100y-230s=

:

a (7a-4b)-(3a+6b)=

b (16x-9y)+(4y-8x)-(7x-6y)=

:

a 340.785= b 534. 0.04=

c 63.7.78.7= d 0.29.0.01789=

:

a 3a.4b= b 7c.8d.2=

c 5e.4.3f.2= d 7a.3c.2a=

10


11/88

e 3x.4y.5z= f 22n.2p.4.2q=

:

a 5(3+4)= b 2(3a+4b-5c)=

c 3a(4b+3-2b)= d (3y+8x-25x)5x=

e -3y(2a+3b-4c)= f (4a-5b+6c)(-x)=

:

a (a+b)(a+b)= b (a+b)(a-b)=

c (a+b)(a-2b)= d (2a+3b)(4a+5b)

e (3a-4x)(5+2c)= f (5u-3v)(4x-2v)=

.

a 3.4+2.5= b 3(4+2.5)=

c 25(1+0.004.70)= d 5b(12c)3c.7)=

11


12/88

.

a 5a.4+3.5.5a= b 5b.3a+4a.2.5b=

c x.6y+3.25y.2x= d a(-3b)+4b(-2a)-5a(-b)=

:

a 56.9:23= b 3697.1:92.5=

c 417:0.17= d 0.815:0.0178=

:

a

3

917 yx =

b=

g

eg

24

412

c

97x

1821

yx=

d

azb

zaxab

4515

9835

12


13/88

1.2. ( )

(, , , .....),

.

.

.

E

1 000 000 000 000 1012 T 1012=1

1 000 000 000 109 G 109Hz=1GHz

1 000 000 106 M 106W=1MW

1 000 103 k 103g=1kg

1 00 102 h 102l=1hl

1 0 101 da

1 100

0,1=1/10 10-1 d 10-1m=1dm

0,01=1/100 10-2 c 10-2m=1cm

13


14/88

0, 001=1/1 000 10-3 m 10-3H=1mH

0, 000 001=1/1 000 000 10-6 10-6F=1F

0, 000 000 001=1/1 000 000 001 10-9 n 10-9A=1nA

0, 000 000 000 001 10-12 p 10-12F=1pF

0, 000 000 000 000 001 10-15 f 10-15H=1fH

0, 000 000 000 000 000 001 10-18 a 10-12C=1aC

:

1. 200mV. .

200mV=200.10-3V=200/1000V=0,2V

2. 3V .

3V=3.103mV=3 000mV

3V=3.106V=3 000 000 V

3. 32k?

32=32.103=32 000

4. 342000 M. 34200=342000.10-

6 M=0,342

5. 18,8 F F.

18,8 F=18,8.10-6 F=0,0000188 F

6. 10.

14


15/88

56 000=

2 500 000=

0.014=

0.000078

7. :

4.3.103= 4.2.10-6=

3.103.4.103= 7.10-6.3.10-3=

7.3.106.5.10-3= 8.3.102.2.10-5=

8. .

0.00012T= 0.00034GHz= 0.032MW=

0.1hl= 32dm= 567cm=

30040F= 900000pF= 1000000fH=

0.56k= 800mH= 4000000000aC=

15


16/88

9. :

3kV 10mV 220V 0.6V 380kV 520mV

V V kV mV V V

10. :

75mA 0.32A 600A 0.8mA 900A 0.9kA

A mA kA A mA A

11. :

100m 1.5 220 3.3k 470k 6.8M

m k M k

16


17/88

1.3.

. : .

:

- 10-2 %10

- 10-1 %5

0 100 -

1 101 %1

2 102 %2

3 103 -

4 104 -

5 105 %5.0

17


18/88

6 106 %25.0

7 107 %1.0

8 108 -

9 109 -

- - %20

.

:

.

.

20%.

1:

?

18

a)


19/88

a) 2 7 100 %5 R=27 5%

b) 6 8 104 %10 R=680k 10%

2:

R = 39k 5%.

= 3 =

= 9 =

= 103 =

= %5 =

.

,

.

19

b)


20/88

2% 2%

.

20


21/88

3:

.

a) 4 0 2 102 %2 R= 40.2 2%

b) 7 1 5 100 %5.0 R= 715 0.5%

21

a)

b)


22/88

2.

. ..

.

=9 1

l =9 1m

l=9 .1m=9m

U=220 .1V=220V

2.1.

.

.

:

1) 11V 10V,

1V.

Uiz=11V, Uv=10V, GA=11V-10V=1V

22


23/88

2) GA=9V-10V=-1V

3) Uiz=101V, Uv=100V, GA=101V-100V=1V

. .

= /

GR=GA/

:

GR%= GR.100

: ?

3) Uiz=11V, Uv=10V, GR=v

viz

UUU =

v

A

UG = 1.0

10

1 =VV GR%=GR

.100=0.1.100=10%

4) Uiz=9V, Uv=10V, GR=v

viz

U

UU =

v

A

U

G= 1.010

1=

V

VGR%=GR

.100=-0.1.100=-10%

5) Uiz=101V, Uv=100V, GR=v

viz

U

UU

=v

A

U

G

= 01.0100

1

=V

VGR%=GR.100=0.01.100=1%

23


24/88

:

. 11 80.1 23.3 12.25 0.222

. 12,5 80 24 12.3 0.23

.

. .

24


25/88

2.2.

.

.

.

:

( - )max/( ).100

%1.0 0.1.

.

.. . %1.0 %2.0 %5.0 %1 %5.1 %5.2 %5

0.1 0.2 0.5 1 1.5 2.5 5

25


26/88

3.

3.1.

3.1.1 :

1) L P a=5m:

a) L=a+a+a+a=4a=4.5m=20m

) P=a.a=a2=5m.5m=52m.m=25m2

26

1m

a=5m


27/88

a=3m a=4cm a=6mm 0.7mm

L= L= L= L=

P= P= P= P=

27


28/88

3.1.2

1) : =3m, =4m.

L=a+b+a+b=2a+2b=2(a+b)

L=2(4m+3m)=2.7m=14m

P=a.b=4m.3m=12m2

2) :

=3, =2 a=4cm, b=5cm a=2mm, b=5mm a=0.2m, b=0.4m

28

a=4m

b=3m


29/88

3.1.3 .

1) r=3m !

L=2r

=3.14

L=2.3m.3.14=18.85m

P=r2=(3m)2=9 m2= 28.27m2

2) :

r=2m r=4cm r=6mm r=0.7mm

L L= L= L= L=

P P= P= P= P=

29

r


30/88

3) r1=2m r2=4m.

P=P2-P1

P2=(r2)2

P1=(r1)2

P=(r2)2(r1)2=[ (r2)2-(r1)2]

P=[(4m)2-(2m)2]=[16m2-4m2]=12m2

P=50,26m2

r 2=3, r1=2 r 2=5cm, r1=4cm r 2=5mm, r1=2mm r 2=0.4m, r1=0.2m

P= P= P= P=

30


31/88

3.2.

.

.

. .

1m,

1mm2 200 C.

:

221

1

11

1

11

1

1

mm

mS

mm

m

mmA

V

m=

=

:

G=/l

l .

.

.=1/ . :

31


32/88

Sm

mm

m

mm

m

mmA

V

11

1

1

11

1

11

122

2

=

=

:

R=l/S

:

[2mm

m

] [

m

mm2]

62 0.0161

56 0.0179

36 0.02826

11.5 0.087

8 0.12

2 0.5

.

32


33/88

:

1) 200m =2.5mm2.

.

R==

=

8.25.2

4000176.02

2

2

mm

mm

mm

A

l

2) b ,

l=18cm h=35m R=0.1.

A= 2

2

00317.01.0

18.00176.0

mmm

m

m

mm

Rl =

=

A=b.h h=A/b=0.00317mm2/35m=0.00317mm2/35.10-3mm=0.9mm

3) d=0.3mm 76m. .

=r2=(d/2)2= d2/4=( 0.3mm)2/4=0.0707mm2

33


34/88

R==

=

5270707.0

7649.0

2

2

mm

mm

mm

A

l

4) =1.5mm2 100m.

5) 10 .

=1.1m

mm2 d=1.6mm.

6) 25mm2. 3.6km. .

7) 0.4mm. 2m 6.7. .

8) 5mm. 300m.

9) r1=4mm,

2mm. 200m.

10) 133.

(CuMn 12 Ni) (=0.43m

mm2) 0.2mm .

.

11) - 14 , 2mm 7 (=8) , 2.4mm. 1km .

34


35/88

4.

4.1

:

.

, .

.

I=R

U

:

1) 300 42 V. .

I=U/R=42V/300=0.14A=140mA

2) 40 220V. .

3) (220V/2W) 24.2. .

4) 2.2k 9.6 V. .

I=U/R

:

35


36/88

R=I

U

.

. .

:

1) 60W- 273mA, 220V. .

2) : (6V/0.3).

.

3) (NTC):

U1=30V, I1=2,1mA

U2=52V, I2=4,7mA

:

R1= R2=

:

U=IR

.

:

1) I=410 R=8.2k. ?

U=IR=410A.8.2k=410.10-6A.8.2.103=3.36V

2) 11mA 1.8k . .

3) 3mA. .

36


37/88

G.

.

:

G=1/R

1/ S ().

:

1) G 1.

G=1/103 [1/]=103

S=1mS

2) :

U 225V 42V V 8V 220V V 1.6V

I A 1.38A 4.5A A 610mA 0.15A A

R 25 900m

G S S 200mS S mS 6.25mS 7.3mS

37


38/88

4.2

:

.

. . .

x- ()

y- ()

38

y

P3(-2;-1.5)

P2

(-3;1)

P4(1;-3)

P1(1;2)

-

-2

-3

3

2

1

-4 -3 -2 -1 1 2 3 4 5 x

1-

4-

2-

3-


39/88

:

: y=2x+3

a) y.

)

a)

x, y

.

x +2 +1 0 -1 -2

y +7 +5 +3 +1 -1

b)

.

39

y

-

-4

-6

6

4

2

-8 -6 -4 -2 2 4 6 8 10 x


40/88

y .

:

y=f(x) (y )

, , .

:

y=kx+n

k . .

n y .

:

1) y=x+1

a)

b) .

c) ()

2) y=2x+1

a)

b) .

40


41/88

c) ()

x +2 +1 0 -1 -2 k

y=x+1

y=2x+1

41

y

-

-4

-6

6

4

2

-8 -6 -4 -2 2 4 6 8 10 x


42/88

-

I U

R. ,

.

I=R

U= R

1U

, .

:

I=f(U)

.

U I

.

.

. R=10:

U 0V 2V 4V 6V k

I= U10

10A 0.2A 0.4A 0.6A 0.1

I=f(U)

I-U R=10

42

1

0.8

0.6

0.4

0.2

0 1 2 3 4 5 6 7 8

U

I


43/88

I=f(U) R=const. . -

.

43


44/88

:

1) : R=500, R=1k, R=2k, R=4k;

)

)

.

U(V) 4V 8V 12V k

I(mA)R=500

I(mA)R=1k

I(mA)R=2k

I(mA)R=4k

.

.

:

U

I

R=1k :

V

A

V

mA

U

I 3101

4

4 ==

=10-3S

44

U

I

0 2 4 6 8 10 12 14 U(V)

14

12

10

8

6

4

2

I(mA)


45/88

2)

225V 42V V 8V 220V V 1.6V

A 1.38A 4.5A A 610mA 0.15A A

25 900m

S S 200mS S mS 6.25mS 7.3S

45


46/88

5.

5.1.

1 .

.1.

. 2.

.

I1=U/R1

I2=U/R2

.

I=I1+I2

R.

R=U/I

.

46

I

I2

R2

R1

I1

U

I

RU


47/88

1:

U=12V, R1=1.2k

R2=680. I1 I2, I R .

I1=U/R1=12V/1,2.103=10 .10-3A=10mA

I2=U/R2=12V/680=0.0176A=17,6mA

I=I1+I2=10mA+17,6mA=27,6mA

R=U/I=12V/27,6.10-3A=435.

:

I=I1+I2

U/R=U/R1+U/R2

U

1/R=1/R1+1/R2

R=

21

11

1

RR+

2:

47


48/88

.

R==

+

21

11

1

RR

=

+

33

1068.0

1

102.1

1

1

435

G=1/R

.

G=G1+G2

3:

:

G1=1/R1=1/1,2.103=0.83 .10-3 S

G2=1/R2=1/0,68.103=1.47.10-3 S

G=G1+G2=2.3

.

10

-3

.

48

U

I=I1+I2

G=G1+G2

1/R=1/R1+1/R2

R=21

21

RR

RR

+


49/88

5.2.

3 .

3)

.

.

.

49

In

I2

I

R2

R1

I1

U R3 Rn

I3

U

I=I1+I2+I3+ +In

G=G1+G2+G3+ +Gn

1/R=1/R 1+1/R2+ +1/Rn


50/88

1.

: R1=12k, R2=1.2k, R3=2.7k,

R4=680, R5=470, U=100V.

:

) a

)

)

)

)1/R=1/R1+1/R2+1/R3+1/R4+1/R5=

=

+

+

+

+

110885.4

1047.01

1

1068.0

1

107.2

1

102.1

1

1012

1 333333

R=

110885.4

1

3 =205

) G=G1+G2+G3+G4+G5=4.885.10-3S

) I=

=

205

100

R

U

) I1= mAV

R

U3.8

12000

100

1

=

= I2= mAV

R

U3.83

1200

100

2

=

=

50


51/88

I3= mAV

R

U37

2700

100

3

=

= I4= mAV

R

U147

680

100

4

=

=

I5= mAVRU 213

470

100

5

=

=

: I=I1+I2+I3+I4+I5=488.6mA

2.

R1=30, R2=60, R3=20, . 60V. :

)

)

)

)

3.

R1 R2, . :

)

)

4.

R1=36, R2=48, R3=60, . :

)

51


52/88

)

5.

40.

60 . .

6.

. 2.6.

R1=8k R2=10k. R3.

7.

60 120 .

220 V. :

)

)

)

)

8.

R1=50M, R2=800k, R3=4.8M, . 24V. :

)

)

)

52


53/88

)

9.

R1=250, R2=120, R3=80, . 300. :

)

)

)

53


54/88

5.3.

. , :

.

, :

4 .

.

4.

1 4 :

I

I1, I2 I3

54

I2

I

R2

R1

I1

U R3

I3

2

1

I2

I

R2

R1

I1

U R3

I3


55/88

2:

I1, I2 I3

I

: I=I1+I2+I3

:

I1=100mA I2=200mA I3, I4, I5

. I4 I3=50mA I5=80mA.

I1+I2=I3+I4+I5

I4=I1+I2-I4-I5

I4=100mA+200mA-50mA-80mA=170mA

:

. I1=1000mA, I3=100mA, I4=500mA

I5=700mA. I2.

5.

55

I3

I4

I5

I2I1


56/88

I1=I2+I3+I4+I5

I2=I1-I3-I4-I5=

=100mA-100mA-500mA-700mA=-300mA

I2 e .

.

56


57/88

5.4.

6 .

. 6.

:

U1=IR1

U2=IR2

U

U1 U2 :

U=U1+U2

:

6 R1=1k, R2=470. 10V R1. I, U2

U.

I=U/R1=10V/(103)=10.10-3A=10mA

U2=IR2=10-2A.470=4.7V

U=U1+U2=10V+4.7V=14.7V

57

I

R2

R1

U

U1

U2


58/88

.

R=21

21RR

I

UU

I

U+=

+=

.

:

.

R=R1+R2=1000+470=1470

58


59/88

5.5.

.

.

.

59

I

R2

R1

U

U1

U2

U3

Un

R3

Rn


60/88

1:

5 R1=12k, R2=1.2k, R3=2.7k, R4=680,

R5=470. U=100V.

:

) R

) I

) U1, U2, U3, U4 U5,

) R=R1+ R2+ R3+ R4+ R5=1.2k+1.2k+2.7k+0.680k+0.470k=6.25k.

) I=U/R=100V/6.25.103=16.10-3A=16mA

) U1=IR1=19.2V

U2=IR2=19.2V

U3=IR3=43.2V

U4=IR4=10.88V

U5=IR5=7.52V

60

U=U1+U2+.Un

I

R=R1+R2+R3+ +Rn

1/G=1/G1+1/G2+

+1/Gn


61/88

2.

R1=8, R2=4 , R3=12 . 48V. :

)

)

)

3.

6 . R2, R1=800 , a R3=400 .

4.

220V R1=250, R2=500 . :

)

)

)

5.

300 . R1=80 ,

R3=180 200mA :

)

) R2

)

61


62/88

62


63/88

5.6.

:

,

.

n

.

U1 U2 U.

U=U1+U2

.

.

U1+U2=UR1+UR2+UR3+.+URn

:

U1+U2+.Un=UR1+UR2+.+URn

.

63

I

R2

R1

U1

UR1

UR2

UR3

URn

R3

Rn

U2

U


64/88

:

: U1=10V, U2=5V, UR1=3V, UR3=10V,

UR2 ?

U1+U2=UR1+UR2+UR3

UR2 = U1+U2 -UR1- UR3

UR2=10V+5V-3V-10V=2V

64


65/88

5.7.

. .

M

2

1

2

1

R

R

U

U=

.

65

U2=U

out

I

R2

R1

Uin

U1

R2

I

R2

R1

Uout1

Uout2

Uout3

R3

R4

Uin


66/88

21

2

RR

R

U

U

in

out

+=

.

Uout=Uin 21

2

RR

R

+

.

R1 R2,

R3. R1 R2 R2. R2 R2. :

Uout=Uin2'

1

2'

RR

R

+

66

R3U

2

=Uout

I

R2

R1

Uin

U1

U2=U

out

I

R2

R1

Uin

U1

R2


67/88

:

Uin=60V R1=100

R2=10. O R3=80. :

) U2

) U2

:

a) U2=Uin21

2

RR

R

+

=60V+

10100

10

=5.45V

) R2==

+

=

+89.8

8010

8010

32

32

RR

RR

U2=Uin2'

1

2'

RR

R

+

=4.9V

:

1) R1=100 R2=50 . 20V. U2.

2) R1=22k R2=10k . 220V.

a)

)

67


68/88

3) R=300 .

12 2.5V. R1 R2

4) 24V 6V. .

R1 1.8k. .

5) : R1:R2=3:7.

Uin:U2

6) Uin=6V R1=560 R2=220.

a) U2 .

) R3=180. U2.

68


69/88

5.8.

P

, :

P=UI

W-

.

.

P=UI=RI.I=RI2

P=UI=U(U/I)=U2/R

:

: 1.5k/0.08A.

.

:

P=UI=RI.I=RI2=1500.(0.08)2=9.6W

:

1)

. 220

.

I 10A 16A 20A 25A 35A 50A

P W W W W W W

69


70/88

2)

220 .

I A A A A A A

P 25W 40W 60W 75W 100W 150W

3) 220 1k. .

4) 220 1W .

.

5) 1.6M 3.2mA

6) .

R 560 680k 4.7M 22k 15 3.3k

P 3W 1/2W 1/4W 1W 2W 1/10W

I(A)

7) 200W//6.6A.

.

70


71/88

6.

6.1.

. .

. :

y=2x+3 .

.

. :,

.

.

.

P=RI2

.

71

y

-

-4

-6

6

4

2

-8 -6 -4 -2 2 4 6 8 10 x


72/88

a : y = a x2

.

=1

y=x2.

x

y

, .

x 1 2 3 4

y 1 4 9 16

72


73/88

:

y=1/x

, .

x -2 -1 0 1 2 4

y -0.5 -1 1 0.5 0.25

y=ax.

73


74/88

:

y=2x

x -2 -1 0 1 2 4

y -0.25 -0.5 1 2 4 8

74


75/88

y=logax.

:

y=log 2x

x 0 1 2 4 8

y - 0 1 2 3

6.2.

.

.

0.1, 1, 10 100. .

.

75


76/88

0.1 1 10 100 1000 10000

10-1 100 101 102 103 104

0.1 1 10 100 1000 10000

.

:

10 cm 1

10 . 2.

: 2 : 0.30103

.

1 2 3 4 5 6 7 8 9 10

. cm 0 3.0 4.8 6.0 6.9 7.8 8.5 9.0 9.5 10

76

log

log


77/88

x- y- .

.

x y

lin-lin

log-lin

lin-log

log-log

.

lin-log .

77

0 1 2 3 4 5 6 7 8 9 10

1 2 3 4 5 6 7 8 9 10


78/88

100

.

R= 4.10-1k = 400

78


79/88

- .

:

500 lux.

:

R=200

79


80/88


81/88

NTC-.

.

:

NTC 33, 140 .

:

2.

81


82/88

NTC .

:

10W .

( 100mW 1W)

.

:

12mA 30V. .

R=U/I=30V/10mA=3k

50mA 20V.

:

R=U/I=20V/50mA=0.4k

82


83/88

83


84/88

.

84


85/88

PTC-

PTC - .

.

PTC

85

PTC

.


86/88

.

LDR-

LDR .

. .

86


87/88

87


88/88

1. Technical mathematics for the electric trade.

GTZ

2. Electrotechnical Fundamentals of Electronics

GTZ