# ΕΠΑΛ ΦΥΣΙΚΗ λυσεις ασκησεων

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Α λυκειου

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• ***

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UAKTIKHN 1

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Y i i o m w . lUlAElAL ) FITCKEYMATQ*

I1AJ \ U I ' l M l

^

, , -.

. ... . - .

• '

: , , , -, , , -) ' , 2010, : I. , I. , . , . , . - . .

: , - ' , , 2010, : . , . , . , . , . , . , . , . . .

• 1.1

1. , :

s - 1 2 0 / - ?n / = - = m / s v=30m/s . t 4

:

u(m/s)>.

..

s(m)> >:;..

2. t, :

s + ^ . s + e . 1.980 + 20 . = t = t = s t = 200s t 10

3. . : S=E j+E2 S = 1 0 1 0 m + 2 0 - 2 0 m S=500m.

, - s , - 5 0 , -. = - = = 12,5m t 4

• .

4. . I 4 -

2

t=0

- t

t=0

(): ( = = >| t ( 1 )

(): 2 = s -

s - = 2 (2)

(1) (2) :

X+Syl('=V lt + V2t s = ^ ^ 2 ) t t = 1.000 -s t =

] + 2 10 + 15 ] x :

=! t x = 1 0 - 4 0 m x = 4 0 0 m . . :

s(m).

40s

Min/s),

-15

10 20 30 40

• 5. . t, : S., = t SM = t . : Sn - 8 = ( -) d = ( -)1

d 500 t = = s t = 50s - 3 0 - 2 0

. : S n =wnt = 30-50m 8 = 1.500m.

6. x = 1 0 t = , - = 10m/s .

:

i'

• s, :

1 2 - at, 2

s = s 2 s i = a t 2 at , 2 = 2 2 2 m - 2 l 2 m s = 3m. 2 2 2

9. A. To -

3 0 + 1 0 . : s = 20m s = 400m.

, . - . - s 400 , . - 40 , . : = = - ^ - m / s = m / s .

10. = 8+2 = 0 + , u0 = 8 m / s a = 2m/s 2 . :

1 2 S = S4 - s2 = 0 4 + - a t 4 V 2 1 at,

s = 0 ( 4 - t 2 ) + ^ - a ( t 4 2 - t 2 2 ) s = 8(4 - 2) + ^ 2(16 - 4) |m

s = 28m

11. ( in/s)Ai

50 I

30

() /

j i -/ ;

'

• () 10s - . : s 2 = 10-30m s 2 = 300m. () () t = 10s s = 300m - 2 5 0 m s = 50m.

. t ' . , -

: 50 = 30t 10t - 50 = 6t t = 12,5s.

12. . :

= + a t 30 = +10 ()

1 9 1 = u A t + at 200 = 10 + 100 ()

() () . () : = 3 0 - 1 0 () () :

200 = (30 - 10) 10 + 50 = 2 m / s 2 . - () :

= (30 - 10-2)m/s u A = 1 0 m / s .

13. 0 ,7s 0 , s , =\)0t, = 20 .0 ,7m s , = 14m.

s = ( 5 0 - 1 4 ) m s = 36m.

:

02 2 0 2 smax = = ^ 7 : m Smax = 20m. 2 2 - 10

s m a x < s .

14. {( + s)m. = 2 m / s 2 ,

1 , 1 , u0 = 20m/s. : (, + s) = 0 t + t 70 + 55 = 20t + 2t .

• t , = -25s t 2 = 5s .

15. . -.

: x! = x 2 1 0 t = 4 t 2 4t = 1 0 t =2,5s. .

^ / s , 0 = 0 a = 8m/s 2 . :

( ) >

n(ni/s)A

20

10

l>2=/ (t) x

, r*

/

/

l= '(f)

2.=; -> L(S)

"= ' ( 0

t(s)

16. . l i s

3 3 . 9 + 5 9 + 2 2 3 m So) = 81m.

:

- S ; m / s = 7,36m / s. t 11

. 3s

9 - 0 , = At

j , 2 m / s~ , = 3m / s , 3s -

3 2 . , 2 2 - ^ m ' s 2 im / s .

17. . :

= 0 - a t -y- = 0 - a t 5 = 10 - 2t t = 2,5s

• 1 2 s = v0 t - a t s =

1 1 0 - 2 , 5 - - 2 - 2 , 5 -

2 , m s = 18,75m.

>

. u = D 0 - a t = 0 -

s t = 5s. n . .

1 0 : 0 = 0 - a t t = = 2

() :

- V . 102 . smax 2 2 2 m S m a" ~ 25m.

18. . ts, (t - 4)s . :

1 ] 2 s = t = a 2 ( t - 4) .

s a 8, :

t2 = ~ 2 ( ~ l6t2 = 2,5^t2 + 16 - 8 t j -

t = 20s

4 * s 4s.

1,8

1 9 s = = s a = 1,6 20 m s = 320m.

. " , m / s )

- : ua = a , t = l , 6 -20m/s = 3 2 m / s = 2 (t - 4) = 2,5 (20 - 4 ) m / s = 4 0 m / s .

-

s : = -t

320

20 m / s = 16m / s.

. = f ( t ) s = f( t ) :

• 19. . : 0 < t < 5s 0 =10 /5 . : 5s < t < 15s = 2 0 m / s . : 15s < t < 2 0 s -

2 . , = = 4m / s .

- - 2 2 - - 4m / s .

. 0 < t < 5s :

, - 2 0 - 1 0 , 2 -, , 2 = = = m / s = 2m / s z . At tx t A 5 - 0

. To - .

10 + 20 5 + 10 20 + - 20 5 + - 5 20 |m = (75 + 200 + 50 + 50)m = 375m 1, 2 2 2

: = (75 + 200 + 50 - 5 0 ) m = 25 . -.

. . . , , - s 375 , -. : = = m / s = 15m / s.

• 1.2.

1. :

F = F j + F 2 = (80 + 60) F = 1 4 0 N .

: F = F 1 - F 2 = (80 - 60) F = 20.

2. F :

F = (20 + 10) -5 F = 25 F = 20 - (10+5) F = 5 F = (20+ 10+5) F = 35

3. . 2 F = F[ + F2 . F = 4F 2 + F2 F 2 = 2 * F j = 4 F 2 F , = 8 N . - .

. - - ^ F = F , - F 2 . f F = 3 F 2 - F 2 F2 = 5N F ! = 3F2 F, = 15N 6.

4. . Hooke : F = KAx. = 20cm F = 80N :

80 80 = -20cm = = 4 . 20 cm cm

• , = - :

(cm) 5 8 10 15 20

() 20 32 40 60 80

. :

so

10 15 20 Ax(cm)

.

20 : - 4 / cm,

.

5. , = 0, = , Z F = 0. F 3 - F 2 , :

F , - F 2 - F 3 = 0 F 3 = F 1 - F 2 = ( 2 2 - 7 ) N F 3 = 1 5 N .

6. , F, F . : F - B = 0 F = B F = 200 .

7. S F ZF = 20 ' , - . , .

• 8. - : At

= m / s 2 = 2,5m / s 2 . 2

: F = m a = 1 0 - 2 , 5 N F = 25N.

9. = 4t = - -

2 > ' ' = 4 m / s . : I F = m a = 1 .4 Z F = 4 .

10. :

1 4 - 1 0 , ? ^ . 2 = = m / s = 2m / s . At 2

: F = m a = 10-2N F = 20N.

11. . :

| 4 2 2 , = - - m / s , = 4m / s m, 1

F^ 15 2 2 2 = - m / s 2 = 5m / s . m2 3

. 18m t S j S 2 : S 2 - S, = (18 -10 )m S 2 - S 1 = 8m. :

2 t2 - a] t2 = 8 5 t2 - 4 t 2 = 8 2 2 1 2 2 2,5 t2 - 2 t2 = 8 t2 = 1 6 t = 4s.

12 . .

. 2 0 , 2 - , , 2 . . , = = m / s a , = l m / s t . , m 20

0 S,. - :

1 2 1 2 s i = 2 ^ s i = ( )

0 = a , t , 0 = t, ()

• 5 2 = = m / s 2 2 = 0,25m / s2

m 20 -

t, t 2 = = 1L () 2 2

2 2 0 t. s2 = = () 22 22

1 2 t 2 s, + s 2 = soX t j + - i - = soX 2 2 cx 2

t j 2 + 2 t , 2 = 4 0 t, = 4s.

F 2

1 2 1 2 s, = t, = 4 s s, = 8m. 2 1 2 1

. :

t. ( 4 ^ = t[ + t2 = t, + = 4 + 77 Is = 2 5 2 V 0,25)

13. . :

1 2 2s 48 , 2 s = a t - = m / s a = 3 m / s . 2 t 16

. I F = m ZF = F 1 + F 2 - F 3 : F , + F 2 - F 3 = m a 6 + 2 - F 3 = l - 3 F 3 = 5N.

14. Z F = F j - F 2 = 4 0 - 2 0 = 20.

= m m =

:

; , . , ' 40 2 ' n / 2 = m = = - m / s = 0,6m / s . m 20 ' 3

, , .

• 15. :

, 1 2 - 2 2h . [2h h = g t t = t : 2 8

t = 2s.

16. t, :

2 , _ [2h h ^ 8^ 1 ~ J ~ t = 6s.

t ' : t' = t - A t t ' = (6 - l ) s = 5s.

h ' = - g t ' 2 = - 1 0 52 m h ' = 125m. 2 2

Ah : Ah = h - h ' = (180 - 125)m Ah = 55m.

17. . :

F 2 4 , 2 2 F = m a = = m / s = 5m / s . m 4.000

: 2

S = - - 0 2 = 2 s 0 = ^ 2 a s

0 = 2 0 m / s . . :

0 20 , 0 = = s t0) = 4s. a 5

. :

*-

KM

• 18. . t.

1 2 : h = g t t

t = 3s. - , t ' = t - A t t ' = ( 3 - l ) s t ' = 2s. :

, h - g '2 / 1 ,2 2 V + - g i 0 = -

= 4 5 - 5 - 2 m / s 0 = 12,5m / s.

. :

30 -am.

)( m/s)

I : SAP

S ) T

. y ?

< ' . - ; . ; .. - 5 5

W Wrfr

s(m/s)T

• 1.3

1. . ^ :

F2 = F , 2 + F 2 2 = 2 F j 2 Fj =

F, = F2 = /50 F, = F, = 5/2

2. F F , :

f = VF,2+F22

F = /4 . - F3 F.

F3 = F = ^4) .

3. F F j , F2 :

F = ^Fj2 -t- F,2

F = . - :

F 1 0 , 2 - , , 2 = = m / s = I Om / s m 1

- F - F 2

: p

= 6 . 3 - 4

• 4. . :

2h g 2 = = t2

I

2 - 7 2 2 2 gx = m / s g x = 1,6m / s . 3

. ) , 3s. 6) : = x = 1 2 - 3 m x = 3 6 m .

5. . y :

1 = t

, =

()

(6)

. () : uy = g t

1 2 2 8 '

2y 2 500 g " g =

g t ' ()

()

m / s 2 g = 10m / s 2 .

. (0) , . , , x = 0 1 = 1 5 0 1 0 m = 1 .500m.

. = 2 = , . -

: B j - = m , (1) T - B 2 = m 2 a (2). . (1) (2) : , - + - 2 = m[ + m 2 , - 2 = (m, +m 2 )

30 - 10 m

, " 1

m,g a - I"2g a =

m

7' m, + m 2 4 s . , .. (1) : = B j - m , = (3-10 - 35) = 1 5 .

• ..

7. . . By, : EF = m = m (1).

. (1) :

m g = m = g =

8. . mg . Mg, F .

. - : F - Mg - mg = ( + m) F = [(1.920 + 80)-2+ 1.920 10 + 80 10] F = 24 .000.

. : - mg = m a = m a + mg = (80-2 + 80- 10) = 960.

9. .

: s = a t 2 = a t. 2

t :

1 s = -2 2

->2

s 2

=

= 10

2 10 m / s = 5m / s .

. : = m = 55 = 25. > : = F - = F - = (30 - 25) = 5.

. :

= = ^ = mg 5 10

= 0,1.

• 26

10. . F , . - :

2

2s

= 30-2 0,2

m / s = 2.250m / s"

: F = m = 60-2.25GN F = 135.000N.

11 . = 0, XF = 0 F - T = 0 T = F = 1 2 0 .

120 = -

250 = 0 ,48.

. ' = = 0 . 4 8 6 0 ' = 76 ,8. F' : F = ' F = 76 ,8N

12. . - .

. - : B t - ' =rn, (1) ' - = m 2 (2)

. - (1) (2) ! - = ( m , + m 2 ) = ' = 2 : m , g - ^ = ( m , + m 2 )

8 10 - 0,25 -12 10 = 12 + :

m / s

= 2 5 m / s .

13. . .

. : = = By = ^, ; = ^

= 6

10 2 ,5. 2

• . :

1 1 0 2,5 ZF = m a - = m ^ - = = m / s2

a = 2 ,5m/s 2 . :

1 2 1 s = a t = 2,5 m s = 1 ,25m. 2 2 '

14. .

2 = 35m/s . : = ,

R

, 0,8 R = = m R = 0 , 4m. 2 2

352 = 7 T T m / s 2 = 3 . 0 6 2 , 5 m / s 2 . ,

2 15. = R, =

: = R = - 6.380 103m / s 24 3.600

u = 4 6 3 m / s . : = 2 4632

= 0 , 0 3 4 m / s 2 .

16. :

= ^ = 2 - 2 3,14 8,5 ^ m / s = 368-10 3 m/s . 2 2

:

2 .,2 (368 103)

= = m / s 2 = 19,6 10 m / s . R 13,8 103

R 6.380 10 3

17. :

780 f = Hz f = 13Hz.

60

• : = R = 2 n f R

= 2 = 2 3,14 13 9 ^ . m / s 2 2

2 2 O = 2 6 , 9 m / s = = m / s2 = 2 . 1 9 3 m / s 2 .

R 0,33

18. , , 25% .

: Fx ( m a x ) = 0 , 2 5 ( 3) = 0 ,25mg. 2 2

Fx ( m a x ) = 0 ,25mg = ^ _

1 = V0.25 gR 13 = 13m/s .

19. : = 12h= 12-3.600s TQ = 43.200S = l h = 1-3.600 T A = 3 .600s.

_ 2 t. = _ ^ 1 (1)

1

2 . ~ 1 ~ 1 (2). - =

3 / \ /^\ ' 2 2 . ( I ) (2) 1 1 =

/

2t l

V J

3

1 . ( 2t

\

3 1 3.600 43.200 / J_ t = 10 ,9min .

3

20. t

d 2 , : t = = s t = 0,005s. - 400

t . 4

* t 0,005s 0,02

• 21. . : 7

= a)(R + h) = (R + h)

-2 3,14

(6.400 3 + 6.400 1 0 3 ) m / s u = 5 . 5 8 1 m / s . 4 3.600

. :

2 2 3,14 = rad / s = 4,36-10" 4 rad/s . 4 3.600

22 . . : Fx + Fy = B = m g - 60

{ \ = / 3 10 1 0 - 4 0

2 = ( - 20/3) = 65,36.

mi m

mwm """ ~r ; w S W % S

. 5s u = a t , .

Fx = m a = Fx 60 4 0 -

10 m / s2 a = 2 m / s 2 .

m m u = a t = 2 -5m/s = 1 0 / 5 . .

:

c c c 1 , 2 1 . 2 -S = S5 - S4 = - a t 5 - a t 4

s = ( 5 2 - U 2 ) = j 2 (52 - 42 jm S = 9m.

• 23. . > F = F = F = = 0,2 1.000 F = 200.

. :

F ' - T ( F ' - T ) g ( 5 0 0 - 2 0 0 ) 1 0 , , = = m / s = 3m / s .

m 1.000 .

1 2 [ . : s = a t t = J

2 t = 4s. :

= = 34/8 = 1 2 / 5 .

24. . y : / 3 - 30 = 0 Fx = m g 30 = 1 10 Fx = 5/3 .

30

. :

30 = - m -Q a = g 3 0 = 5 m / s 2 . m

. 0 = 0,

1 2 . h 1 2 - 2h : S = at = at t = 2 30 2 \ 30

t = 2s. = = 52/8 = 10m/s .

.

a ' = g 4 5 S ' = -. -45

, 2h t = r V g 4 5

• 2h = ^/2gh . - = ' t ' = g 45

\ g 45

h , - = 10m/s .

25. . : F - T = m , a (1)

T = m 2 a (2) (1) (2) :

F = (m, + m 2 ) o = 5 l 5 L < 1 = l L 5 2 . |

F = 20 + 500 ^ . F = g 7 _ 5 R

. F (2) :

-, g , = m2 = - = - - = 62 ,5.

7 F | < ,

• 2.1

1. - :

W = = 4 W = 4-30-50J W = 6000J

2. . : U = m g h = 1010-20J U = 2.000J.

. : U = m g x

:

I (J)

20(1(1

x(m)

3. :

2 - WT = 0 ~ = x

1 2

mu; 0 1000 152

- = m = 15m 7500

4. . :

1 2 1 2 0 + WB = mu mgh = mu

u = 20m/s

h - .

• 5. ,

F = F = m g () :

s h = - = ()

P = F u () () :

= mg = 2000 10 W = 10.000W t 120

6. :

0 + WB - WT = j ran2 mgh - () = - j 2

^()30 - () = 2

2g(A)30 - 2g(A) = 2 : u = 6 m / s .

7. . T = F : W T = W F = F x = 40-5J W T = 200J .

. - :

WT , t = : t

WT W x 2 0 0 4 , , L = 1 = - J / s W T = 160J/s

8. - Q :

m g h ! + 0 = mgh 2 + 0 + Q Q = mg (h [ - h 2) = 2 10 (20 - 18)J Q = 40J

:

Q 40 100 = 100 = 10% nigh, 400

• 9. F , . : F = = ^ = 0,5 100-

F = 5 0 0 F.

: = W F = F x = 5 0 0 10J = 5.000J.

10. . . : W B = Bh = mgh = 80 10-300 0,2J W B = 48000J .

. :

W = 4 0 < * > , i s * . 8 0 J / s t 1 0 - 6 0 t

11. . : W F = F-x = 4-10J W F = 40J .

x ( m )

. F-x.

W F = j 10 10J W F = 50J

12. . F Fx .

: WF = WFx = F 60 x = 50 10J W F = 250J

. :

1 0 + Wp = = F 2 = 5 m / s .

2 - 2 W f . . - - - ' : m

• 2 13. . hm a x =

2g 0 : 0 = V2ghmax V0V800m / S :

1 2 ^ 1 2 ' ^ 2 - m 0 + 0 = - - 0 + mgx - 0 = mgx 2 2 2 4

- 8 0 0 x = m = 20m

1 10 . ' ,

= i 0 = ^ Vs00m / s.

:

1 2 1 2 0 + 0 = + mgx'

, 2 - 2 8 0 0 - 2 0 0 , , = = m = 30m 29 20

14. . -:

1 2 p 1 2 - mn - F = 2 0 2

= mug - 2F ,

v=8m/s . m

. :

. muo 4 2 1 2 0 F = 0 x = = m x=20m 2 0 F 10

15. :

1 ? 0 + WF = mv ()

• F :

F(N)A 8

x

• , : = gt. :

AU 2 , AU = mg gt = mg t = lOOt At At

1 .2

( a )

= gt

: t = t = 2 s.

( ) :

w

200

18. :

0 + WF = 2 () 2

F . :

WF = 10J WF = 30J.

() :

= J 2 * = V30m / s m

19. . :

1 2 1 2 - WT = 0 ^ = 0

= ] 2 ^ = y[60m / s .

• . . - W T . : W a j n m = U A + W T .

1 2 , 1 , U A = - m u r WT = . 2 2

: W = 2 - i m = 2 - 2 60J 2 2

W "rt 120J

20. . :

^32 3 2 1 7 1 7 = = 65 7 2 : 3600

J

= 2,57 10 l o J . ' 50% , :

= 2 2 1 0 3 = 22-745 ,7-10 3 W = 16405 103W. - . :

= t = 2,57 10

16405 10 s

t = 1,57-10 s t = 2 6 m i n

21. . F , FK = 0. : = (10 + 5 ) 0 , 8 = 2 0 , x = 3m.

. - 3m :

0 + WFo>M) - w T = J m " 2 ()

: = = ( ^ - ) = 0 , 2 5 [ 2 0 - (10 + 5 ) 0 , 8 ] = 3 -

• Fouv0 = (lO + 5x)O,6 FODV0 = 6 + 3X. Fouv0.

()

WT= f3-3= 4,5J

Fni)vO(N) 18 IS

W F < n ,ve= J i Y A 3 = 31,5J

x(m) *(m)

() :

2Wf - 2WT . r~ t2 1 2 5 - = 3v3m / s m

22. A. To :

F(NU

20 30 *(m)

1 WF = - 30 30J WF = 450J

B. To , : I F = 0 mg = 30 - x x = 20m. - :

1 2 0 + WF - mgx =

3 0 + 1 0 20 - 10 20 = - 12 = 20m / s 2 2

• . . 0 + W F - mgx ( i = 0

w - 3 0 - 3 0 W F . 2 mg 1 1 0

m x = 45m

. To . :

0 + mgx(1 = ^ '2 ' = ^2gx f l

' = 30m / s .

• 2*2

1. Q = AU + W : AU = Q - W = (80 - 30)J AU = 50J.

2. Q = + W : Q = (30 + 50)J Q = 80J.

3. Q = + W = 0. : Q = 0 + W Q = 50J.

4. Q = + W :

W = Q - AU = (400 - 250)J W = 1 5 0 J .

W 150 W = F = = m = 0,1 m. F 1.500

5. , , .

: = mgh = 0,8 10-3J = 24J.

6. 350kcal . , .

. 3 5 0 gr. 2kg, 2.000gr

-7,-)

2.000 , . 2.000 -9,5 = 54,28 . 350 350 9,5

7. .

108 103 , , . = m / s = 30m / s, : 3.600 * ^

= m 2 = 1.000 302 J K = 4,5-105J. 2 2

• . , , F . = W F = F x = 450 1.000J E = 4 , 5 1 0 S J .

. 3-107J 30%, 0 ,910 7 J . F, .

- TJ C ' ' ' ^> 10 , 4 = F = = m =2-10 4m. c 450

• 3.1

1. q = C V => q = 48(HiC

q = e => = - => = 3 15 e

I = -3- => I = 24mA . At

2. I = i = > I = - = > I = e- v = I = 9,28 1(4. t

3. ud ' ' ( ).

s At - s h = ud , V = s h = s ud .

: n = - => x = n V => = s u. At V

: I = -3 => I = => I = At At

I

n s ud At e

At mm => u d = 1.25 10" => u d = 12,5

n s e s s

4. R, = I

R,= v 2L

R, ( ( = 2 R, = 2 - R 2 = > q = 2 -Rn s, s,

s- = 2 s, => St = 0,4 mm".

5. .

6. R = -

m = d V = > m = d - s - = > s =

(1). (2) => R = g d e d-e

R = 52,5 .

(1)

(2)

• 7. , :

= => s-e = s'-e' => s' =

:

R = e

R'=Q -s'

R; = ' s

R s' (

(1)

= f ) => ' = c A [ ^ - => c = 4m . R W / V R

8 = Q0(l + ) => 2 Q0 = Qn(l + ) => 2 = 1 + => = 1

=> = - = = 256,4C.

, . , .

9. , = V

Ri

= R,

I, _ R 2 _ I , _R(1 + 2) I,

2 R, 2 R u ( l + a 0 1 ) I,

1 + , => = grad 1 + , 2480

10. R . = R. + R, => R , = 20 1 2

I = => I = 5 ,,

V, = I R, => V, = 25V V, = I R, => V = 75V.

11. 1 + J _ = , R ( A = R l R 2 => R, = 20

R.A R| R:

I = => I = 6A R,v.

R-l + R-2

• I, = => . = 4 R,

I, = => h = 2A. R,

12. ) R p = R ' R 2 => R P = 2 R, + R,

= ^12 + ^3 ^ R . =

I, = ^ => I, = A

I = => I = 10A

VBr = I R3 => VBr = 40V => v3 = 40V VAB = I R p => VAB = 20V => V, = V, = 20V ( V a b = 60 - VBr => VAB = 20V)

V, R, ' 3

I , = ^ = > I, = I A R, " 3

I, = I = 10A.

) R23 = R, + R, => R23 = 90

R, R^ R(, = => R = 9 R, + R23

I = => I = 10A r , a

I, = => I, = 9A R .

I2 = I3 = => I2 = I, = 1A R23

V, = => v , = 90V VAr = I2 R , => = 40V => V, = 40V VrB = I3 R 3 => VrB = 50V => V3 = 50V.

13. R p = R, R , / R , + R , = 2 R,,, = Rp + R, = 10 12.> 12 j R4, = R4 + R, = 10

R.17^ ' R45 K , = = 5 R | 2 ! + R l 5

• I = = 12

3 = R ,

= 6

V r B = I 3 - R 3 => V r B = 48V = = !3 ' 12 =* = 1 2

3 = 48V > , = = 12V

I. = R ,

=>, = 4

, = = -V a R-

> 4 = 5 = 6

4 = I. R . => 4 = 42V => V = 42V 4 4 4 v a b = I4 R 5 => = 8 5 = 18 V.

14. 1 , - i V =

h

4 4V 4

=

1| = I, + 3 => Ij = 2 V, = 2 R j => V, = 4V = + V 123 1 23 V = 45 123

V.23 = 8V

= 45 1 45 " Rt5

1 = I. + 45

=> V45 = 8V

45 = 0,5 => = 0,5

=> I = 2,5

V . = V - I R => IR = V - V , => Rs = 123 123 ^ V - V K

I R = 0,8. '

15. = 10cm RgP = R* => R B r = 50 R B A r = R* ( + ) => R B r = 70

V R r f

J r i = 0,28A

1 RAT RR

- = 0,2A.

16. a ) R p = R t + R., => R p = 3, R,4 = R3 + R4 => R34 = 15

V R|i

1,2 = I = 10A

• V R

=> I u = 2

= 12 ' R , = > V r A = 2 0 V = > - V A = 2 0 V

- 34 R 3 = > = 10V => - (2)-(

10V - = 1 0 - 2 0 = VAB = -10V.

(1) (2)

) R- . R4 R s : R4< = -R, + R,

R 3 4 5 = R 3 + R 4 5

V I'l2 = I 12 = 10A

(3)

(4)

V 30 30 1 345 RU5 ^ 1 345 R, + R45 ^ 1 345 5 + R45

V r A = l ' i 2 - R i

V = I R IB 345 3

V r A = 20V => v r - v 4 = 20V

V r 5 =* V r - VB = 5 + R1S 1 B 5 + R ,

(6), (5) => V A - V F _ 150 5 + R4,

- 2 0 0 150

- 2 0 5 4- R45

150 5 + R45

: 20 50 = 20 R, R4 , = 2,5

10 (3) : R5 = .

17. ) :

(5)

(6)

.

1 1 - 1 + 1 + 1 , + + R,A R R R

- => R, = R => R,v = 10 . Rv. R 3

• ) :

^ R R _ R R + R 2

RAB = RAR 4- R = R + R = ^ 2 2

R , v . = R a r R

3 R R 3R

= = 3R = 18Q . Rab + R j^ R + r 5R

18. BZ V,

: I R, + R,

1 =

: V z = 0 - = => = => = " = 2 => - = => = - .

- = I R, => -(10) = 1 10 => + 10 = 10 => = - = I R2 => -10 - = 1 10 => = -10 - 10 => ,- = -20V.

19. , R, , .

: I = => 1 = 1. R ,

, R , R3 - R,. :

R, R, R23 = R, + R,

= 10

• R a = R j + R2 , = 20

I = = 0,5A r a

Vj = I RJ = 5V V2 = V, = I R23 = 5V

V, 12 = = 0,25 A R 2

13 = = 0,25A . R3

20. ) R .

-,. _ R 3R : % = 4 4

v ab . 60 240 , = -> = => , =

RAB R R 4

= => => \ 240 Rai B j R 3 R

4

: RAr = 2

: V A r = I2 R A r => V A r = | => V A r - 40V.

) = 0

Rvr = 4

: R . r =

">40 R V . r = I? RA r => V A r = - => VA r = 20V => 1 2 ^

=> - = 20V => 0 - = 20V => = -20V.

21. R j R4 , R | 4 = 10, R , R , , R2 , = 10 R | 4 R1? , R ) ? = 5. : V, = I, R 3 => V_, = 2 6 => V, = 12V V2 = I, R2 => v 2 = 2 4 => V, = 8V : V . = V, + V, => V . = 20V

^ 2 3 /.

Yv : 1 = => I = 2. 4 R

• 22. ' . V

R, + R, = =

: q = C V => q = 4000.

: I = => I = 2

: V = VA r = V,tI. = I R = 2 10 = 20V c lii 3

23. : I = (1)

(i) V 5V V AB-=- I 5 R =* V A B = 5 R => V A R = (2)

ci, = c i vAB ^ qt = c, ~ (3)

(1) V W I ' 3R => V f A = ? R 3R =* V r A = (4)

q 2 = C 2 - V r A ^ 1 2 = C 2 C, = c 2 y => - -

24. R . : R, = R + R => R, = 2R

R R R R, = => R: = R + R 2

: , = => , = R, 2R

n V : 2V : , => I' -~ R2 ~ R

: >

25. ) : f = I2 R, , = I2 R2

R, > R , > ,.

) : , = R,

R, > R , < ,.

• 26. R P = = 5 R, + R :

Rm = R12 + R3 = 10 RPI ' RJ RP.,4 = 4 = 9

R,23 + R4

R x = R .234 + R 5 = 2 0

I = v . = 9 A

V. = I R, = 99V V , 2 3 4 = 1 * R . 2 3 4 = * 1 V

I4 = = 0,9 A RJ

I, = = 8 , 1 A R . 2 3

V3 = 13 R3 = 40,5V 1

V,

V12 = I, R12 = 40,5V

I, = - = 4.05A R,

I2 = = 4,05 A R,

Q i = I" R j t = 9.841,5J

0 2 = I2 R2 t = 9.841,5J

Q3 = I3 R 3 t = 19.683J

Q4 - I4 ' R 4" t = 4.374J

Q = I, R t = 53.46J.

-77 80 V2 , AQ 27. t = m c => 100 R

. YL t = d V c => 100 R

221 t = 1 1 5 _ 20 10"3 1 80 => t = 1727,27s => t = 0.48h 100 10 10-" 10~3

PHA = => PHa = 4,84KW

• w = t => W = 2 32KWh 1 ^ ,^-

, = 2,33KWh 25 = 58,1. KWh

28. : , = V, I, => Ij = 6,81 : P., = V2 I, => 2 = 9,09 : 3 = V3 I, => 3 = 4,54

: 4 = V4 4 => 4 = 2,21

= . + 2 + 3 + 4 = * U = 2 2 > 7 1 A

, 25. : = + P., + 4 => = 5KW. WHA = , ' 1 => WH A = 50KWh. = 50KWh 25./\ = 1.250.

29. ) R , = R, + R2 = R o , = 60

I = => = 2 R *

: = I2 R, => = 160W

R R ) R. , = - = 20 R \ = R. , + R-, => R - = 40 V) .3 R ] + R } - 13 2

V I = => 1 = 3 R

V13 = I ' R 1 3 => V13 = 60V

V13 I, = => I, = 1,5 R ,

' = \] R, => ' = 90W A l l ' - 9 0 - 1 6 0

(%) = 100% => (%) = 6 0 - % => (%) - -43,75%.

30. R j R , , R12 = R j + R2 = 6. R r R, R.2 R 3

R,2 + Ri RoX = R123 + R4 = 11.

, R p 3 = 3. R123 R4

v 3 V3 : P3 = -J- => V3 = 12V, I, = - 1 = 2A R3 R3

• V P = 12V, 12 = = 12= 2 R, :

: 4 = I p + I, => 4 = 4

: = R, => = 128W. 4 4 4 4

31. :

D ^ D 10 in-8 100 3 O = => R = 1,8 10 => R = 180 s 10 10

1 0 , => I2 R = , => 100 100

10 100

2 . 180 = 720 - 3 => I = 20

, = V, I => V, = => V, = 36.000V I

, , = , => Vo = => V2 = 32.400V . I

32. = 2000W VK = 200V.

V2 V2 : = - => R = - => R = 20 R '

= VK => = PK/VK => = 10

160V, :

^ , 1602

R 20 V ^ = 160 R 20

= => = => = 1280W

, = V ^ i = 1 6 0 ^ I = 8 A .

33. = 1000W VK = 100V.

: = VK IR => = ^ => = 10

: VK + IR = 220 => 100 + VR = 220 => VR = 120V

: IR = 10A

: IR = => R = => R = 12 . R IK

• 34. : .. = 100W V,,,H. = 200V MB) .() 2

: () = ('" = 0 , 5 R , = = 4 0 0 ^() RR(0)

: () = 24V VK(A) = 12V

: ( = ^() = 2 RA = ^() = 6 *() ^()

: = R N + R. => R . = 4 0 6

/ .

_ V 1 - - - => I = 0 . 4 9

() > I, .

35. ) :

= ' => = ^ => = ! ' 5 V

V2 V2 ,. = => R , = - => R = 4 0

R j R, RT 4 0 40 R = => R , Y = - => R , _ = 2 0

2 2 + 2 4 0 + 40 2

R 2 = R I + 2 => 12 4 0 + 20 => R J 2 2 = 6 0

I = => I = = I = 2 R122: 6 0

2 = I R 2 i => 2 = 2 2 0 => 2 = 4 0

4 0 = - => = => = . 1 40 1

V2T < VK ( < ), .

) , V22 = 60V = 1,5. V 2 50 : I = - => I = - => I = 1,5. R 2 4 0 2

: I , = 2 + => 3 = 3 .

: V = V2Z + V3 => 120 = 60 + V, => V3 = 60V.

V3 V, : I, = - => R 3 = => R 3 = 2 0 .

R 3 I3

• 36. I, - => % = I, (R. + r) (1) 1 R, + r V 1 W

I, = D =* = I , ( R , + r) (2) R, + r -

(1) (2) : % = 10V r = 1.

% 37. V , = I, R, => V, = R ' R ! ( 1 )

V , = 2 R , => V , = * - ( 2 ) -

(1) (2) : % = 30V r = 2.

% % 38. 1 = => 1 , => I = 2.

R, R, + R, + r

: V = V, = I R = 2 3 = 6V. C 2 2

: q = C Vc => q = 4 6V => q = 24(1

% % 39. ) I = => I - => I = 2A. ; R,v R, + R : + r

) v n = % - 1 r = V n = 10V.

) = % I => = 24W.

) = I2 r => Pr = 4W.

) = V I => p t = 20W. 7

) , = I2 R, => , = 8W.

, = I2 R, => 2 = 12W.

40. : % = 24V.

: V n = % - I r => 20 = 24 - 2 r => r = 2.

% % 41. I = - => I = => I = 2A.

R0). R, + R2 + r

: V r = 0

• V A - V r = I - R , => V A - 0 = 2 - 1 7 => V a = 34V

- = I R2 => - = 2 8 => VB = -16V.

42. R, = => R, = 4 1 4 1

R, = 3 R => R, = 12 4 RL R ; 4 1 2 R n = =\$ R ] 9 = => R1? = 3

12 R, + R, 12 4 + 1 2 12

R . = R , + r => R = 4 1 2

% I = => I = 1A

r* V = % - => V = 3V

I, = => I. = 0,75A R| 1

h = ^ => l2 = 0'25

43. ) , - . , :

% % 1 = => I = => r = 2. R* r + R + r'

) = I~(R + + ') => = 24W.

) , : = * * \ => = 4 8 W

: = () + => 48 = 24 + => = 24W.

) : = - - =>

r R

! = ^ I-, - I , - I2 R 2 2 2 = 32W , :

2 4 ( % ) = % => (%) = 100% => (%) = 75%.

3 2

• 44. ) , - . , : Vj = % - \ r => Ij = 4

% I, = r => ' = 2. 1 +

) = 2 2 ( + ' ) = > = 1 2 W .

) , : V, = % - 1 2 r => I, = 2

= ^ 2 = > = 2 4 W

: = + => 24 = 12 + => = 12W.

) :

(%) = 1 0 0 % => (%) = f - 1 0 0 % => (%) = 50%. ^4

45. I , I, I, , . Kirchhoff : , + 2 = 3 (!)

- Ii , - 1 , R, - 1 3 R 3 = 0 (2) VA | = I jR, + I, R, =>

V = 4 5V A r t,-> .

46. I,, , I, . Kirchhoff :

I, , 2 = , 3 = 2 VAB = 12V.

47. .

• , - . , - . - 7 1129 15/21 1946 ( 1946, 108, ).