Ðîçâ’ÿçàííÿ âïðàâ òà çàâäàíü äî ï³äðó÷íèêà «Ô³çèêà» Ô. ß. Áîæèíîâî¿ òà ³í.
Ðîçä³ë 1. Åëåêòðè÷íå ïîëå
§ 1. Çàðÿä ³ åëåêòðîìàãí³òíà âçàºìîä³ÿ
Âïðàâà ¹ 1 1. Ïåðøà êóëüêà â³äøòîâõóºòüñÿ â³ä ïîçèòèâíî çàðÿäæåíî¿ êóë³, – òîìó ¿¿
çàðÿä ïîçèòèâíèé. Äðóãà ïðèòÿãóºòüñÿ, – òîìó ¿¿ çàðÿä íåãàòèâíèé. 2. Åáîí³òîâà ïàëè÷êà, ïîòåðòà âîâíîþ, íàáóâຠíåãàòèâíîãî çàðÿäó. Òðåáà
ï³äíåñòè ïàëè÷êó äî êóëüêè: ÿêùî êóëüêà â³äøòîâõóºòüñÿ – ¿¿ çàðÿä íåãàòèâíèé, ïðèòÿãóºòüñÿ – ïîçèòèâíèé.
3. Ó íåéòðàëüíîìó àòîì³ Ne = Np = 12; 12 2 10.eN ′ = − =4. Àòîì ˳ò³þ ìຠ3 åëåêòðîíè. Ïîçèòèâíèé ³îí ˳ò³þ ìîæå ìàòè 0, 1, 2
åëåêòðîíè, òîáòî àòîì âòðà÷ຠ3, 2 ÷è 1 åëåêòðîí.
§ 2. Åëåêòðè÷íå ïîëå. Âçàºìîä³ÿ çàðÿäæåíèõ ò³ë
Âïðàâà ¹ 2 1. ×àñòèíêà ìîæå ìàòè çàðÿä, êðàòíèé |e|, òîáòî ±å = ±1,6 ⋅ 10—19 Êë. 8 ⋅ 10—19
Êë = 5 ⋅ |e| – ìîæëèâî, —2,4 ⋅ 10—19 Êë = 1,5å – íåìîæëèâî; 2,4 ⋅ 10—18 Êë = 15 ⋅ |e| – ìîæëèâî.
2. Äàíî: Ðîçâ’ÿçàííÿ: Q = 1 Êë |e| = 1,6 ⋅ 10—19 Êë N – ?
191810
6,25 10 .1,6
QN
e= = = ⋅
³äïîâ³äü: N = 6,25 ⋅ 1018 åëåìåíòàðíèõ çàðÿä³â. 3. Äàíî: Ðîçâ’ÿçàííÿ:
m = 0,3 ìã = 0,3 ⋅ 10—
6 êã g = 9,8 Í/êã F – ?
F = mg = 0,3 ⋅ 10—6 ⋅ 9,8 ≅ 3 ⋅ 10—6 (Í).
êã Í[ ] Í.
êãF
⋅= =
³äïîâ³äü: F = 3 ⋅ 10—6 Í.
§ 3. Ìåõàí³çì åëåêòðèçàö³¿. Åëåêòðîñêîï
Âïðàâà ¹ 3
1. Ìàñà çàðÿäæåíî¿ ïàëè÷êè çìåíøóºòüñÿ íà ìàñó åëåêòðîí³â, ÿê³ ïåðåéøëè
íà ïàï³ð ïðè òåðò³. 2. ßêùî åëåêòðîñêîï ìàâ çàðÿä Q ³ îòðèìàâ ïðè äîòèêó çàðÿä —Q, òî ï³ñëÿ
äîòèêó éîãî çàðÿä áóäå Q — Q = 0. 3. Ïîçèòèâíî çàðÿäæåí³ ñìóæêè åëåêòðîñêîïà ðîç³éøëèñÿ á³ëüøå, òîáòî ¿õ
ïîçèòèâíèé çàðÿä çá³ëüøèâñÿ. Öå ìîæå áóòè, ÿêùî åëåêòðîíè ïåðåéäóòü äî êîíäóêòîðà ï³ä âïëèâîì ïîëÿ ïîçèòèâíî çàðÿäæåíî¿ ïàëè÷êè.
4. Àíòèñòàòèê íà äåÿêèé ÷àñ íàäຠìàòåð³àëó îäÿãó âëàñòèâîñò³ ïðîâ³äíèêà, òîáòî çàðÿä ñò³êຠç îäÿãó.
1
5. Äàíî: Ðîçâ’ÿçàííÿ: q1 = 3 ⋅ 10—9 Êë q2 = —9 ⋅ 10—9 Êë
1 – ?q ′ 2 – ?q ′
1 2 ;q q′ ′= 1 2 1 2;q q q q′ ′+ = +9 9
91 21 2
3 10 9 103 10
2 2
q qq q
− −−+ ⋅ − ⋅′ ′= = = = − ⋅ (Êë).
³äïîâ³äü: Êë. 91 2 3 10q q −′ ′= = − ⋅
6. Ðîçïîâ³äü ïðî ïîæåæó ïðàâäîïîä³áíà: öèñòåðíà ìîæå åëåêòðèçóâàòèñÿ, â
ïàðàõ áåíçèíó ìîæå ïðîñêî÷èòè ³ñêðà. Ðîçïîâ³äü ïðî çàçåìëåííÿ íåïðàâäîïîä³áíà, öèñòåðíà, êîëåñà, ðåéêè – ïðîâ³äíèêè, ¿õ íå íåîáõ³äíî çàçåìëÿòè.
7. Ïðèïóñòèìî, ùî ïàëè÷êà çàðÿäæåíà
íåãàòèâíî. Ñïî÷àòêó åëåêòðîíè ã³ëüçè ïåðåì³ñòÿòüñÿ íà äàëüí³é â³ä ïàëè÷êè á³ê, ã³ëüçà ïðèòÿãíåòüñÿ äî ïàëè÷êè, òîðêíåòüñÿ ¿¿, ÷àñòèíà åëåêòðîí³â ç ïàëè÷êè ïåðåì³ñòèòüñÿ äî ã³ëüçè. Äâà íåãàòèâíî çàðÿäæåíèõ ò³ëà â³äøòîâõíóòüñÿ. ßêùî ïàëè÷êà ïîçèòèâíî çàðÿäæåíà, òî ã³ëüçà áóäå ïîâîäèòèñü òàê ñàìî, ò³ëüêè åëåêòðîíè áóäóòü ïåðå- ì³ùóâàòèñÿ â³ä ã³ëüçè äî ïàëè÷êè.
§ 4. Çàêîí Êóëîíà
1. Äàíî: Ðîçâ’ÿçàííÿ:
q1 = q2 1 ⋅ 10—4 Êë r = 1 ì k = 9 ⋅ 109 Íì2/Êë2 F – ?
9 4 41 22 9 10 10 10 90
q qF k
r− −= = ⋅ ⋅ ⋅ = (Í);
2
2 2
Í ì Êë Êë[ ] Í.
Êë ìF
⋅ ⋅ ⋅= =⋅
³äïîâ³äü: F = 90 Í. 2. Äàíî: Ðîçâ’ÿçàííÿ:
1 12q q′ =
2 22q q′ =
r′ = 4r
– ?FF′
1 22 ;
q qF k
r=
1 2 1 2 1 22 2 2
4.
16 4 4
q q q q q q FF k k k
r r r
′ ′= = = =′
′
³äïîâ³äü: ñèëà çìåíøèòüñÿ â 4 ðàçè.
3. Äàíî: Ðîçâ’ÿçàííÿ:
F′ = 9F
1 1q q ′=
2 2q q ′=
– ?rr′
1 22 ;
q qF k
r=
21 2 1 2
2 2 2; 9;q q q q F r
F k kr r F r
′ ′ ′= = = =′′ ′ ′
2
9;rr⎛ ⎞ =⎜ ⎟⎝ ⎠′
3;rr
=′
1
.3
rr′ =
2
³äïîâ³äü: â³äñòàíü çìåíøèëàñü ó 3 ðàçè. 4. Äàíî: Ðîçâ’ÿçàííÿ:
q1 = q2 N = 1011 r = 10 ñì = 0,1 ì F – ?
1 22 ;
q qF k
r= q1 = q2 = Nå;
2 9 19 11 25
2 2
( ) 9 10 (1,6 10 10 )23 10
0,1
k NeF
r
−−⋅ ⋅ ⋅ ⋅ ⋅= = ≅ ⋅
(Í) = 2,3 ⋅ 10—4 (Í). ³äïîâ³äü: F = 2,3 ⋅ 10—4 Í.
5. Äàíî: Ðîçâ’ÿçàííÿ:
|q1| = 5|q2|
1 2q q q′ ′= = ′
– ?FF′
– ?FF′′
1) Êóëüêè çàðÿäæåí³ îäíîéìåííî:
1 2 1 2 ;q q q q′ ′+ = + 5q2 + q2 = 2q′; q′ = 3q2;
1 2 2 2 22 2
5 5;
q q q q kqF k k
r r r⋅
= = =
21 2 2 2
2 2 2r
2
(3 ) 9;
q q q kqF k k
r r
′ ′= = =′
91,8;
5
FF′ = = F′ = 1,8F.
2) Êóëüêè çàðÿäæåí³ ð³çíîéìåííî:
1 2 1 2 ;q q q q′ ′+ = + 5q2 — q2 = 2q′; 4q2 = 2q′; q′ = 2q2; 2
1 2 22 2
5;
q q kqF k
r r= =
2 22 2
2 2
(2 ) 4;
k q kqF
r r= =′′
40,8;
5
FF′′ = = F″ = 0,8F;
11,25.
0,8
FF
= =′′
³äïîâ³äü: ïðè îäíîéìåííî çàðÿäæåíèõ êóëüêàõ ñèëà âçàºìî䳿 çá³ëüøèòüñÿ â 1,8 ðàç³â; ïðè ð³çíîéìåííî çàðÿäæåíèõ – çìåíøèòüñÿ â 1,25 ðàç³â.
Çàâäàííÿ äëÿ ñàìîïåðåâ³ðêè çà ðîçä³ëîì 1 «Åëåêòðè÷íå ïîëå»
11. Äàíî: Ðîçâ’ÿçàííÿ:
1
2
16FF
=
1
2
– ?rr
1 21 2
1
;q q
F kr
= 1 22 2
2
;q q
F kr
=
2
1 2
2 1
16;F rF r
⎛ ⎞= =⎜ ⎟⎝ ⎠
2
1
4;rr
= 1
2
1.
4
rr
=
³äïîâ³äü: â³äñòàíü çá³ëüøèëàñü âó4 ðàçè. 12. Äàíî: Ðîçâ’ÿçàííÿ:
1 13q q′ =
2 23q q′ =
– ?FF′
1 22
;q q
F kr
⋅=
1 21 2 1 2
2 2 2
3 39 9
q q q q q q;F k k k
r r r
′ ′⋅ ⋅ ⋅ ⋅= = = =′ F
9.FF′ =
³äïîâ³äü: ñèëà âçàºìî䳿 çá³ëüøèòüñÿ
3
ó 9 ðàç³â. 13. Äàíî: Ðîçâ’ÿçàííÿ:
q1 = 2 ⋅ 10—5 Êë r = 6 ñì = 0,6 ì F = 0,1 Í q2 – ?
1 22 ;
q qF k
r=
2
21
;Fr
qkq
= 2
2 2
2
Í ì[ ] Êë;
Í ìÊë
Êë
q⋅= =
⋅ ⋅
3
92 9 5
0,1 3,6 102 10
9 10 2 10q
−−
−
⋅ ⋅= =⋅ ⋅ ⋅
⋅ (Êë).
³äïîâ³äü: q2 = 2 ⋅ 10—9 Êë. 14. Äàíî: Ðîçâ’ÿçàííÿ:
q1 = —4 ìêÊë = —4 ⋅ 10—6 Êë r = 8 ñì = 8 ⋅ 10—2 ì F = 0,9 Í N – ?
2 ;q
Ne
= 1 22 ;
q qF k
r=
2
21
;Fr
qkq
=
2
2 2
2
Í ì[ ] Êë;
Í ìÊë
Êë
q⋅= =
⋅ ⋅
47
2 9 6
0,9 64 101,6 10
9 10 4 10q
−−
−
⋅ ⋅= = −⋅ ⋅ ⋅
⋅ Êë;
712
19
1,6 1010 .
1,6 10N
−
−
− ⋅= =− ⋅
³äïîâ³äü: 1012 åëåêòðîí³â. 15. Äàíî: Ðîçâ’ÿçàííÿ:
q1 = 1,8 ⋅ 10—8 Êë q2 = —0,3 ⋅ 10—8 Êë q3 = 0 r = 5 ñì = 5 ⋅ 10—2 ì
1 – ?q ′ q 2 – ?′
3 – ?q ′ F′ – ?
1 2 3 1 2 3 ;q q q q q q′ ′ ′+ + = + + 1 2 3 ;q q q q′ ′ ′= = = ′8 8
81 2 3 1,8 10 0,3 100,5 10
3 3
q q qq
− −−+ + ⋅ − ⋅= = =′ ⋅ (Êë);
2 9 165
2 46
9 10 0,25 109 10
25 10
qF k
r
−−
−
⋅ ⋅ ⋅′= = = ⋅′⋅
(Í) =
= 90 (ìêÍ). ³äïîâ³äü: q′ = 0,5 ⋅ 10—8 Êë; F′ = 90 ìêÍ.
Ðîçä³ë 2. Åëåêòðè÷íèé ñòðóì
§ 8. Åëåêòðè÷íå êîëî òà éîãî åëåìåíòè
Âïðàâà ¹ 8
1. 2.
4
3. 4. 5. 6.
§ 9. Ñèëà ñòðóìó. Îäèíèö³ ñèëè ñòðóìó. Àìïåðìåòð
Âïðàâà ¹ 9 1. à) 0,1 À; I = 0,2 À; á) 0,5 ìÀ; I = 4,5 ìÀ; â) 0,2 À; I = 1,8 À. 2. Àìïåðìåòð ìîæíà ïðèºäíàòè â áóäü-ÿêîìó ì³ñò³ ïîñë³äîâíîãî êîëà. 3. Äàíî: Ðîçâ’ÿçàííÿ:
I = 200 ìÀ = 0,2 À q = 24 Êë t – ?
;q
It
= ;q
tI
= Êë À ñ
[ ] ñ;À À
t⋅= = =
24
1200,2
t = = ñ = 2 (õâ.).
³äïîâ³äü: t = 2 õâ. 4. Äàíî: Ðîçâ’ÿçàííÿ:
I = 3 À t = 15 õâ = 900 ñ Q – ?
;Q
It
= Q = I ⋅ t; [Q] = À ⋅ ñ = Êë; Q =
= 3 ⋅ 900 = 2700 (Êë).
5
³äïîâ³äü: Q = 2700 Êë. 5. Äàíî: Ðîçâ’ÿçàííÿ:
I = 0,2 À t = 10 õâ = 600 ñ Q – ?
;Q
It
= Q = I ⋅ t; [Q] = À ⋅ ñ = Êë;
Q = 0,2 ⋅ 600 = 120 Êë. ³äïîâ³äü: Q = 120 Êë.
6. Äàíî: Ðîçâ’ÿçàííÿ:
t = 10 ñ N = 2 ⋅ 1020 I – ?
;Q
It
= Q = N|e|; ;Ne
It
= Êë
[ ] À;ñ
I = =
20 192 10 1,6 103,2 (À).
10I
−⋅ ⋅ ⋅= =
³äïîâ³äü: I = 3,2 À.
§ 10. Åëåêòðè÷íà íàïðóãà, îäèíèöÿ íàïðóãè, âîëüòìåòð
Âïðàâà ¹ 10
1. à) 10 0
110VC−= = (Â); U = 4 Â; 2.
á) 5 0
0,510VC−= = (Â); U = 6 Â;
â) 5 0
15VC−= = (Â); U = 8 Â.
3. Äàíî: Ðîçâ’ÿçàííÿ:
q = 3 Êë A = 0,12 êÄæ U – ?
A = U ⋅ q; 120
40;3
AU
q= = =
Äæ[ ] Â.
ÊëU = =
³äïîâ³äü: U = 40 Â. 4. Äàíî: Ðîçâ’ÿçàííÿ:
q = 4 Êë U = 5 Â A – ?
A = U ⋅ q; [A] =  ⋅ Êë = Äæ; F = 12 ⋅ 4 = 48 Äæ. ³äïîâ³äü: À = 48 Äæ.
5. Äàíî: Ðîçâ’ÿçàííÿ:
q = 60 Êë m = 200 ã = 0,2 êã h = 360 ì U – ?
A1 = q ⋅ U; A2 = mgh; A1 = A2; q ⋅ U = mgh;
;mgh
Uq
=
Íêã ì Í ì Äæêã[ ] Â;
Êë Êë ÊëU
⋅ ⋅ ⋅= = = =
0,2 10 36012 Â.
60U
⋅ ⋅= =
6
³äïîâ³äü: U = 12 Â. § 11. Åëåêòðè÷íèé îï³ð. Çàêîí Îìà
Âïðàâà ¹ 11
1. ;U
IR
= ;U
RI
= I R = 3 Îì; II R = 3,3 Îì; III R = 5 Îì; IV R = 10 Îì.
2. Äàíî: Ðîçâ’ÿçàííÿ: I = 1,5 À R = 150 Îì U – ?
U = I ⋅ R = 1,5 ⋅ 150 = 225 (Â). ³äïîâ³äü: U = 225 Â.
3. Äàíî: Ðîçâ’ÿçàííÿ:
U = 12 Â I = 0,6 À U1 = 6 Â U2 = 20 Â U3 = 1 Â I1 – ? I2 – ? I3 – ?
;U
IR
= 12
200,6
UR
I= = = (Îì);
11
60,3
20
UI
R= = = (À); 2
2
201
20
UI
R= = = (À);
33
10,05
20
UI
R= = = (À).
³äïîâ³äü: 0,3 À; 1 À; 0,05 À. 4. Äàíî: Ðîçâ’ÿçàííÿ:
U = 120  I = 15 ìÀ = 15 ⋅ 10—3 À R – ?
;U
IR
= 3
1208000
15 10
UR
I −= = =⋅
(Îì) = 8 (êÎì).
³äïîâ³äü: R = 8 êÎì.
5. R = 2 Îì; 0,5 ;2
U UI U
R= = =
U (Â) 0 2 4… I (À) 0 1 2…
6. Äàíî: Ðîçâ’ÿçàííÿ:
U = 12 Â t = 5 õâ = 300 ñ q = 60 Êë R – ?
;U
IR
= ;U
RI
= ;q
It
= ;Ut
Rq
=
 Êë[ ] Îì;
ñR
⋅= = 12 300
6060
R⋅= = (Îì).
³äïîâ³äü: R = 60 Îì. 7. Äàíî: Ðîçâ’ÿçàííÿ:
I = 1,2 À U = 18 Â R – ?
;U
IR
= 18
151,2
UR
I= = = (Îì).
³äïîâ³äü: R = 15 Îì.
7
8. Äàíî: Ðîçâ’ÿçàííÿ:
U = 6 Â R = 1,5 Îì N = 16 CA – ?
;A
IC
N=
64
1,5
UI
R= = = (À);
40,25
16AC = = (À).
³äïîâ³äü: CA = 0,25 À.
9. .l
RS
= ρ Îï³ð ïðîâ³äíèêà çàëåæèòü â³ä éîãî ðîçì³ðó ³ ìàòåð³àëó.
§ 12. Ïèòîìèé îï³ð ðå÷îâèíè
Âïðàâà ¹ 12
1. Äàíî: Ðîçâ’ÿçàííÿ:
Rç = Rì = Rñ Sç = Sì = Sñ ρñ > ρç > ρì
lç, lì, lñ – ?
;l
RS
= ρ S = const; ρñ ⋅ lñ = ρç ⋅ lç = ρì ⋅ lì;
ρñ > ρç > ρì; lñ > lç > lì. ³äïîâ³äü: 3 – ñâèíåöü, 2 – çàë³çî, 1 – ì³äü.
3. Äàíî: Ðîçâ’ÿçàííÿ:
l = 1 êì = 103 ì S = 0,68 ñì2 = 68 ìì2 ρ = 0,017 (Îì⋅ìì2)/ì R – ?
;l
RS
= ρ 2
2
Îì ìì ì[ ] Îì;
ì ììR
⋅= ⋅ =
30,017 100,25
68R
⋅= = (Îì).
³äïîâ³äü: R = 0,25 Îì. 4. Äàíî: Ðîçâ’ÿçàííÿ:
R = 25 Îì l1 = 0,5l S1 = 2S R1 – ?
;l
RSρ= 1
11
0,50,25 0,25 ;
2
l l lR R
S S Sρ ρ ρ= = = = R1 = 0,25 R.
³äïîâ³äü: îï³ð çìåíøèâñÿ ó 4 ðàçè.
5. I = 1,4 À; U = 4,2 Â; 4,2
31,4
UR
I= = = (Îì).
Ïðè ïåðåñóâàíí³ ïîâçóíêà ðåîñòàòà âïðàâî éîãî îï³ð çìåíøèòüñÿ, íàïðóãà íå çì³íèòüñÿ, ñòðóì çá³ëüøèòüñÿ. 6. Äàíî: Ðîçâ’ÿçàííÿ:
S = 0,2 ìì2 ρ = 1,1 (Îì⋅ìì2)/ì I = 0,4 À U = 4,4 Â l – ?
;l
RSρ= ;
RSl =
ρ ;
UR
I= ;
USl
I=
ρ
2 2
2 2
 ìì Îì ìì ì[ ] = = ì;
Îì ìì Îì ììÀ
ì
l⋅ ⋅ ⋅=
⋅ ⋅⋅
4,4 0,22
0,4 1,1l
⋅= =⋅
(ì).
8
³äïîâ³äü: l = 2 ì. 7. Äàíî: Ðîçâ’ÿçàííÿ:
I = 15 À l = 10 ì U = 0,85 Â ρ = 0,017 (Îì⋅ìì2)/ì d – ?
2
;4
dS
π= 2 ;S
d =π
;l
RSρ= ;
l lIS
R Uρ ρ= =
2 ;lI
dUρ=π
2 2Îì ìì À ì Îì ìì[ ] ìì;
ì Â Îìd
⋅ ⋅ ⋅ ⋅= =⋅
=
0,017 10 152 2
0,85 3,14d
⋅ ⋅= ≅⋅
(ìì).
³äïîâ³äü: d = 2 ìì. 8. Äàíî: Ðîçâ’ÿçàííÿ:
l = 100 ì U = 1 Â I = 15 À ρ = 0,028 (Îì⋅ìì2)/ì η = 2700 êã/ì3 m – ?
m = η ⋅ V = η ⋅ l ⋅ S; ;l
RSρ= ;
l lIS
R Uρ ρ= =
2 22Îì ìì ì À Îì ìì
[ ] ìì ;ì Â Îì
S⋅ ⋅ ⋅ ⋅= =
⋅=
0,028 100 1542
1S
⋅ ⋅= = ìì2 = 42 ⋅ 10—6 ì2.
23
êã[ ] ì ì êã;
ìm = ⋅ ⋅ =
m = 2700 ⋅ 100 ⋅ 42 ⋅ 10—6 = 11,34 (êã). ³äïîâ³äü: m = 11,34 êã.
Âïðàâà ¹ 13
1. Äàíî: Ðîçâ’ÿçàííÿ:
R = 65 Îì R1 = R2 = 15 Îì R3 – ?
R = R1 + R2 + R3; R3 = R — R1 — R2 = 65 — 15 — 15 = = 35 (Îì). ³äïîâ³äü: îï³ð ðåîñòàòà 35 Îì.
2. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 15 Îì R2 = 10 Îì U = 100 Â U1 – ?
U1 = I⋅ R1; 1 2
;U
IR R
=+
11
1 2
;UR
UR R
=+
1
 Îì[ ] Â;
Îì + ÎìU
⋅= = 1
100 1560
25U
⋅= = (Â).
³äïîâ³äü: íàïðóãà ì³æ êëåìàìè k1 ³ k2 60 Â. 3. Äàíî: Ðîçâ’ÿçàííÿ:
I1 = 0,3 À U = 220 Â R = 1100 Îì I – ?
2200,2
1100
UI
R= = = (À) – òàêèé ñòðóì ïîòå÷å êð³çü
ïîñë³äîâíî ç’ºäíàí³ ëàìïè. I < I1, òîìó ëàìïó äëÿ ë³õòàðèêà òàê ìîæíà âìèêàòè. ³äïîâ³äü: ìîæíà.
9
4. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 650 Îì I = 80 ìÀ = 0,08 À U = 72  R2 – ?
R = R1 + R2; R2 = R — R1; ;U
IR
= ;U
RI
=
2 1;U
R RI
= − 2
72650 250
0,08R = − = (Îì).
³äïîâ³äü: 250 Îì. 5. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 5 Îì R2 = 8 Îì R3 = 15 Îì U2 = 1,6 Â I – ? U – ?
22
2
1,60,2
8
UI I
R= = = = (À); U = I ⋅ R; R = R1 + R2 + R3;
U = I ⋅ (R1 + R2 + R3) = 0,2 ⋅ (5 + 8 + 15) = 5,6 (Â). ³äïîâ³äü: I = 0,2 À; U = 5,6 Â.
§ Âïðàâà ¹ 14
1. 2. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 100 Îì R2 = 150 Îì I = 2,4 À U – ?
U = I ⋅ R; 1 2
1 1 1 1 10,0167;
100 150R R R= + = + =
1
600,0167
R = ≅ (Îì); U = 2,4 ⋅ 60 ≅ 144 (Â).
³äïîâ³äü: U = 144 Â. 3. Äàíî: Ðîçâ’ÿçàííÿ:
U = 120 Â R1 = 200 Îì R2 = 300 Îì I – ? I1 – ? I2 – ?
;U
IR
=
1 2
1 1 1 1 10,005 0,0033 0,0083;
200 300R R R= + = + = + =
1120
0,0083R = ≅ (Îì);
1201
120I = = (À);
U1 = U2 = U; 11
1 1
1200,6
200
U UI
R R= = = = (À);
22
2 2
1200,4
300
U UI
R R= = = = (À).
³äïîâ³äü: I = 1 À; I1 = 0,6 À; I2 = 0,4 À.
10
4. Äàíî: Ðîçâ’ÿçàííÿ:
ρç > ρì > ρñ
Iç – ? Iì – ? Iñ – ? ;
UI
R= U1 = U2 = U3 = U; з
з
;U
IR
= ìì
;U
IR
=
ññ
;U
IR
= ;l
RSρ= Rç > Rì > Rñ; Iç > Iì > Iñ.
³äïîâ³äü: ó ñð³áíîìó äðîò³ ñèëà ñòðóìó á³ëüøà.
5. Äàíî: Ðîçâ’ÿçàííÿ: R1 = 2 Îì R2 = 3 Îì R3 = R4 = 4 Îì R5 = 0,8 Îì U = 4 Â
R – ? I – ? åêâ³âàëåíòà åëåêòðè÷íà ñõåìà
6 1 2
1 1 1 1 10,83;
2 3R R R= + = + = R6 = 1,2 (Îì);
7 3 4
1 1 1 1 1 1;
4 4 2R R R= + = + = R7 = 2 (Îì);
T = R5 + R6 + R7 = 0,8 + 1,2 + 2 = 4 (Îì);
41
4
UI
R= = = (À).
³äïîâ³äü: R = 4 Îì; I = 1 À. 6. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 3 Îì R2 = 2 Îì R3 = 8 Îì I3 = 0,1 À U – ?
U3 = I3 ⋅ R3 = 0,1 ⋅ 8 = 0,8 (Â); U3 = U2 = 0,8 Â;
22
2
0,80,4
2
UI
R= = = (À); I1 = I2 + I3 = 0,4 + 0,1 = 0,5 (À);
U = I ⋅ R = 0,5 ⋅ 3 = 1,5 (Â); U = U1 1 1
= 2,3 (Â). 1 + U2 = 1,5 + 0,8 =
³äïîâ³äü: U = 2,3 Â.
Âïðàâà ¹ 15 1. Äàíî: Ðîçâ’ÿçàííÿ:
Àê = 2174 êÂò⋅ãîä Àï = 1298 êÂò⋅ãîä  = 24,36 êîï/(êÂò⋅ãîä) À – ? à – ?
À = Àê — Àï = 2174 — 1298 = 876 (êÂò⋅ãîä); à = À ⋅  = 876 ⋅ 24,36 = 21 339 (êîï.) = = 213 ãðí. 30 êîï. ³äïîâ³äü: À = 876 êÂò⋅ãîä; à = 213 ãðí. 39 êîï.
11
2. A = U ⋅ I ⋅ t; [A] = Äæ; [U ⋅ I ⋅ t] = Â ⋅ À ⋅ ñ. 3. Äàíî: Ðîçâ’ÿçàííÿ:
I = 0,8 À U = 3,4 Â t = 15 õâ = 900 ñ A – ?
A = U ⋅ I ⋅ t = 3,4 ⋅ 0,8 ⋅ 900 = 2448 (Äæ) = = 2,448 (êÄæ). ³äïîâ³äü: A = 2,448 êÄæ.
4. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 10 Îì R2 = 25 Îì U = 100 Â t = 5 õâ = 300 ñ A1 – ? A2 – ? A3 – ? A4 – ?
à) Ïàðàëåëüíå ç’ºäíàííÿ ïðîâ³äíèê³â: 2
;U
A UIt tR
= =
2 2
11
100300 300 000
10
UA t
R= = ⋅ = (Äæ) = 300 (êÄæ);
2 2
22
100300 120 000
25
UA t
R= = ⋅ = (Äæ) = 120 (êÄæ).
á) Ïîñë³äîâíå ç’ºäíàííÿ ïðîâ³äíèê³â:
R = R1 + R2 = 10 + 25 = 35 Îì; 100
2,8635
UI
R= = = (À); A = UIt = I2 Rt;
A3 = I2 R1t = 2,862 ⋅ 10 ⋅ 300 ≅ 24 490 (Äæ) ≅ 24,5 (êÄæ); A4 = I2R2t = 2,862 ⋅ 25 ⋅ 300 = 61,2 (êÄæ). ³äïîâ³äü: à) 300 êÄæ; 120 êÄæ; á) 24,5 êÄæ; 61,2 êÄæ.
5. Äàíî: Ðîçâ’ÿçàííÿ:
P1 = 90 Âò P2 = 40 Âò U = 220 Â I1 – ? I2 – ? R1 – ? R2 – ?
2
;U
P UIR
= = 2
11
;U
PR
= 2 2
11
220538
90
UP
R= = = (Îì);
2 2
22
2201210
40
UP
R= = = (Îì); 1
1
2200,41
538
UI
R= = = (À);
22
2200,18
1210
UI
R= = = (À).
³äïîâ³äü: I1 = 0,41 À; I2 = 0,18 À; R1 = 538 Îì; R2 = 1210 Îì.
6. Äàíî: Ðîçâ’ÿçàííÿ:
m = 1 ò = 103 êã h = 19 ì t = 50 ñ η = 80 % U = 380 Â I – ?
êîð.
ïîâí.
;A
Aη = Aêîð. = mgh; Aïîâíà = UIt; ;
mghUIt
η =
310 10 1912,5
380 50 0,8
mghI
Ut⋅ ⋅= = =
η ⋅ ⋅ (À);
êã ì Í Í ì Äæ êã[ ] = = = À.
Äæêã  ñ Äæ ññÊë
I⋅ ⋅ ⋅= ⋅⋅ ⋅ ⋅
³äïîâ³äü: I = 12,5 À.
12
*7. Äàíî: Ðîçâ’ÿçàííÿ:
U = 127 Â P = 50 Âò U1 = 220 Â R – ?
P = UI; 50
0,39127
PI
U= = = (À);
U1 — U = IR;
1 220 127238
0,39
U UR
I− −= = =
(Îì). ³äïîâ³äü: R = 238 Îì.
8*. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = R2 = R Pïîñë. – ? Pïàð. – ?
2
;U
P UIR
= = 2
ïîñë.ïîñë.
;U
PR
= Rïîñë. = R1 + R2 = 2R;
2
ïîñë. ;2
UR
R=
2
ïàð.ïàð.
;U
PR
= ïàð. 1 2
1 1 1 2;
R R R R= + =
2
ïàð.
2;
UP
R= ïàð.
ïîñë.
4.R
P=
³äïîâ³äü: ïàð
ïîñ
4.R
P=
Âïðàâà ¹ 16
1. Q = I2Rt; Râîëîñêà Rïðîâîä³â; Qâîëîñêà Qïðîâîä³â. 2. Äàíî: Ðîçâ’ÿçàííÿ:
R = 30 Îì I = 4 À t = 10 õâ = 600 ñ Q – ?
Q = I2Rt = 42 ⋅ 30 ⋅ 600 = 288 000 (Äæ) = 288 (êÄæ). ³äïîâ³äü: Q = 288 êÄæ.
3. Äàíî: Ðîçâ’ÿçàííÿ:
R1 = 10 Îì R2 = 20 Îì U = 100 Â t = 5 ñ Q1 – ? Q2 – ?
2
;U
Q tR
= 2 2
11
1005 5000
10
UQ t
R= = ⋅ = (Äæ) =
= 5 (êÄæ); 2 2
22
1005 2500
20
UQ t
R= = ⋅ = (Äæ) =
= 2,5 (êÄæ). ³äïîâ³äü: Q1 = 5 êÄæ; Q2 = 2,5 êÄæ.
4. Äàíî: Ðîçâ’ÿçàííÿ:
t1° = 20 °Ñ t2° = 100 °Ñ V = 1,5 ë P = 600 Âò η = 80 % t – ?
Qêîð = ηQïîâíà; Qïîâíà = Pt; Qêîð = cm(t2° — t1°); cm(t2° — t1°) = ηPt;
2 1( ) 4200 1,5 (100 20)1050
0,8 600
cm t tt
P° − ° ⋅ ⋅ −= = =η ⋅
(ñ).
³äïîâ³äü: t = 1050 ñ.
13
5. Äàíî: Ðîçâ’ÿçàííÿ:
t = 5 õâ = 6000 ñ m = 0,2 êã t1° = 14 °Ñ t2° = 100 °Ñ I = 2 À U – ?
Q = UIt; Q = cm(t2° — t1°);
2 1( ) 4200 0,2 (100 14)120
2 300
cm t tQU
It It° − ° ⋅ ⋅ −= = = =
⋅ (Â).
³äïîâ³äü: U = 120 Â.
*6. Äàíî: Ðîçâ’ÿçàííÿ:
U = 120 Â Q = 1 ÌÄæ = 106 Äæ t = 1 ãîä = 3600 ñ d = 0,5 ìì ρ = 1,1 (Îì⋅ìì2)/ì l – ?
2
;U t
QR
= 2
;U t
RQ
= 2
4;
l lR
S dρ ρ= =
π
2 2 2 2
6
3,14 0,25 120 36009,2
4 4 4 1,1 10
d R d U tl
Qπ π ⋅ ⋅ ⋅= = = =
ρ ρ ⋅ ⋅ (ì).
³äïîâ³äü: l = 9,2 ì.
Âïðàâà ¹ 17 4. Äàíî: Ðîçâ’ÿçàííÿ:
Imax = 6 À U = 220 Â Pmax – ?
Pmax = UImax = 220 ⋅ 6 = 1320 (Âò) = 1,32 (êÂò). ³äïîâ³äü: Pmax = 1,32 êÂò.
Âïðàâà ¹ 18
1. Êîòóøêà ç äðîòîì îáåðòàºòüñÿ çà ãîäèííèêîâîþ ñòð³ëêîþ, ï³ñëÿ ¿¿
çóïèíêè åëåêòðîíè â äðîò³ òàêîæ çà ³íåðö³ºþ áóäóòü ðóõàòèñÿ çà ãîäèííèêîâîþ ñòð³ëêîþ. Íàïðÿì ñòðóìó – ïðîòèëåæíèé (öå íàïðÿì ðóõó ïîçèòðîí³â).
2. ³äîìî, ùî ïèòîìèé îï³ð (à ç íèì ³ îï³ð) ïðîâ³äíèê³â çá³ëüøóºòüñÿ ç
íàãð³âàííÿì. 2
;U
Q tR
= .l
RSρ= ßêùî â ã³ïîòåòè÷í³é ïëèòö³ Q2 = Q ïðè
R2 = R ³ ρ2 = ρ, òðåáà çá³ëüøèòè äîâæèíó ñï³ðàë³ l2 > l. *3. Ó ìîìåíò âìèêàííÿ âîëîñîê íå ðîç³ãð³òèé, éîãî îï³ð ì³í³ìàëüíèé, ñèëà
ñòðóìó – ìàêñèìàëüíà.
Âïðàâà ¹ 19
1. m = kIt = kq; ;m
kq
= êã
[ ] .Êë
k =
2. Ó âîäîïðîâ³äí³é, ð³÷êîâ³é òà ìîðñüê³é âîä³ º ð³çíîìàí³òí³ äîì³øêè, ÿê³ ðîçïàäàþòüñÿ íà éîíè, ðîç÷èí ïðîâîäèòü ñòðóì.
3. Ìîëåêóëè ñîë³ ðîçïàäàþòüñÿ ó âîä³ íà ³îíè, à ìîëåêóëè öóêðó íå ðîçïàäàþòüñÿ.
4. Äàíî: Ðîçâ’ÿçàííÿ:
m = 25 ã I = 0,5 À k = 1,2 ìã/Êë t – ?
m = kIt; 3
325 1044,6 10 (ñ)
1,12 0,5
mt
kI⋅= = = ⋅⋅
=
= 44 600 ñ = 744 õâ = 12,4 (ãîä). ³äïîâ³äü: t = 12,4 ãîä.
14
5. Äàíî: Ðîçâ’ÿçàííÿ:
t = 2 ãîä = 7200 ñ U = 2 Â R = 0,4 Îì k = 1,2 ìã/Êë m – ?
1,12 2 720040 320
0,4
kUtm kIt
R⋅ ⋅= = = = (ìã) =
= 40,32 (ã). ³äïîâ³äü: m = 40,32 ã.
6. Äàíî: Ðîçâ’ÿçàííÿ:
t = 50 õâ = 3000 ñ m = 3 ã = 3000 ìã R = 0,4 Îì k = 1,12 ìã/Êë P – ?
m = kIt; 3000
0,91,12 3000
mI
kt= = =
⋅ (À);
P = UI = I2R = 0,92 ⋅ 0,4 ≅ 0,32 (Âò). ³äïîâ³äü: P = 0,32 Âò.
Âïðàâà ¹ 20
1. Äàíî: Ðîçâ’ÿçàííÿ:
I = 1,4 À U = 11 Â k = 1,12 ìã/Êë = 1,12 ⋅ 10—6 êã/Êë ρ = 10,5 ã/ñì3 = 10,5 ⋅ 103 êã/ì3 S = 0,03 ì2 d = 8 ìêì = 8 ⋅ 10—6 ì t – ? A – ?
m = kIt; ;m
tkI
= m = ρV = ρSd;
3 6
6
10,5 10 0,03 8 10
1,12 10 1,4
Sdt
kI
−
−
ρ ⋅ ⋅ ⋅ ⋅= =⋅ ⋅
=
(ñ) = 26,8 õâ; 31,6 10= ⋅A = UIt = 11 ⋅ 1,4 ⋅ 1,6 ⋅ 103 = = 24,6 ⋅ 103 (Äæ) = 24,6 (êÄæ). ³äïîâ³äü: t = 26,8 õâ; A = 24,6 êÄæ.
2. Äàíî: Ðîçâ’ÿçàííÿ:
I = 0,48 À t = 15 õâ = 900 ñ S = 0,01 ì2 ρ = 7,1 ã/ñì3 = 7,1 ⋅ 103 êã/ì3 k = 0,34 ìã/Êë = 0,34 ⋅ 10—6 êã/Êë d – ?
m = kIt; m = ρSd; 6
3
0,34 10 0,48 900
7,1 10 0,01
m kItd
S S
−⋅ ⋅ ⋅= = =ρ ρ ⋅ ⋅
=
(ì) = 2 (ìêì). 62 10−= ⋅³äïîâ³äü: d = 2 ìêì.
3. Äàíî: Ðîçâ’ÿçàííÿ: I = 1,8 À S = 50 ñì2 = 5 ⋅ 10—3 ì2 N = 12 d = 58 ìêì = 58 ⋅ 10—6 ì ρ = 10,5 ã/ñì3 = 10,5 ⋅ 103 êã/ì3 k = 1,12 ìã/Êë = 1,12 ⋅ 10—6 êã/Êë t – ?
m = kIt; ;m
tkI
= m = NρSd;
;N Sd
tkIρ=
3 3 6
6
12 10,5 10 5 10 58 10
1,12 10 1,8t
− −
−
⋅ ⋅ ⋅ ⋅ ⋅ ⋅= =⋅ ⋅
= 18 000 (ñ) = 5 (ãîä). ³äïîâ³äü: t = 5 ãîä.
15
Âïðàâà ¹ 21
1. 2. ϳä 䳺þ ìàãí³òíîãî ïîëÿ ìàãí³òà íà áëèæ÷îìó äî íüîãî áîö³ êóëüêè
ñòâîðèòüñÿ ï³âí³÷íèé ìàãí³òíèé ïîëþñ, êóëüêà ïðèòÿãíåòüñÿ äî ìàãí³òà. 3. Ó ìàãí³òíîìó ïîë³ êîæåí îøóðîê ñàì ñòຠìàãí³òîì. Äî ïîëþñó ìàãí³òà
ïðèòÿãóþòüñÿ ð³çíîéìåíí³ ç íèì ïîëþñè îøóðê³â, à îäíîéìåíí³ â³äøòîâõóþòüñÿ ì³æ ñîáîþ.
4. Êîæåí çàë³çíèé ïðåäìåò ó ìàãí³òíîìó ïîë³ ïîñò³éíîãî ìàãí³òà ñàì ñòຠìàãí³òîì ³, ó ñâîþ ÷åðãó, ïðèòÿãóº ³íøèé çàë³çíèé ïðåäìåò – ñòâîðþºòüñÿ ëàíöþæîê.
5. Ïðèïóñòèìî, ùî ïëàñòèíà 1 çàðÿäæåíà, 2 – í³. ϳäíåñåìî ïë. 1 áóäü-ÿêèì ê³íöåì äî ñåðåäèíè ïë. 2 – â³äáóäåòüñÿ ïðèòÿãàííÿ. Òåïåð ïðèïóñòèìî, ùî ïëàñòèíà 1 íåçàðÿäæåíà, 2 – çàðÿäæåíà. ϳäíåñåìî çíîâ ïë. 1 áóäü-ÿêèì ê³íöåì äî ñåðåäèíà ïë. 2 – ïðèòÿãàííÿ íå â³äáóäåòüñÿ.
Âïðàâà ¹ 22 1. Íà ϳâí³÷íîìó ïîëþñ³ Çåìë³. 2. Òîìó ùî âîíè çíàõîäÿòüñÿ â ìàãí³òíîìó ïîë³ Çåìë³. 3. Öåé ìàòåð³àë ïîâèíåí íå íàìàãí³÷óâàòèñÿ â ìàãí³òíîìó ïîë³ Çåìë³.
Âïðàâà ¹ 23 1. 2. 3. 4.
16
5. 6.
à) â³äøòîâõíåòüñÿ á) ïðèòÿãíåòüñÿ
Âïðàâà ¹ 24
1. Íàïðÿìîê ñòðóìó – â³ä «+» äî «—». Ïîëþñè
ìàãí³òó âèçíà÷àºìî çà äîïîìîãîþ ïðàâèëà ïðàâî¿ ðóêè.
2. Äî B ³ C – êîòóøêà ñòàíå åëåêòðîìàãí³òîì. 3. ˳âà ÷àñòèíà ñõåìè àâòîìàòà –
åëåêòðîìàãí³ò, ìàãí³òíå ïîëå ÿêîãî çàëåæèòü â³ä ñèëè ñòðóìó â êîë³ ìàãí³òà. Ñèëà ñòðóìó çàëåæèòü â³ä îïîðó ïðîâ³äíèê³â, ÿêèé, ó ñâîþ ÷åðãó çàëåæèòü â³ä òåìïåðàòóðè. Ïðè ïåâí³é òåìïåðàòóð³ ÿê³ð ó ïðàâ³é ÷àñòèí³ ñõåìè àâòîìàòà çàìêíå åëåêòðè÷íå êîëî äçâ³íêà, äçâ³íîê çàäçâåíèòü. Ïðèñòð³é ìîæíà âèêîðèñòîâóâàòè ó ïðèì³ùåííÿõ, äå ïîòð³áíî ï³äòðèìóâàòè ïîñò³éíó òåìïåðàòóðó, íàïðèêëàä, â îâî÷åñõîâèùàõ.
4. Ïðè ïåðåñóâàíí³ ïîâçóíêà ðåîñòàòà ïðàâîðó÷ îï³ð ðåîñòàòà ³ âñüîãî êîëà åëåêòðîìàãí³òà çìåíøèòüñÿ, ñòðóì çá³ëüøèòüñÿ, ï³ä³éìàëüíà ñèëà åëåêòðîìàãí³òà òàêîæ çá³ëüøèòüñÿ.
Âïðàâà ¹ 25 1. Íàïðÿìîê ñòðóìó â ïðîâ³äíèêó – â³ä «+» äî «—»,
íàïðÿìîê â³äõèëåííÿ çá³ãàºòüñÿ ç íàïðÿìêîì ñèëè Àìïåðà, íàïðÿìîê ìàãí³òíîãî ïîëÿ (³ ïîëþñè ìàãí³òà) âèçíà÷àºìî çà äîïîìîãîþ ïðàâèëà ë³âî¿ ðóêè.
2. Çà äîïîìîãîþ ïðàâèëà ë³âî¿ ðóêè âèçíà÷àºìî
íàïðÿìîê ìàãí³òíîãî ïîëÿ ³ ïîëþñè ìàãí³òà.
17
3. Çà äîïîìîãîþ ïðàâèëà ë³âî¿ ðóêè âèçíà÷àºìî íàïðÿìîê
ñèëè Àìïåðà ³ ðóõó àëþì³í³ºâîãî ñòðèæíÿ. 4. Êîðèñòóºìîñÿ ïðàâèëîì ë³âî¿ ðóêè äëÿ
ë³âî¿ òà ïðàâî¿ ÷àñòèí ðàìêè. Çà â³äîìèìè íàïðÿìàìè ìàãí³òíîãî ïîëÿ òà FA âèçíà÷àºìî íàïðÿì ñòðóìó.
5. Ïðîâ³äíèê 1 çíàõîäèòüñÿ â ìàãí³òíîìó ïîë³
ïðîâ³äíèêà 2. Âèçíà÷àºìî íàïðÿìîê ìàãí³òíîãî ïîëÿ ïðîâ³äíèêà 2 çà ïðàâèëîì ñâåðäëèêà. Çà ïðàâèëîì ë³âî¿ ðóêè âèçíà÷àºìî íàïðÿìîê ñèëè Àìïåðà, ÿêà 䳺 â öüîìó ïîë³ íà ïðîâ³äíèê 1.
7. ϳñëÿ çàìèêàííÿ êëþ÷à ïî âñüîìó êîëó ïîòå÷å ñòðóì. Ó âèòêàõ êîòóøêè
áóäå ñòðóì îäíîãî íàïðÿìêó, òîìó âèòêè ïðèòÿãíóòüñÿ, ïðóæèíà ñòèñíåòüñÿ, öâÿõ ï³äí³ìåòüñÿ, êîëî ðîç³ìêíåòüñÿ, ïðóæèíà ðîçòÿãíåòüñÿ ³ öâÿõ çàíóðèòüñÿ â ðîç÷èí ñîë³. Òàêèì ÷èíîì, ï³ñëÿ çàìèêàííÿ êëþ÷à öâÿõ áóäå êîëèâàòèñÿ.
Âïðàâà ¹ 26
1. Ó ìàãí³òîåëåêòðè÷íèõ âèì³ðþâàëüíèõ ïðèëàäàõ ðàìêà, à ðàçîì ç íåþ ³
ñòð³ëêà ìîæóòü îáåðòàòèñÿ ÿê çà ÷àñîâîþ ñòð³ëêîþ, òàê ³ ïðîòè íå¿. Çà â³äñóòíîñò³ ñòðóìó ñòð³ëêà âñòàíîâëþºòüñÿ íà «0». Ïðè ïðàâèëüíîìó ï³äêëþ÷åíí³ ñòð³ëêà â³äõèëÿºòüñÿ ïðàâîðó÷ äî ïîòð³áíî¿ ïîä³ëêè, ïðè íåïðàâèëüíîìó – ë³âîðó÷, äå øêàëè íåìຠ³ ñòð³ëêà ìîæå ïîãíóòèñÿ.  åëåêòðîìàãí³òíèõ âèì³ðþâàëüíèõ ïðèëàäàõ ïðè áóäü-ÿêîìó íàïðÿì³ ñòðóìó îñåðäÿ çàâæäè âòÿãóºòüñÿ â êîòóøêó ³ ïîâåðòຠñòð³ëêó ïðàâîðó÷.
18
2. Àìïåðìåòð âìèêàþòü ó êîëî ïîñë³äîâíî, éîãî îï³ð ìàëèé ³ íå âïëèâຠíà
ñèëó ñòðóìó, ùî âèì³ðþºòüñÿ: ;U
IR
= 1 ;A
UI
R R=
+ ;AR R I1 ≈ I.
3. Âîëüòìåòð ìຠâåëèêèé îï³ð, ùîá ïðè ïàðàëåëüíîìó ç’ºäíàíí³ ñèëà ñòðóìó â êîë³ íå çìåíøèëàñü. Ïðè ïîñë³äîâíîìó ç’ºäíàíí³ âîëüòìåòðà:
;U
IR
= 1 ;V
UI
R R=
+ ;VR R 1 ;
V
UI
R≈ 1 .I I
4. Ðàìêà ç³ ñòðóìîì ïîâåðòàºòüñÿ â ìàãí³òíîìó ïîë³ ïîñò³éíîãî ìàãí³òó. Ðàìêà ³ ñòð³ëêà æîðñòêî ïðèêð³ïëåí³ äî îñ³. Ïîâîðîò ðàìêè çàëåæèòü â³ä ñèëè ³ íàïðÿìó ñòðóìó.
Âïðàâà ¹ 27
1. ²íäóêö³éíèé ñòðóì ó êîòóøö³ íå âèíèêàº, òîìó ùî ìàãí³òíå ïîëå, ùî ¿¿
ïðîíèçóº, íå çì³íþºòüñÿ. 2. ßêùî ó âíóòð³øí³é êîòóøö³ ñòðóì áóäå çì³íþâàòèñÿ. *3. Ïðè ïåðåì³ùåíí³ ìàãí³òà â³äíîñíî ñóö³ëüíîãî ê³ëüöÿ, â ê³ëüö³ âèíèêàº
³íäóêö³éíèé ñòðóì. ßêùî ìàãí³ò íàáëèæàºòüñÿ, âèíèêຠòàêèé ñòðóì, ÿêèé çìåíøóº çì³íó ìàãí³òíîãî ïîëÿ êð³çü ê³ëüöå, òîáòî â³äøòîâõóº ìàãí³ò. ßêùî ìàãí³ò â³äñóâàºòüñÿ, âèíèêຠñòðóì ïðîòèëåæíîãî íàïðÿìêó, ùîá ïðèòÿãíóòè ìàãí³ò. Ó ðîçð³çàíîìó ê³ëüö³ ñòðóì íå âèíèêàº, âîíî íå âçàºìî䳺 ç ìàãí³òîì.
Âïðàâà ¹ 28
1. Nå = Nð = 5. 2. Z = Np = 31 – ãàë³é.
3. N4018 pAr N 18;→ = n = 40 — 18 = 22.
4. 20Ca — Np = Ne = 20; 29Cu — Ne = 29; 32Ge — Ne = 32; 51Sb — Ne = 51;
15P — Ne = 15. Max Ne — y51Sb.
5. ʳëüê³ñòþ íåéòðîí³â: 23892U 238 92 146;nN− = − =
23592U 235 92 143.nN− = − =
Âïðàâà ¹ 29
1. Z = 88 — 2 = 86; A = 226 — 4 = 222; 226 4 A88 2 ZRa He X;
α→ + 222 222
86 86X R= n.
.
..
2. Z = 91 + 1 = 92; A = 234; 234 0 A91 1 ZPa e X;
β
−→ + 234 23492 92X U=
3. 238 4 234 0 234 0 23492 2 90 1 92 1 92U He Th e Pa e U.
β βα
− −→ + → + → +
4. 0,69
;N
AT
= NU = NRa = NRn; TU TRa TRn; AU ARa ARn.
Àêòèâí³ñòü Ðàäîíó íàéá³ëüøà. 6. Äàíî: Ðîçâ’ÿçàííÿ:
PU – 239 ν = 0,05 ìîëü λ = 9 ⋅ 10—13 ñ—1
A = λN; N = νNA; A = λνNA; [A] = ñ—1 ⋅ ìîëü ⋅ ìîëü—1 = ñ—1; A = 9 ⋅ 10—13 ⋅ 5 ⋅ 10—2 ⋅ 6,02 ⋅ 10—23 =
19
NA = 6,02 ⋅ 1023 ìîëü—1 A – ?
= 2,7 ⋅ 1010 ñ—1 = 2,7 ⋅ 1010 (Áê). ³äïîâ³äü: A = 2,7 ⋅ 1010 Áê.
7. Äàíî: Ðîçâ’ÿçàííÿ:
m = 0,2 ã λ = 3,14 ⋅ 10—17 ñ—1 NA = 6,02 ⋅ 1023 ìîëü—1 M = 235 ã/ìîëü A – ?
A = λN; ;AmNN
M= ;AmN
AM
λ=
1ã ìîëü[ ] ñ ;
ìîëü ñ ãA −⋅= =
⋅ ⋅
17 2343,14 10 0,2 6,02 10
1,6 10235
A−
−⋅ ⋅ ⋅ ⋅= = ⋅ ñ—1 =
= 1,6 ⋅ 104 (Áê). ³äïîâ³äü: A = 1,6 ⋅ 104 Áê.
Âïðàâà ¹ 30
1. Äàíî: Ðîçâ’ÿçàííÿ: PD = 2 ⋅ 10—9 Ãð/ñ t = 1 ãîä = 3600 ñ D – ?
D = PD ⋅ t = 2 ⋅ 10—9 ⋅ 3600 = 7,2 ⋅ 10—6 (Ãð) = = 7,2 (ìêÃð). ³äïîâ³äü: D = 7,1 ìêÃð.
2. Äàíî: Ðîçâ’ÿçàííÿ:
N = 108 m = 1 ã = 10—3 êã Eα = 8,3 ⋅ 10—13 Äæ k = 20 H – ?
H = kD; ;W
Dm
= w = NEα; ;kNE
Hm
α=
Äæ[ ] Çâ;
êãH = =
8 13
3
20 10 8,3 101,66
10H
−
−
⋅ ⋅ ⋅= = (Çâ).
³äïîâ³äü: H = 1,66 Çâ. 3. Äàíî: Ðîçâ’ÿçàííÿ:
t = 1 ãîä = 3600 ñ PD = 25 ⋅ 10—9 Ãð/ñ k = 1 D – ? H – ?
D = PD ⋅ t; Ãð
[ ] ñ = Ãð;ñ
D = ⋅ H = kD;
[H] = Çâ; D = 25 ⋅ 10—9 ⋅ 3,6 ⋅ 103 = = 9 ⋅ 10—5 Ãð = 90 ìêÃð; H = 90 (ìêÇâ). ³äïîâ³äü: D = 90 ìêÃð; H = 90 ìêÇâ.
Çàâäàííÿ äëÿ ñàìîïåðåâ³ðêè
8. PD = 25 ìêÐ/ãîä; (ìêÐ/ãîä) ⋅ 24 ãîä = 900 ìêÐ. 25DD P t= =
9. N = 7,2 ⋅ 1010 ãîä—1 = 10
77,2 102 10
3600
⋅ = ⋅ ñ—1; A = 2 ⋅ 107 Áê.
10. H = 0,01 ìêÇâ; t = 4 ãîä; 0,01 ìêÇâ
0,00254 ãîä
HP
t= = = ìêÇâ/ãîä.
11. 237 Z = 93 — 2 = 91; A = 237 — 4 = 233; A 493 p Z 2N X H→ + e; a.
i.
233 23391 91X P=
12. 210 Z = 82 + 1 = 83; A = 210; 210 A 082 Z 1Pb X e;−= + 210
83 83X B=
20
13. P = 7 ìêÃð/ãîä; t = 200 ⋅ 6 = 1200 ãîä; D = Pt = 7 ⋅ 1200 = 8400 (ìêÃð) = 8,4 ìÃð; D + Dô = 8,4 + 2 = 10,4 (ìÃð); D + Dô < 50 ìÃð – ïðàöþâàòè áåçïå÷íî.
14. N0 = 2 ⋅ 10—10 ìîëü; NA = 6,02 ⋅ 1023 ìîëü—1; λ = 1,37 ⋅ 10—11 ñ—1; N = N0 ⋅ NA ⋅ λ = 2 ⋅ 10—10 ⋅ 6,02 ⋅ 1023 ⋅ 1,37 ⋅ 10—11 = 1649 (ñ—1).
21