Misali na Tambayoyin Makamashi Mai Yiwuwa na Lantarki
1. Ana hanzarta wutar lantarki daga hutawa ta hanyar bambancin wutar lantarki na volts 12. Menene canjin makamashin wutar lantarki?
Tattaunawa
An san cewa:
Loda 1 na'urar lantarki (e) = -1,60 x 10-19 Coulomb
Bambancin yuwuwar lantarki = ƙarfin lantarki (V) = Volts 12
An tambaya: Canji a cikin makamashin lantarki (ΔEP)
Amsa:
ΔEP = q V = (-1,60 x 10-19 C)(12 V) = -19,2 x 10-19 Joule
Alamar korau tana nufin makamashin wutar lantarki yana raguwa. Idan aka kusa da farantin da aka caji mara kyau, ƙarfin wutar lantarki na electron yana da matuƙar ƙarfi. Bayan isa kusa da farantin da aka caji mai kyau, ƙarfin wutar lantarki na electron yana da ƙarancin ƙarfi.
2. Faranti biyu masu layi daya kowannensu yana da caji mai kyau da mara kyau. Filin wutar lantarki tsakanin faranti biyu shine Volts 500/mita. Nisa tsakanin faranti biyu shine cm 2. Ka tantance canjin kuzarin da proton zai iya samu idan ya motsa daga faranti mai caji mai kyau zuwa faranti mai caji mara kyau!
Tattaunawa
An san cewa:
Filin lantarki tsakanin faranti biyu (E) = Volts 500/mita
Nisa tsakanin faranti biyu = 2 cm = mita 0,02
Cajin Proton = +1,60 x 10-19 Coulomb
An tambaya: Canji a cikin makamashin wutar lantarki (ΔEP)
Amsa:
Da farko kirga bambancin da zai iya faruwa ko ƙarfin lantarki :
V = Es
V = (Volts 500/mita)(mita 0,02)
V = Volt 10
Canje-canje a cikin makamashin wutar lantarki:
ΔEP = q V
ΔEP = (1,60 x 10-19 C)(V 10)
ΔEP = 16 x 10-19 Joule
ΔEP = 1,6 x 10-18 Joule
Idan aka kusa da farantin da aka caji mai kyau, ƙarfin wutar lantarki na proton yana da matuƙar ƙarfi. Da zarar an isa kusa da farantin da aka caji mai kyau, ƙarfin wutar lantarki na proton yana da ƙarancin ƙarfi. Saboda haka, lokacin da aka matsa daga farantin da aka caji mai kyau zuwa farantin da aka caji mai kyau, ƙarfin wutar lantarki na proton yana raguwa.
3. An shirya caji guda biyu kamar yadda aka nuna a hoton da ke ƙasa. Cajin da ke A shine +9 μC kuma cajin da ke B shine -4 μC. Madaidaitan Coulomb (k) = 9 x 109 Nm2C-2, 1 μC = 10-6 C. Nawa ne ƙarfin wutar lantarki na cajin B zai canza idan ya koma caji A?
Tattaunawa
An san cewa:
Cajin A (q)1) = +9 μC = +9 x 10-6 C
Caji B (q)1) = -4 μC = -4 x 10-6 C
Madaidaitan Coulomb (k) = 9 x 109 Nm2C-2
Nisa tsakanin caji A da B (r) = 10 cm = mita 0,1 = 10-1 mita
An tambaya: Canji a cikin ƙarfin wutar lantarki na cajin B idan ya koma caji A
Amsa:
Caji B yana motsawa zuwa ga caji A ta yadda ƙarfin wutar lantarkinsa zai ragu da Joules 2,4.
Wannan yayi kama da wani abu mai yawa da ke tafiya ƙasa zuwa ƙasa don haka tsayinsa da ƙarfin ƙarfinsa na nauyi suna raguwa.
4. An sanya wani barbashi mai cajin \( q = 5 \sau 10^{-6} \) C a cikin filin lantarki tare da yuwuwar \( V = 300 \) V. Menene kuzarin ƙarfin lantarki na barbashin?
Tattaunawa:
Ana bayar da makamashin wutar lantarki ta hanyar:
\[ U = q \sau V \]
\[ U = 5 \sau 10^{-6} \sau 300 \]
\[ U = 1.5 \sau 10^{-3} \] J
5. Ana sanya na'urar lantarki a cikin filin lantarki mai ƙarfin V 500. Menene ƙarfin lantarki na na'urar lantarki?
Tattaunawa:
Cajin lantarki \( q = -1.6 \sau 10^{-19} \) C.
\[ U = q \sau V \]
\[ U = -1.6 \sau 10^{-19} \sau 500 \]
\[ U = -8 \sau 10^{-17} \] J
6. Proton yana motsawa daga ƙarfin V 100 zuwa V 200. Menene canjin ƙarfin makamashinsa?
Tattaunawa:
Cajin Proton \( q = 1.6 sau 10^{-19} \) C.
\[ \Delta U = q \times \Delta V \]
\[ \Delta U = 1.6 \sau 10^{-19} \sau (200 - 100) \]
\[ \Delta U = 1.6 \sau 10^{-17} \] J
7. Abubuwa biyu masu caji \( q_1 = 2 \sau 10^{-6} \) C da \( q_2 = -3 \sau 10^{-6} \) C an sanya su a cikin filin lantarki tare da yuwuwar \( V = 400 \) V. Menene jimlar kuzarin yuwuwar abubuwa biyu?
Tattaunawa:
\[ U_1 = q_1 \sau V \]
\[ U_2 = q_2 \sau V \]
\[ U_{jimlar} = U_1 + U_2 \]
\[ U_{jimlar} = (sau 2 10^{-6} + (-3 sau 10^{-6})) \sau 400 \]
\[ U_{jimlar} = -4 \sau 10^{-3} \] J
8. ion mai caji \( q = 4e \) (inda \( e \) shine cajin farko) yana cikin filin lantarki mai yuwuwa \( V = 250 \) V. Menene kuzarin ƙarfin lantarki na ion?
Tattaunawa:
\[ U = q \sau V \]
\[ U = 4 \sau 1.6 \sau 10^{-19} \sau 250 \]
\[ U = 1.6 \sau 10^{-16} \] J
9. An san cewa ƙwayar cuta mai caji na \( q = -7 \sau 10^{-5} \) C tana da ƙarfin kuzari na \( sau 2 \sau 10^{-2} \) J. Menene ƙarfin filin lantarki inda ƙwayar cuta take?
Tattaunawa:
\[ U = q \sau V \]
\[ V = \frac{U}{q} \]
\[ V = \frac{2 \sau 10^{-2}}{-7 \sau 10^{-5}} \]
\[ V = -285.71 \] V
10. Abubuwa biyu masu caji \( q_1 = 5e \) da \( q_2 = -2e \) suna cikin filin lantarki mai yuwuwar \( V = 300 \) V. Menene jimlar kuzarin yuwuwar abubuwa biyu?
Tattaunawa:
\[ U_1 = q_1 \sau V \]
\[ U_2 = q_2 \sau V \]
\[ U_{jimlar} = U_1 + U_2 \]
\[ U_{jimlar} = (5 \sau 1.6 \sau 10^{-19} – 2 \sau 1.6 \sau 10^{-19}) \sau 300 \]
\[ U_{jimlar} = 1.44 \sau 10^{-16} \] J
11. Ion mai caji \( q = -3e \) yana da ƙarfin kuzari na \( -9.6 \sau 10^{-19} \) J. Menene ƙarfin filin lantarki inda ion yake?
Tattaunawa:
\[ U = q \sau V \]
\[ V = \frac{U}{q} \]
\[ V = \frac{-9.6 \sau 10^{-19}}{-3 \sau 1.6 \sau 10^{-19}} \]
\[ V = 200 \] V
12. An san cewa ƙarfin wutar lantarki na caji \( q \) a cikin filin lantarki mai yuwuwa \( V = 450 \) V shine \( 9 \sau 10^{-18} \) J. Menene cajin \( q \)?
Tattaunawa:
\[ U = q \sau V \]
\[ q = \frac{U}{V} \]
\[ q = \frac{9 \sau 10^{-18}}{450} \]
\[ q = sau 2 10^{-20} \] C
13. Cajin mai kyau \( q = 1.5 \sau 10^{-19} \) C ana motsa shi daga wurin da ke da yuwuwar \( V_1 = 100 \) V zuwa \( V_2 = 500 \) V. Menene canjin makamashi mai yuwuwar?
Tattaunawa:
\[ \Delta U = q \times \Delta V \]
\[ \Delta U = 1.5 \sau 10^{-19} \sau (500 - 100) \]
\[ \Delta U = 6 \sau 10^{-17} \] J
