Cajin lantarki shine sifar zahiri da ke sa ɓangarori su fuskanci karfin lantarki. Akwai shi a cikin tabbatacce da korau. Cajin da suka yi kama da juna suna turewa, masu adawa suna jan hankali. Mahimmanci ga dukkan sunadarai da lantarki.

• 1 coulomb = 6.24×10¹⁸ lantarki
• Proton: +1e, Lantarki: -1e
• Ana kiyaye cajin (ba a taɓa ƙirƙira/lalacewa)
• An ƙididdige shi a cikin ninki na e = 1.602×10⁻¹⁹ C

Halin yanzu (I) shine yawan gudun cajin. Q = I × t. Ampere 1 = coulomb 1 a sakan daya. Karfin batir a Ah cajin ne, ba halin yanzu ba. 1 Ah = 3600 C.

• Halin yanzu = cajin a kowane lokaci (I = Q/t)
• 1 A = 1 C/s (ma'ana)
• 1 Ah = 3600 C (ampere 1 na awa 1)
• mAh ƙarfin cajin ne, ba iko ba

Batura suna adana cajin. An ƙididdige su a cikin Ah ko mAh (cajin) ko Wh (makamashi). Wh = Ah × Wutar lantarki. Batirin waya: 3000 mAh @ 3.7V ≈ 11 Wh. Wutar lantarki tana da mahimmanci ga makamashi, ba cajin ba.

• mAh = milliampere-hour (cajin)
• Wh = watt-hour (makamashi = cajin × wutar lantarki)
• mAh mafi girma = tsawon lokacin gudu (wutar lantarki iri ɗaya)
• 3000 mAh ≈ 10,800 coulombs

Kafin fahimtar cajin a kididdiga, masana kimiyya sun bincika wutar lantarki ta tsaye da kuma 'ruwan lantarki' mai ban mamaki. Kirkirar batura ta ba da damar auna daidai yadda cajin ke gudana a kai a kai.

• 1600: William Gilbert ya bambanta wutar lantarki da maganadisu, ya kirkiro kalmar 'lantarki'
• 1733: Charles du Fay ya gano nau'ikan wutar lantarki guda biyu (tabbatacce da korau)
• 1745: An kirkiro kwalbar Leyden — na'urar adana wuta ta farko, tana adana cajin da za a iya aunawa
• 1785: Coulomb ya wallafa dokar murabba'i mai juyawa F = k(q₁q₂/r²) don karfin lantarki
• 1800: Volta ya kirkiro batir — yana ba da damar gudun cajin da za a iya aunawa a kai a kai
• 1833: Faraday ya gano dokokin electrolysis — yana danganta cajin da sunadarai (tsayayyen Faraday)

Coulomb ya samo asali ne daga ma'anoni masu amfani da suka dogara da ka'idodin lantarki-sunadarai zuwa ma'anar zamani da ke da alaƙa da ampere da sakan.

• 1881: An bayyana coulomb na farko mai amfani ta hanyar ka'idar rufe azurfa
• 1893: Baje kolin Duniya na Chicago ya daidaita coulomb don amfanin duniya
• 1948: CGPM ya bayyana coulomb a matsayin ampere-sakan 1 (1 C = 1 A·s)
• 1960-2018: An bayyana Ampere ta hanyar karfi tsakanin masu gudanarwa masu kama da juna, wanda ya sa coulomb ya zama kai tsaye
• Matsala: Ma'anar Ampere da ta dogara da karfi tana da wahalar cimmawa da babban daidaito
• 1990s-2010s: Jimlar metrology (tasirin Josephson, tasirin jimlar Hall) yana ba da damar kirga lantarki

A ranar 20 ga Mayu, 2019, an gyara cajin farko daidai, wanda ya sake fasalin ampere kuma ya sa coulomb ya zama mai iya sake haifarwa daga tsayayyun abubuwa na asali.

• Sabon ma'anar: e = 1.602176634 × 10⁻¹⁹ C daidai (rashin tabbas sifili ta hanyar ma'ana)
• Cajin farko yanzu tsayayyen abu ne da aka ayyana, ba darajar da aka auna ba
• 1 coulomb = 6.241509074 × 10¹⁸ cajin farko (daidai)
• Na'urorin rami na lantarki guda ɗaya na iya ƙirga lantarki ɗaya bayan ɗaya don ingantattun ka'idodin cajin
• Jimlar metrology triangle: wutar lantarki (Josephson), juriya (jimlar Hall), halin yanzu (famfon lantarki)
• Sakamako: Duk wani dakin gwaje-gwaje da kayan aikin jimla na iya gane coulomb da kansa

Sake fasalin na 2019 yana wakiltar ci gaban sama da shekaru 135 daga ka'idodin lantarki-sunadarai zuwa daidaiton jimla, wanda ke ba da damar na'urorin lantarki na gaba da ajiyar makamashi.

• Fasahar batir: Mafi ingantattun ma'aunin ƙarfin motocin lantarki, ajiyar wutar lantarki
• Jimlar lissafi: Daidaitaccen ikon cajin a cikin qubits da transistor na lantarki guda ɗaya
• Metrology: Dakunan gwaje-gwaje na ƙasa na iya gane coulomb da kansu ba tare da kayan tarihi na tunani ba
• Sunadarai: Faraday constant yanzu daidai yake, yana inganta lissafin lantarki-sunadarai
• Kayan lantarki na masu amfani: Mafi kyawun ka'idoji don kimar ƙarfin batir da ka'idojin caji mai sauri

• Gajeren hanya daga mAh zuwa C: Ninka da 3.6 → 1000 mAh = 3600 C daidai
• Ah zuwa C: Ninka da 3600 → 1 Ah = 3600 C (ampere 1 na awa 1)
• Sauri mAh zuwa Wh (3.7V): Raba da ~270 → 3000 mAh ≈ 11 Wh
• Wh zuwa mAh (3.7V): Ninka da ~270 → 11 Wh ≈ 2970 mAh
• Cajin farko: e ≈ 1.6 × 10⁻¹⁹ C (an zagaye daga 1.602)
• Faraday constant: F ≈ 96,500 C/mol (an zagaye daga 96,485)

Fahimtar kimar batir yana hana rikicewa tsakanin cajin (mAh), wutar lantarki (V), da makamashi (Wh). Waɗannan dokokin suna adana lokaci da kuɗi.

• mAh yana auna CAJIN, ba iko ko makamashi ba — shine adadin lantarkin da zaku iya motsawa
• Don samun makamashi: Wh = mAh × V ÷ 1000 (wutar lantarki tana da mahimmanci!)
• mAh iri ɗaya a wutar lantarki daban-daban = makamashi daban-daban (12V 1000mAh ≠ 3.7V 1000mAh)
• Bankunan wuta: Yi tsammanin 70-80% na ƙarfin da za a iya amfani da shi (rasa a cikin canjin wutar lantarki)
• Lokacin gudu = Karfin ÷ Halin yanzu: 3000 mAh ÷ 300 mA = awanni 10 (mafi kyau, ƙara gefen 20%)
• Li-ion na yau da kullun: 3.7V na al'ada, 4.2V cike, 3.0V babu komai (kewayon da za a iya amfani da shi ~80%)

• Cajin daga halin yanzu: Q = I × t (coulombs = amperes × sakanni)
• Lokacin gudu: t = Q / I (awanni = amp-hours / amperes)
• Makamashi daga cajin: E = Q × V (watt-hours = amp-hours × volts)
• An daidaita shi don inganci: Mai amfani = Wanda aka ƙididdige × 0.8 (yi la'akari da asara)
• Electrolysis: Q = n × F (coulombs = moles na lantarki × Faraday constant)
• Makamashin na'urar adana wuta: E = ½CV² (joules = ½ farads × volts²)

• Rikita mAh da mWh — cajin vs makamashi (ana buƙatar wutar lantarki don canzawa!)
• Yin watsi da wutar lantarki lokacin kwatanta batura — yi amfani da Wh don kwatanta makamashi
• Yin tsammanin ingancin bankin wuta 100% — 20-30% an rasa ga zafi da canjin wutar lantarki
• Rikita C (coulombs) da C (yawan fitarwa) — ma'anoni daban-daban gaba ɗaya!
• Yin zaton mAh = lokacin gudu — kuna buƙatar sanin yadda halin yanzu yake (lokacin gudu = mAh ÷ mA)
• Fitar da Li-ion a ƙasa da 20% — yana rage tsawon rayuwa, ƙarfin da aka ƙididdige ≠ ƙarfin da za a iya amfani da shi

Coulomb (C) shine naúrar SI ta asali don cajin. An bayyana shi daga ampere da sakan: 1 C = 1 A·s. Karin kalmomi daga pico zuwa kilo sun rufe dukkan kewayon aiki.

• 1 C = 1 A·s (daidai ma'ana)
• mC, µC, nC don ƙananan caji
• pC, fC, aC don aikin jimla/daidaito
• kC don manyan tsarin masana'antu

Amp-hour (Ah) da milliamp-hour (mAh) sune ka'idodin batura. Masu amfani saboda suna da alaƙa kai tsaye da yadda ake amfani da halin yanzu da lokacin gudu. 1 Ah = 3600 C.

• mAh — wayoyin hannu, kwamfyutoci, belun kunne
• Ah — kwamfyutoci masu ɗaukuwa, kayan aikin wuta, baturan mota
• kAh — motocin lantarki, UPS na masana'antu
• Wh — ƙarfin makamashi (ya dogara da wutar lantarki)

Cajin farko (e) shine naúrar asali a kimiyyar lissafi. Faraday constant a sunadarai. Raka'o'in CGS (statcoulomb, abcoulomb) a cikin tsoffin littattafan karatu.

• e = 1.602×10⁻¹⁹ C (cajin farko)
• F = 96,485 C (Faraday constant)
• 1 statC ≈ 3.34×10⁻¹⁰ C (ESU)
• 1 abC = 10 C (EMU)

Duk cajin an ƙididdige shi a cikin ninki na cajin farko e. Ba za ku iya samun lantarki 1.5 ba. Quarks suna da cajin kashi (⅓e, ⅔e) amma ba sa kasancewa su kaɗai.

• Mafi ƙarancin cajin kyauta: 1e = 1.602×10⁻¹⁹ C
• Lantarki: -1e, Proton: +1e
• Duk abubuwa suna da cajin N×e (lambar gaba ɗaya N)
• Gwajin digo na mai na Millikan ya tabbatar da jimla (1909)

Mole 1 na lantarki yana ɗauke da cajin 96,485 C. Ana kiran shi Faraday constant (F). Mahimmanci ga lantarki-sunadarai da sunadarai na batir.

• F = 96,485.33212 C/mol (CODATA 2018)
• 1 mol e⁻ = 6.022×10²³ lantarki
• Ana amfani da shi a lissafin electrolysis
• Yana danganta cajin da aikin sunadarai

Karfi tsakanin caji: F = k(q₁q₂/r²). Cajin da suka yi kama da juna suna turewa, masu adawa suna jan hankali. Karfin asali na yanayi. Yana bayyana dukkan sunadarai da lantarki.

• k = 8.99×10⁹ N·m²/C²
• F ∝ q₁q₂ (samfurin caji)
• F ∝ 1/r² (dokar murabba'i mai juyawa)
• Yana bayyana tsarin atomic, haɗi

Kowace na'ura mai amfani da batir tana da kimar ƙarfin. Wayoyin hannu: 2500-5000 mAh. Kwamfyutoci masu ɗaukuwa: 40-100 Wh. Bankunan wuta: 10,000-30,000 mAh.

• iPhone 15: ~3,349 mAh @ 3.85V ≈ 13 Wh
• MacBook Pro: ~100 Wh (iyakar jirgin sama)
• AirPods: ~500 mAh (haɗe)
• Bankin wuta: 20,000 mAh @ 3.7V ≈ 74 Wh

An ƙididdige baturan EV a kWh (makamashi), amma ƙarfin yana a kAh a wutar lantarki na fakitin. Tesla Model 3: 75 kWh @ 350V = 214 Ah. Babba idan aka kwatanta da wayoyi!

• Tesla Model 3: 75 kWh (214 Ah @ 350V)
• Nissan Leaf: 40 kWh (114 Ah @ 350V)
• Cajin EV: 50-350 kW DC mai sauri
• Cajin gida: ~7 kW (32A @ 220V)

Rufin lantarki, electrolysis, bankunan na'urorin adana wuta, tsarin UPS duk sun haɗa da manyan musayar cajin. UPS na masana'antu: ƙarfin 100+ kAh. Supercapacitors: farads (C/V).

• Rufin lantarki: ayyukan 10-1000 Ah
• UPS na masana'antu: 100+ kAh ajiyar wuta
• Supercapacitor: 3000 F = 3000 C/V
• Bugun walƙiya: ~15 C na yau da kullun

Ninka mAh da 3.6 don samun coulombs. 1000 mAh = 3600 C.

• 1 mAh = 3.6 C (daidai)
• 1 Ah = 3600 C
• Sauri: mAh × 3.6 → C
• Misali: 3000 mAh = 10,800 C

Raba mAh da ~270 don Wh a wutar lantarki na Li-ion 3.7V.

• Wh = mAh × V ÷ 1000
• A 3.7V: Wh ≈ mAh ÷ 270
• 3000 mAh @ 3.7V = 11.1 Wh
• Wutar lantarki tana da mahimmanci ga makamashi!

Lokacin gudu (h) = Batirin (mAh) ÷ Halin yanzu (mA). 3000 mAh a 300 mA = awanni 10.

• Lokacin gudu = Karfin ÷ Halin yanzu
• 3000 mAh ÷ 300 mA = 10 h
• Halin yanzu mafi girma = gajeren lokacin gudu
• Rasa inganci: yi tsammanin 80-90%

Batirin 3500 mAh. App yana amfani da 350 mA. Yaya tsawon lokacin da zai ɗauka har ya mutu?

Lokacin gudu = Karfin ÷ Halin yanzu = 3500 ÷ 350 = awanni 10 (mafi kyau). A zahiri: ~8-9h (rasa inganci).

Bankin wuta na 20,000 mAh. Cajin waya 3,000 mAh. Sau nawa za a yi cikakken caji?

Yi la'akari da inganci (~80%): 20,000 × 0.8 = 16,000 mai tasiri. 16,000 ÷ 3,000 = caji 5.3.

Sanya mole 1 na jan karfe (Cu²⁺ + 2e⁻ → Cu). Nawa ne coulombs?

Moles 2 na e⁻ a kowace mole na Cu. 2 × F = 2 × 96,485 = 192,970 C ≈ 53.6 Ah.

Jikinka yana da ~10²⁸ protons da kuma adadin lantarki iri ɗaya. Idan ka rasa 0.01% na lantarki, za ka ji karfin janyewa na 10⁹ newtons—wanda ya isa ya rushe gine-gine!

Bugun walƙiya: cajin ~15 C kawai, amma wutar lantarki biliyan 1! Makamashi = Q×V, don haka 15 C × 10⁹ V = 15 GJ. Wannan shine 4.2 MWh—zai iya ba da wutar lantarki ga gidanka na watanni!

Gwajin kimiyya na gargajiya yana gina cajin zuwa miliyoyin volts. Jimlar cajin? ~10 µC kawai. Mai ban tsoro amma lafiya—ƙarancin halin yanzu. Wutar lantarki ≠ haɗari, halin yanzu yana kashewa.

Batirin mota: 60 Ah = 216,000 C, yana fitar da shi a cikin sa'o'i. Supercapacitor: 3000 F = 3000 C/V, yana fitar da shi a cikin sakanni. Yawan makamashi vs. yawan iko.

1909: Millikan ya auna cajin farko ta hanyar kallon digon mai da aka caje yana faɗuwa. Ya sami e = 1.592×10⁻¹⁹ C (na zamani: 1.602). Ya lashe kyautar Nobel a 1923.

Jimlar cajin lantarki tana da daidai sosai, ana amfani da ita don ayyana ka'idar juriya. Daidaito: kashi 1 cikin 10⁹. Tsayayyun abubuwa na asali sun ayyana dukkan raka'o'i tun 2019.

mAh yana auna cajin (adadin lantarki). Wh yana auna makamashi (cajin × wutar lantarki). mAh iri ɗaya a wutar lantarki daban-daban = makamashi daban-daban. Yi amfani da Wh don kwatanta batura a kan wutar lantarki daban-daban. Wh = mAh × V ÷ 1000.

Karfin da aka ƙididdige na al'ada ne, ba mai amfani ba. Li-ion: yana fitarwa daga 4.2V (cike) zuwa 3.0V (babu komai), amma tsayawa a 20% yana kiyaye tsawon rayuwa. Rasa canji, zafi, da tsufa suna rage ƙarfin tasiri. Yi tsammanin 80-90% na abin da aka ƙididdige.

Ba kawai rabon ƙarfin bane. Bankin wuta na 20,000 mAh: ~70-80% mai inganci (canjin wutar lantarki, zafi). Mai tasiri: 16,000 mAh. Don waya 3,000 mAh: 16,000 ÷ 3,000 ≈ caji 5.3. A zahiri: 4-5.

Cajin farko (e = 1.602×10⁻¹⁹ C) shine cajin proton ɗaya ko lantarki ɗaya. Duk cajin an ƙididdige shi a cikin ninki na e. Mahimmanci ga kimiyyar lissafin jimla, yana bayyana tsayayyen tsarin daidai. Tun 2019, e daidai yake ta hanyar ma'ana.

Ee! Cajin korau yana nufin wuce gona da iri na lantarki, tabbatacce yana nufin rashi. Jimlar cajin aljebra ce (zai iya soke). Lantarki: -e. Protons: +e. Abubuwa: galibi kusan ba su da cajin (daidai + da -). Cajin da suka yi kama da juna suna turewa, masu adawa suna jan hankali.

Li-ion: aikin sunadarai yana lalata kayan lantarki a hankali. Kowace zagayowar caji tana haifar da ƙananan canje-canje marasa juyawa. Fitarwa mai zurfi (<20%), zafi mai zafi, caji mai sauri suna hanzarta tsufa. Batura na zamani: zagayowar 500-1000 zuwa ƙarfin 80%.