Mai Canza Juriya na Lantarki
Guzurin Lantarki: Daga Karantar Kwayoyin Halitta zuwa Cikakkun Masu Kariyar Wuta
Daga manyan masu sarrafa wuta da ba su da guzur zuwa masu kariyar wuta da suka kai teraohms, guzirin lantarki ya mamaye tsawon digiri 27 na girma. Binciki duniyar ban sha'awa ta auna guzur a fadin ilimin lantarki, kimiyyar lissafin kwayoyin halitta, da kimiyyar kayan aiki, kuma ku kware a jujjuyawar tsakanin raka'a 19+ ciki har da ohms, siemens, da guzirin kwayoyin halitta—daga gano Georg Ohm a 1827 zuwa ma'aunin da aka ayyana ta kwayoyin halitta na 2019.
Tushen Guzurin Lantarki
Menene Guzur?
Guzur yana hana wutar lantarki, kamar gogayya ga wutar lantarki. Babban guzur = yana da wuya wuta ta kwarara. Ana auna shi da ohms (Ω). Kowane abu yana da guzur—har ma da wayoyi. Guzur sifili yana cikin manyan masu sarrafa wuta ne kawai.
- 1 ohm = 1 volt a kowace ampere (1 Ω = 1 V/A)
- Guzur yana iyakance wuta (R = V/I)
- Masu sarrafa wuta: ƙaramin R (jan ƙarfe ~0.017 Ω·mm²/m)
- Masu kariyar wuta: babban R (roba >10¹³ Ω·m)
Guzur da Yaduwa
Yaduwa (G) = 1/Guzur. Ana auna shi da siemens (S). 1 S = 1/Ω. Hanyoyi biyu don bayyana abu ɗaya: babban guzur = ƙaramar yaduwa. Yi amfani da wanda ya fi dacewa!
- Yaduwa G = 1/R (siemens)
- 1 S = 1 Ω⁻¹ (jujjuyawa)
- Babban R → ƙaramar G (masu kariyar wuta)
- Ƙaramin R → babbar G (masu sarrafa wuta)
Dogaro da Zafin Jiki
Guzur yana canzawa da zafin jiki! Ƙarfe: R yana ƙaruwa da zafi (ingantaccen ma'aunin zafin jiki). Rabin masu sarrafa wuta: R yana raguwa da zafi (mara kyau). Manyan masu sarrafa wuta: R = 0 a ƙasa da yanayin zafi mai mahimmanci.
- Ƙarfe: +0.3-0.6% a kowace °C (jan ƙarfe +0.39%/°C)
- Rabin masu sarrafa wuta: yana raguwa da zafin jiki
- Termistors na NTC: ma'auni mara kyau
- Manyan masu sarrafa wuta: R = 0 a ƙasa da Tc
- Guzur = hana wuta (1 Ω = 1 V/A)
- Yaduwa = 1/guzur (ana auna shi da siemens)
- Babban guzur = ƙaramin wuta don wannan ƙarfin lantarki
- Zafin jiki yana shafar guzur (ƙarfe R↑, rabin masu sarrafa wuta R↓)
Juyin Halittar Auna Guzurin
Gwajin Farko da Lantarki (1600-1820)
Kafin a fahimci guzur, masana kimiyya sun yi ta fama don bayyana dalilin da yasa wuta ke canzawa a cikin abubuwa daban-daban. Batir na farko da kayan aiki na auna marasa inganci sun kafa harsashin kimiyyar lantarki na adadi.
- 1600: William Gilbert ya bambanta tsakanin 'masu lantarki' (masu kariyar wuta) da 'marasa lantarki' (masu sarrafa wuta)
- 1729: Stephen Gray ya gano yaduwar lantarki da kariyar wuta a cikin abubuwa
- 1800: Alessandro Volta ya ƙirƙiro batir—tushen wuta na farko mai dogaro da kai
- 1820: Hans Christian Ørsted ya gano ilimin lantarki da maganadisu, wanda ya ba da damar gano wuta
- Kafin Ohm: An lura da guzur amma ba a ƙididdige shi ba—wuta 'mai ƙarfi' da 'mai rauni'
Juyin Halittar Dokar Ohm da Haihuwar Guzurin (1827)
Georg Ohm ya gano alaƙar adadi tsakanin ƙarfin lantarki, wuta, da guzur. Dokarsa (V = IR) ta kasance mai kawo sauyi amma da farko an ƙi ta daga al'ummar kimiyya.
- 1827: Georg Ohm ya wallafa 'Die galvanische Kette, mathematisch bearbeitet'
- Gano: Wuta tana daidai da ƙarfin lantarki, kuma ta juye da guzur (I = V/R)
- Ƙin farko: Al'ummar kimiyyar lissafi ta Jamus ta kira shi 'yanar gizo na zato tsirara'
- Hanyar Ohm: Ya yi amfani da thermocouples da galvanometers na torsion don auna daidai
- 1841: Royal Society ta ba Ohm lambar yabo ta Copley—shari'a bayan shekaru 14
- Gado: Dokar Ohm ta zama harsashin dukkan ilimin injiniyan lantarki
Zamanin Daidaitawa (1861-1893)
Yayin da fasahar lantarki ta bunƙasa, masana kimiyya sun buƙaci raka'o'in guzur da aka daidaita. An ayyana ohm ta amfani da kayan tarihi na zahiri kafin ma'aunin kwayoyin halitta na zamani.
- 1861: Ƙungiyar Burtaniya ta karɓi 'ohm' a matsayin rukunin guzur
- 1861: An ayyana ohm na B.A. a matsayin guzurin ginshiƙin mercury mai tsawon 106 cm × 1 mm² a 0°C
- 1881: Babban Taron Lantarki na Farko na Duniya a Paris ya ayyana ohm na zahiri
- 1884: Taron Duniya ya daidaita ohm = 10⁹ raka'o'in lantarki na CGS
- 1893: Taron Chicago ya karɓi 'mho' (℧) don yaduwa (ohm da aka rubuta a baya)
- Matsala: Ma'anar da ta dogara da mercury ba ta da amfani—zafin jiki, tsabta sun shafi daidaito
Juyin Halittar Tasirin Quantum Hall (1980-2019)
Gano tasirin Quantum Hall ya samar da ƙididdigar guzur da ta dogara da ma'aunin asali, wanda ya kawo sauyi a cikin auna daidai.
- 1980: Klaus von Klitzing ya gano tasirin Quantum Hall
- Gano: A ƙananan zafin jiki + babban filin maganadisu, guzur yana ƙididdigewa
- Guzurin kwayoyin halitta: R_K = h/e² ≈ 25,812.807 Ω (ma'aunin von Klitzing)
- Daidaito: Daidai zuwa kashi 1 cikin 10⁹—ya fi kowane kayan tarihi na zahiri
- 1985: Von Klitzing ya lashe lambar yabo ta Nobel a fannin kimiyyar lissafi
- 1990: An sake ayyana ohm na duniya ta amfani da guzurin Quantum Hall
- Tasiri: Kowane dakin gwaje-gwaje na auna zai iya samun ainihin ohm da kansa
Sake Ayyana SI na 2019: Ohm daga Ma'auni
A ranar 20 ga Mayu, 2019, an sake ayyana ohm dangane da daidaita cajin farko (e) da kuma ma'aunin Planck (h), wanda ya sa ya zama mai yiwuwa a sake shi a ko'ina a cikin sararin samaniya.
- Sabon ma'ana: 1 Ω = (h/e²) × (α/2) inda α shine ma'aunin tsari mai kyau
- Dangane da: e = 1.602176634 × 10⁻¹⁹ C (daidai) da h = 6.62607015 × 10⁻³⁴ J·s (daidai)
- Sakamako: An ayyana Ohm yanzu daga kimiyyar lissafin kwayoyin halitta, ba kayan tarihi ba
- Ma'aunin von Klitzing: R_K = h/e² = 25,812.807... Ω (daidai da ma'anar)
- Sake haɓakawa: Kowane dakin gwaje-gwaje da ke da saitin Quantum Hall zai iya samun ainihin ohm
- Dukkan raka'o'in SI: Yanzu sun dogara da ma'aunin asali—babu sauran kayan tarihi na zahiri
Ma'anar kwayoyin halitta na ohm yana wakiltar nasarar da ɗan adam ya samu a fannin auna lantarki, wanda ke ba da damar fasahohi daga kwamfutoci na kwayoyin halitta zuwa na'urori masu auna firikwensin da suka fi kowa hankali.
- Ilimin lantarki: Yana ba da damar daidaito a ƙasa da 0.01% don nassoshin ƙarfin lantarki da daidaitawa
- Na'urorin kwayoyin halitta: Auna yaduwar kwayoyin halitta a cikin ƙananan tsari
- Kimiyyar kayan aiki: Siffanta kayan aiki na 2D (graphene, masu kariyar wuta na topological)
- Ilimin auna: Ma'auni na duniya—dakunan gwaje-gwaje a ƙasashe daban-daban suna samun sakamako iri ɗaya
- Bincike: Ana amfani da guzurin kwayoyin halitta don gwada ka'idodin kimiyyar lissafi na asali
- Gaba: Yana ba da damar na'urori masu auna firikwensin kwayoyin halitta da kwamfutoci na gaba
Taimakon Tunawa da Dabaru na Juyawa da Sauri
Lissafin Hankali Mai Sauƙi
- Dokar ikon 1000: Kowane matakin SI prefix = ×1000 ko ÷1000 (MΩ → kΩ → Ω → mΩ)
- Jujjuyawar guzur-yaduwa: 10 Ω = 0.1 S; 1 kΩ = 1 mS; 1 MΩ = 1 µS
- Triangle na dokar Ohm: Rufe abin da kuke so (V, I, R), sauran yana nuna dabarar
- Guzurin daidai a layi daya: R_total = R/n (guzurin 10 kΩ guda biyu a layi daya = 5 kΩ)
- Dabi'u na yau da kullun: 1, 2.2, 4.7, 10, 22, 47 tsarin yana maimaitawa a kowace shekara goma (jerin E12)
- Ikon 2: 1.2 mA, 2.4 mA, 4.8 mA... wuta tana ninka a kowane mataki
Dabaru na Tunawa da Lambar Launi na Guzur
Kowane dalibin ilimin lantarki yana buƙatar lambobin launi! Ga wasu dabaru na tunawa waɗanda a zahiri suke aiki (kuma sun dace da aji).
- Tsohuwar dabara: 'Baki, Kasa, Ja, Lemu, Rawa, Kore, Shudi, Hoda, Toɓo, Fari' (0-9)
- Lambobi: Baki=0, Kasa=1, Ja=2, Lemu=3, Rawa=4, Kore=5, Shudi=6, Hoda=7, Toɓo=8, Fari=9
- Juriya: Zinariya=±5%, Azurfa=±10%, Babu=±20%
- Tsarin sauri: Kasa-Baki-Lemu = 10×10³ = 10 kΩ (mafi yawan pull-up)
- Guzurin LED: Ja-Ja-Kasa = 220 Ω (mai iyakance wutar LED na 5V na gargajiya)
- Ka tuna: Biyu na farko lambobi ne, na uku shine mai ninka (sifili da za a ƙara)
Binciken Sauri na Dokar Ohm
- Tunawa da V = IR: 'Karfin lantarki shine Guzur sau wuta' (V-I-R a jere)
- Lissafin sauri na 5V: 5V ÷ 220Ω ≈ 23 mA (da'irar LED)
- Lissafin sauri na 12V: 12V ÷ 1kΩ = 12 mA daidai
- Binciken sauri na wutar lantarki: 1A ta 1Ω = 1W daidai (P = I²R)
- Raba ƙarfin lantarki: V_out = V_in × (R2/(R1+R2)) don guzur a jere
- Raba wuta: I_out = I_in × (R_other/R_total) don layi daya
Dokokin Da'ira na Aiki
- Guzurin pull-up: 10 kΩ shine lamba mai sihiri (mai ƙarfi sosai, ba wuta da yawa ba)
- Iyakance wutar LED: Yi amfani da 220-470 Ω don 5V, daidaita ta dokar Ohm don sauran ƙarfin lantarki
- Bus na I²C: 4.7 kΩ pull-ups na yau da kullun don 100 kHz, 2.2 kΩ don 400 kHz
- Babban juriya: >1 MΩ don juriyar shigarwa don guje wa loda da'irori
- Ƙaramin guzurin lamba: <100 mΩ don haɗin wutar lantarki, <1 Ω mai karɓa don sigina
- Sanya ƙasa: <1 Ω guzur zuwa ƙasa don aminci da kariya daga hayaniya
- Rudani a layi daya: Guzurin 10 Ω guda biyu a layi daya = 5 Ω (ba 20 Ω ba!). Yi amfani da 1/R_total = 1/R1 + 1/R2
- Matsayin wutar lantarki: Guzurin 1/4 W da 1 W na watsawa = hayaƙi mai sihiri! Lissafa P = I²R ko V²/R
- Ma'aunin zafin jiki: Da'irori masu daidaito suna buƙatar ƙaramin ma'aunin zafin jiki (<50 ppm/°C), ba ±5% na yau da kullun ba
- Haɗewar juriya: Guzurin 5% guda biyar na iya ba da kuskuren 25%! Yi amfani da 1% don rabon ƙarfin lantarki
- AC vs DC: A babban mitar, inductance da capacitance suna da mahimmanci (juriya ≠ guzur)
- Guzurin lamba: Masu haɗin da suka lalace suna ƙara guzur mai yawa—tsabtace lamba yana da mahimmanci!
Ma'aunin Guzur: Daga Kwayoyin Halitta zuwa Mara Iyaka
| Ma'auni / Guzur | Raka'o'in da ke Wakilta | Amfani na yau da kullun | Misalai |
|---|---|---|---|
| 0 Ω | Cikakken mai sarrafa wuta | Manyan masu sarrafa wuta a ƙasa da yanayin zafi mai mahimmanci | YBCO a 77 K, Nb a 4 K—guzur sifili daidai |
| 25.8 kΩ | Guzurin kwayoyin halitta (h/e²) | Tasirin Quantum Hall, auna guzur | Ma'aunin von Klitzing R_K—iyaka na asali |
| 1-100 µΩ | Microohm (µΩ) | Guzurin lamba, haɗin waya | Lambobin wuta masu yawa, guzur shunt |
| 1-100 mΩ | Milliohm (mΩ) | Auna wuta, guzurin waya | Wayar jan ƙarfe 12 AWG ≈ 5 mΩ/m; shunts 10-100 mΩ |
| 1-100 Ω | Ohm (Ω) | Iyakance wutar LED, guzur mai ƙaramin daraja | Guzurin LED 220 Ω, kebul na coaxial 50 Ω |
| 1-100 kΩ | Kiloohm (kΩ) | Guzur na yau da kullun, pull-ups, rabon ƙarfin lantarki | Pull-up na 10 kΩ (mafi yawan), I²C na 4.7 kΩ |
| 1-100 MΩ | Megaohm (MΩ) | Shigarwa masu babban juriya, gwajin kariya | Shigarwar multimeter na 10 MΩ, binciken oscilloscope na 1 MΩ |
| 1-100 GΩ | Gigaohm (GΩ) | Kariya mai kyau, auna na'urar lantarki | Kariyar kebul >10 GΩ/km, auna tashoshin ion |
| 1-100 TΩ | Teraohm (TΩ) | Masu kariyar wuta kusan cikakke | Teflon >10 TΩ, iska kafin fashewa |
| ∞ Ω | Guzur mara iyaka | Mai kariyar wuta mai kyau, da'ira a buɗe | Mai kariyar wuta mai kyau na ka'ida, rata ta iska (kafin fashewa) |
Bayyana Tsarin Raka'o'i
Raka'o'in SI — Ohm
Ohm (Ω) shine rukunin SI da aka samo don guzur. An ba shi suna bayan Georg Ohm (dokar Ohm). An ayyana shi a matsayin V/A. prefixes daga femto zuwa tera sun rufe dukkan iyakoki masu amfani.
- 1 Ω = 1 V/A (ma'ana daidai)
- TΩ, GΩ don guzurin kariya
- kΩ, MΩ don guzur na yau da kullun
- mΩ, µΩ, nΩ don wayoyi, lambobi
Yaduwa — Siemens
Siemens (S) shine jujjuyawar ohm. 1 S = 1/Ω = 1 A/V. An ba shi suna bayan Werner von Siemens. A baya ana kiransa 'mho' (ohm a baya). Yana da amfani ga da'irori a layi daya.
- 1 S = 1/Ω = 1 A/V
- Tsohon suna: mho (℧)
- kS don guzur mai ƙaramin daraja
- mS, µS don matsakaicin yaduwa
Tsoffin Raka'o'in CGS
Abohm (EMU) da statohm (ESU) daga tsohon tsarin CGS. Ba a cika amfani da su a yau ba. 1 abΩ = 10⁻⁹ Ω (ƙarami). 1 statΩ ≈ 8.99×10¹¹ Ω (babba). Ohm na SI shine ma'auni.
- 1 abohm = 10⁻⁹ Ω = 1 nΩ (EMU)
- 1 statohm ≈ 8.99×10¹¹ Ω (ESU)
- Tsohon; ohm na SI yana da duniya
- A cikin tsoffin littattafan kimiyyar lissafi ne kawai
Kimiyyar Lissafin Guzur
Dokar Ohm
V = I × R (ƙarfin lantarki = wuta × guzur). Alaƙa ta asali. Ka san biyu, ka nemo na uku. Layi ɗaya don guzur. Watsawar wutar lantarki P = I²R = V²/R.
- V = I × R (ƙarfin lantarki daga wuta)
- I = V / R (wuta daga ƙarfin lantarki)
- R = V / I (guzur daga auna)
- Wutar lantarki: P = I²R = V²/R (zafi)
Jere & Layi daya
Jere: R_total = R₁ + R₂ + R₃... (ana ƙara guzur). Layi daya: 1/R_total = 1/R₁ + 1/R₂... (ana ƙara jujjuyawa). Don layi daya, yi amfani da yaduwa: G_total = G₁ + G₂.
- Jere: R_tot = R₁ + R₂ + R₃
- Layi daya: 1/R_tot = 1/R₁ + 1/R₂
- Yaduwar layi daya: G_tot = G₁ + G₂
- Guzurin daidai guda biyu a layi daya: R_tot = R/2
Guzurin & Yanayin
R = ρL/A (guzur = guzur × tsayi / yanki). Halayen abu (ρ) + yanayi. Wayoyi masu tsayi da sirara suna da babban R. Wayoyi gajeru da kauri suna da ƙaramin R. Jan ƙarfe: ρ = 1.7×10⁻⁸ Ω·m.
- R = ρ × L / A (dabarar yanayi)
- ρ = guzur (halayen abu)
- L = tsayi, A = yanki mai faɗi
- Jan ƙarfe ρ = 1.7×10⁻⁸ Ω·m
Ma'aunin Guzurin
| Yanayi | Guzur | Bayanan kula |
|---|---|---|
| Babban mai sarrafa wuta | 0 Ω | A ƙasa da yanayin zafi mai mahimmanci |
| Guzurin kwayoyin halitta | ~26 kΩ | h/e² = ma'aunin asali |
| Wayar jan ƙarfe (1m, 1mm²) | ~17 mΩ | Zafin jiki na ɗaki |
| Guzurin lamba | 10 µΩ - 1 Ω | Ya dogara da matsin lamba, kayan aiki |
| Guzurin wutar LED | 220-470 Ω | Da'irar 5V ta yau da kullun |
| Guzurin pull-up | 10 kΩ | Darajar da aka saba amfani da ita don dabaru na dijital |
| Shigarwar multimeter | 10 MΩ | Juriya ta shigarwar DMM ta yau da kullun |
| Jikin mutum (bushe) | 1-100 kΩ | Daga hannu zuwa hannu, fata bushe |
| Jikin mutum (jike) | ~1 kΩ | Fata jike, mai haɗari |
| Kariya (mai kyau) | >10 GΩ | Gwajin kariyar lantarki |
| Rata ta iska (1 mm) | >10¹² Ω | Kafin fashewa |
| Gilashi | 10¹⁰-10¹⁴ Ω·m | Mai kariyar wuta mai kyau |
| Teflon | >10¹³ Ω·m | Ɗaya daga cikin mafi kyawun masu kariyar wuta |
Dabi'un Guzurin da aka saba amfani da su
| Guzur | Lambar Launi | Amfani na yau da kullun | Wutar Lantarki ta yau da kullun |
|---|---|---|---|
| 10 Ω | Kasa-Baki-Baki | Auna wuta, wutar lantarki | 1-5 W |
| 100 Ω | Kasa-Baki-Kasa | Iyakance wuta | 1/4 W |
| 220 Ω | Ja-Ja-Kasa | Iyakance wutar LED (5V) | 1/4 W |
| 470 Ω | Rawa-Hoda-Kasa | Iyakance wutar LED | 1/4 W |
| 1 kΩ | Kasa-Baki-Ja | Amfani na gaba ɗaya, rabon ƙarfin lantarki | 1/4 W |
| 4.7 kΩ | Rawa-Hoda-Ja | Pull-up/down, I²C | 1/4 W |
| 10 kΩ | Kasa-Baki-Lemu | Pull-up/down (mafi yawan) | 1/4 W |
| 47 kΩ | Rawa-Hoda-Lemu | Shigarwar babban-Z, nuna son kai | 1/8 W |
| 100 kΩ | Kasa-Baki-Rawa | Babban juriya, lokaci | 1/8 W |
| 1 MΩ | Kasa-Baki-Kore | Babban juriya sosai | 1/8 W |
Amfani a Rayuwa ta Zahiri
Ilimin Lantarki & Da'irori
Guzur: 1 Ω zuwa 10 MΩ na yau da kullun. Pull-up/down: 10 kΩ na yau da kullun. Iyakance wuta: 220-470 Ω don LED. Rabon ƙarfin lantarki: iyakar kΩ. Guzur masu daidaito: 0.01% juriya.
- Guzur na yau da kullun: 1 Ω - 10 MΩ
- Pull-up/pull-down: 1-100 kΩ
- Iyakance wutar LED: 220-470 Ω
- Daidaito: 0.01% juriya akwai
Wutar Lantarki & Auna
Guzurin shunt: iyakar mΩ (auna wuta). Guzurin waya: µΩ zuwa mΩ a kowace mita. Guzurin lamba: µΩ zuwa Ω. Juriya ta kebul: 50-75 Ω (RF). Sanya ƙasa: <1 Ω ake buƙata.
- Shunt na wuta: 0.1-100 mΩ
- Waya: 13 mΩ/m (jan ƙarfe 22 AWG)
- Guzurin lamba: 10 µΩ - 1 Ω
- Coax: 50 Ω, 75 Ω na yau da kullun
Guzurin da ya wuce kima
Manyan masu sarrafa wuta: R = 0 daidai (a ƙasa da Tc). Masu kariyar wuta: iyakar TΩ (10¹² Ω). Fatar mutum: 1 kΩ - 100 kΩ (bushe). Lantarki na tsaye: auna GΩ. Iska: guzur mara iyaka (mai kariyar wuta mai kyau).
- Manyan masu sarrafa wuta: R = 0 Ω (T < Tc)
- Masu kariyar wuta: GΩ zuwa TΩ
- Jikin mutum: 1-100 kΩ (fata bushe)
- Rata ta iska: >10¹⁴ Ω (fashewa ~3 kV/mm)
Lissafin Juyawa da Sauri
Juyawar Sauri na SI Prefix
Kowane matakin prefix = ×1000 ko ÷1000. MΩ → kΩ: ×1000. kΩ → Ω: ×1000. Ω → mΩ: ×1000.
- MΩ → kΩ: ninka da 1,000
- kΩ → Ω: ninka da 1,000
- Ω → mΩ: ninka da 1,000
- A baya: raba da 1,000
Guzur ↔ Yaduwa
G = 1/R (yaduwa = 1/guzur). R = 1/G. 10 Ω = 0.1 S. 1 kΩ = 1 mS. 1 MΩ = 1 µS. Alaƙar jujjuyawa!
- G = 1/R (siemens = 1/ohms)
- 10 Ω = 0.1 S
- 1 kΩ = 1 mS
- 1 MΩ = 1 µS
Binciken Sauri na Dokar Ohm
R = V / I. Ka san ƙarfin lantarki da wuta, ka nemo guzur. 5V a 20 mA = 250 Ω. 12V a 3 A = 4 Ω.
- R = V / I (Ohms = Volts ÷ Amps)
- 5V ÷ 0.02A = 250 Ω
- 12V ÷ 3A = 4 Ω
- Ka tuna: raba ƙarfin lantarki da wuta
Yadda Juyawa ke Aiki
- Mataki na 1: Canza tushe → ohms ta amfani da ma'aunin toBase
- Mataki na 2: Canza ohms → abin da kake so ta amfani da ma'aunin toBase na abin da kake so
- Yaduwa: Yi amfani da jujjuyawa (1 S = 1/1 Ω)
- Binciken lafiya: 1 MΩ = 1,000,000 Ω, 1 mΩ = 0.001 Ω
- Ka tuna: Ω = V/A (ma'ana daga dokar Ohm)
Nassoshin Juyawa da aka saba amfani da su
| Daga | Zuwa | Ninka Da | Misali |
|---|---|---|---|
| Ω | kΩ | 0.001 | 1000 Ω = 1 kΩ |
| kΩ | Ω | 1000 | 1 kΩ = 1000 Ω |
| kΩ | MΩ | 0.001 | 1000 kΩ = 1 MΩ |
| MΩ | kΩ | 1000 | 1 MΩ = 1000 kΩ |
| Ω | mΩ | 1000 | 1 Ω = 1000 mΩ |
| mΩ | Ω | 0.001 | 1000 mΩ = 1 Ω |
| Ω | S | 1/R | 10 Ω = 0.1 S (jujjuyawa) |
| kΩ | mS | 1/R | 1 kΩ = 1 mS (jujjuyawa) |
| MΩ | µS | 1/R | 1 MΩ = 1 µS (jujjuyawa) |
| Ω | V/A | 1 | 5 Ω = 5 V/A (daidai) |
Misalai na Sauri
Matsalolin da aka warware
Iyakance wutar LED
Tushen 5V, LED yana buƙatar 20 mA kuma yana da ƙarfin lantarki na 2V. Wane guzur?
Raguwar ƙarfin lantarki = 5V - 2V = 3V. R = V/I = 3V ÷ 0.02A = 150 Ω. Yi amfani da guzur na 220 Ω na yau da kullun (mafi aminci, ƙaramin wuta).
Guzur a Layi daya
Guzurin 10 kΩ guda biyu a layi daya. Menene jimlar guzur?
Layi daya daidai: R_tot = R/2 = 10kΩ/2 = 5 kΩ. Ko: 1/R = 1/10k + 1/10k = 2/10k → R = 5 kΩ.
Watsawar wutar lantarki
12V a kan guzur na 10 Ω. Wuta nawa?
P = V²/R = (12V)² / 10Ω = 144/10 = 14.4 W. Yi amfani da guzur 15W+! Hakanan: I = 12/10 = 1.2A.
Kuskuren da ya kamata a guje wa
- **Rudani game da guzur a layi daya**: Guzurin 10 Ω guda biyu a layi daya ≠ 20 Ω! Shine 5 Ω (1/R = 1/10 + 1/10). Layi daya koyaushe yana rage jimlar R.
- **Matsayin wutar lantarki yana da mahimmanci**: Guzurin 1/4 W da 14 W na watsawa = hayaƙi! Lissafa P = V²/R ko P = I²R. Yi amfani da gefen aminci na 2-5×.
- **Ma'aunin zafin jiki**: Guzur yana canzawa da zafin jiki. Da'irori masu daidaito suna buƙatar guzur masu ƙaramin ma'aunin zafin jiki (<50 ppm/°C).
- **Haɗewar juriya**: Guzurin 5% da yawa na iya haifar da manyan kurakurai. Yi amfani da 1% ko 0.1% don rabon ƙarfin lantarki masu daidaito.
- **Guzurin lamba**: Kada ka yi watsi da guzurin haɗi a manyan wuta ko ƙananan ƙarfin lantarki. Tsabtace lamba, yi amfani da masu haɗin da suka dace.
- **Yaduwa don layi daya**: Ƙara guzur a layi daya? Yi amfani da yaduwa (G = 1/R). G_total = G₁ + G₂ + G₃. Ya fi sauƙi sosai!
Gaskiya masu ban sha'awa game da Guzur
Guzurin Kwayoyin Halitta shine 25.8 kΩ
Guzurin kwayoyin halitta h/e² ≈ 25,812.807 Ω shine ma'aunin asali. A ma'aunin kwayoyin halitta, guzur yana zuwa a cikin ninki na wannan darajar. Ana amfani da shi a cikin tasirin Quantum Hall don ma'aunin guzur masu daidaito.
Manyan masu sarrafa wuta ba su da Guzur
A ƙasa da yanayin zafi mai mahimmanci (Tc), manyan masu sarrafa wuta suna da R = 0 daidai. Wuta tana kwarara har abada ba tare da asara ba. Da zarar an fara, madauki mai sarrafa wuta yana riƙe wuta na shekaru ba tare da wutar lantarki ba. Yana ba da damar maganadisu masu ƙarfi (MRI, masu hanzarta barbashi).
Walƙiya tana haifar da Hanyar Plasma na wucin gadi
Guzurin tashar walƙiya yana faɗuwa zuwa ~1 Ω yayin bugawa. Iska yawanci tana da >10¹⁴ Ω, amma plasma mai ionized tana sarrafa wuta. Tashar tana zafi zuwa 30,000 K (sau 5 na saman rana). Guzur yana ƙaruwa yayin da plasma ke sanyaya, yana haifar da bugun jini da yawa.
Tasirin Fata yana Canza Guzurin AC
A manyan mitoci, wutar AC tana kwarara ne kawai a saman mai sarrafa wuta. Guzurin da ke aiki yana ƙaruwa da mitar. A 1 MHz, guzurin wayar jan ƙarfe yana da sau 100 fiye da DC! Yana tilasta injiniyoyin RF su yi amfani da wayoyi masu kauri ko masu sarrafa wuta na musamman.
Guzurin Jikin Mutum yana Canzawa sau 100
Fata bushe: 100 kΩ. Fata jike: 1 kΩ. Cikin jiki: ~300 Ω. Wannan shine dalilin da yasa girgizar lantarki ke kashewa a cikin bandakuna. 120 V a kan fata jike (1 kΩ) = 120 mA wuta—mai kisa. Karfin lantarki iri ɗaya, fata bushe (100 kΩ) = 1.2 mA—tsoratarwa.
Dabi'un Guzurin da aka saba amfani da su suna da Logarithmic
Jerin E12 (10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82) yana rufe kowace shekara goma a cikin matakai na ~20%. Jerin E24 yana ba da matakai na ~10%. E96 yana ba da ~1%. Dangane da ci gaban lissafi, ba na layi ba—ƙirƙira mai ban mamaki ta injiniyoyin lantarki!
Juyin Halittar Tarihi
1827
Georg Ohm ya wallafa V = IR. Dokar Ohm ta bayyana guzur a adadi. Da farko an ƙi ta daga al'ummar kimiyyar lissafi ta Jamus a matsayin 'yanar gizo na zato tsirara.'
1861
Ƙungiyar Burtaniya ta karɓi 'ohm' a matsayin rukunin guzur. An ayyana shi a matsayin guzurin ginshiƙin mercury mai tsawon 106 cm, faɗin 1 mm² a 0°C.
1881
Babban Taron Lantarki na Farko na Duniya ya ayyana ohm na zahiri. Ohm na doka = 10⁹ raka'o'in CGS. An ba shi suna bayan Georg Ohm (shekaru 25 bayan mutuwarsa).
1893
Babban Taron Lantarki na Duniya ya karɓi 'mho' (ohm a baya) don yaduwa. Daga baya an maye gurbinsa da 'siemens' a 1971.
1908
Heike Kamerlingh Onnes ya narkar da helium. Yana ba da damar gwajin kimiyyar lissafi a ƙananan zafin jiki. Ya gano babban sarrafa wuta a 1911 (guzur sifili).
1911
An gano babban sarrafa wuta! Guzurin mercury yana faɗuwa zuwa sifili a ƙasa da 4.2 K. Ya kawo sauyi ga fahimtar guzur da kimiyyar lissafin kwayoyin halitta.
1980
An gano tasirin Quantum Hall. An ƙididdige guzur a cikin raka'o'in h/e² ≈ 25.8 kΩ. Yana ba da ma'aunin guzur mai daidaito sosai (daidai zuwa kashi 1 cikin 10⁹).
2019
Sake ayyana SI: An ayyana ohm yanzu daga ma'aunin asali (cajin farko e, ma'aunin Planck h). 1 Ω = (h/e²) × (α/2) inda α shine ma'aunin tsari mai kyau.
Shawarwari na Kwararru
- **Sauri kΩ zuwa Ω**: Ninka da 1000. 4.7 kΩ = 4700 Ω.
- **Guzurin daidai a layi daya**: R_total = R/n. Guzurin 10 kΩ guda biyu = 5 kΩ. Guzurin 15 kΩ guda uku = 5 kΩ.
- **Dabi'u na yau da kullun**: Yi amfani da jerin E12/E24. 4.7, 10, 22, 47 kΩ sune mafi yawan.
- **Bincika matsayin wutar lantarki**: P = V²/R ko I²R. Yi amfani da gefen 2-5× don dogaro.
- **Dabarar lambar launi**: Kasa(1)-Baki(0)-Ja(×100) = 1000 Ω = 1 kΩ. Layin zinariya = 5%.
- **Yaduwa don layi daya**: G_total = G₁ + G₂. Ya fi sauƙi sosai fiye da dabarar 1/R!
- **Rubutun kimiyya ta atomatik**: Dabi'un da suka gaza 1 µΩ ko sun wuce 1 GΩ suna bayyana a cikin rubutun kimiyya don sauƙin karantawa.
Cikakken Nassoshin Raka'o'i
Raka'o'in SI
| Sunan Rukuni | Alama | Daidai da Ohm | Bayanan kula na Amfani |
|---|---|---|---|
| ohm | Ω | 1 Ω (base) | Rukunin SI da aka samo; 1 Ω = 1 V/A (daidai). An ba shi suna bayan Georg Ohm. |
| teraohm | TΩ | 1.0 TΩ | Guzurin kariya (10¹² Ω). Masu kariyar wuta masu kyau, auna na'urar lantarki. |
| gigaohm | GΩ | 1.0 GΩ | Babban guzurin kariya (10⁹ Ω). Gwajin kariya, auna zubewa. |
| megaohm | MΩ | 1.0 MΩ | Da'irori masu babban juriya (10⁶ Ω). Shigarwar multimeter (yawanci 10 MΩ). |
| kiloohm | kΩ | 1.0 kΩ | Guzur na yau da kullun (10³ Ω). Guzurin pull-up/down, amfani na gaba ɗaya. |
| milliohm | mΩ | 1.0000 mΩ | Ƙaramin guzur (10⁻³ Ω). Guzurin waya, guzurin lamba, shunts. |
| microohm | µΩ | 1.0000 µΩ | Guzur mai ƙaramin daraja (10⁻⁶ Ω). Guzurin lamba, auna daidai. |
| nanoohm | nΩ | 1.000e-9 Ω | Guzur mai ƙaramin daraja (10⁻⁹ Ω). Manyan masu sarrafa wuta, na'urorin kwayoyin halitta. |
| picoohm | pΩ | 1.000e-12 Ω | Guzurin ma'aunin kwayoyin halitta (10⁻¹² Ω). Auna daidai, bincike. |
| femtoohm | fΩ | 1.000e-15 Ω | Iyakar kwayoyin halitta ta ka'ida (10⁻¹⁵ Ω). Amfani da bincike ne kawai. |
| volt a kowace ampere | V/A | 1 Ω (base) | Daidai da ohm: 1 Ω = 1 V/A. Yana nuna ma'ana daga dokar Ohm. |
Gudanarwa
| Sunan Rukuni | Alama | Daidai da Ohm | Bayanan kula na Amfani |
|---|---|---|---|
| siemens | S | 1/ Ω (reciprocal) | Rukunin SI na yaduwa (1 S = 1/Ω = 1 A/V). An ba shi suna bayan Werner von Siemens. |
| kilosiemens | kS | 1/ Ω (reciprocal) | Yaduwar guzur mai ƙaramin daraja (10³ S = 1/mΩ). Manyan masu sarrafa wuta, kayan aiki masu ƙaramin R. |
| millisiemens | mS | 1/ Ω (reciprocal) | Matsakaicin yaduwa (10⁻³ S = 1/kΩ). Yana da amfani ga lissafin layi daya a cikin iyakar kΩ. |
| microsiemens | µS | 1/ Ω (reciprocal) | Ƙaramar yaduwa (10⁻⁶ S = 1/MΩ). Babban juriya, auna kariya. |
| mho | ℧ | 1/ Ω (reciprocal) | Tsohon suna na siemens (℧ = ohm a baya). 1 mho = 1 S daidai. |
Na gargajiya & na Kimiyya
| Sunan Rukuni | Alama | Daidai da Ohm | Bayanan kula na Amfani |
|---|---|---|---|
| abohm (EMU) | abΩ | 1.000e-9 Ω | Rukunin CGS-EMU = 10⁻⁹ Ω = 1 nΩ. Tsohon rukunin lantarki. |
| statohm (ESU) | statΩ | 898.8 GΩ | Rukunin CGS-ESU ≈ 8.99×10¹¹ Ω. Tsohon rukunin lantarki na tsaye. |
Tambayoyi da Amsoshi
Menene bambanci tsakanin guzur da yaduwa?
Guzur (R) yana hana kwararar wuta, ana auna shi da ohms (Ω). Yaduwa (G) shine jujjuyawa: G = 1/R, ana auna shi da siemens (S). Babban guzur = ƙaramar yaduwa. Suna bayyana abu ɗaya daga bangarori daban-daban. Yi amfani da guzur don da'irori a jere, yaduwa don layi daya (lissafi mai sauƙi).
Me yasa guzur ke ƙaruwa da zafin jiki a cikin ƙarfe?
A cikin ƙarfe, lantarki suna kwarara ta cikin tsarin kristal. Babban zafin jiki = atam suna rawar jiki da yawa = ƙarin karo da lantarki = babban guzur. Ƙarfe na yau da kullun suna da +0.3 zuwa +0.6% a kowace °C. Jan ƙarfe: +0.39%/°C. Wannan shine 'ingantaccen ma'aunin zafin jiki'. Rabin masu sarrafa wuta suna da tasiri akasin haka (ma'auni mara kyau).
Yaya zan lissafa jimlar guzur a layi daya?
Yi amfani da jujjuyawa: 1/R_total = 1/R₁ + 1/R₂ + 1/R₃... Don guzur guda biyu daidai: R_total = R/2. Hanyar da ta fi sauƙi: yi amfani da yaduwa! G_total = G₁ + G₂ (kawai ƙara). Sannan R_total = 1/G_total. Misali: 10 kΩ da 10 kΩ a layi daya = 5 kΩ.
Menene bambanci tsakanin juriya da ma'aunin zafin jiki?
Juriya = bambancin masana'anta (±1%, ±5%). Kuskure tsayayye a zafin jiki na ɗaki. Ma'aunin zafin jiki (tempco) = nawa R ke canzawa a kowace °C (ppm/°C). 50 ppm/°C yana nufin canjin 0.005% a kowace digiri. Dukansu suna da mahimmanci ga da'irori masu daidaito. Guzur masu ƙaramin tempco (<25 ppm/°C) don aiki mai karko.
Me yasa dabi'un guzur da aka saba amfani da su suna da logarithmic (10, 22, 47)?
Jerin E12 yana amfani da matakai na ~20% a ci gaban lissafi. Kowane daraja yana da ≈1.21× na baya (tushen 12 na 10). Wannan yana tabbatar da ɗaukar hoto daidai a duk faɗin shekaru goma. Tare da juriya na 5%, dabi'u masu kusanci suna mamayewa. Zane mai ban mamaki! E24 (matakai 10%), E96 (matakai 1%) suna amfani da ka'ida iri ɗaya. Yana sa rabon ƙarfin lantarki da matattara su zama masu iya faɗi.
Shin guzur zai iya zama mara kyau?
A cikin abubuwan da ba sa aiki, a'a—guzur koyaushe yana da inganci. Koyaya, da'irori masu aiki (masu ƙarfafa aiki, transistors) na iya haifar da halayen 'guzur mara kyau' inda ƙara ƙarfin lantarki ke rage wuta. Ana amfani da shi a cikin masu juyawa, masu ƙarfafawa. Diodes na rami a zahiri suna nuna guzur mara kyau a cikin wasu iyakokin ƙarfin lantarki. Amma ainihin R da ba sa aiki koyaushe > 0.
Cikakken Jagoran Kayan Aiki
Dukan kayan aiki 71 da ke akwai a kan UNITS