Chitsanzo cha Mafunso Okambirana pa Mitundu ya Kukana
Kukana mphamvu ndi lingaliro lofunikira mu maginito amagetsi komanso gawo lofunikira pakuphunzira za sayansi ya fizikisi, makamaka m'mabwalo amagetsi. Nkhaniyi ikambirana zitsanzo zingapo za mavuto okana mphamvu, ndi mafotokozedwe ndi mayankho.
Kodi Mtundu wa Cholepheretsa ndi Chiyani?
Kukana (\(\rho\)) ndi muyeso wa katundu wa chinthu chomwe chimazindikira kuchuluka kwa momwe chimalepheretsa kuyenda kwa magetsi. Kukana kumayesedwa mu ohm-meters (Ω·m). Kukana kwa chinthu kukakhala kwakukulu, kumakhala kovuta kuti magetsi adutsemo.
Fomula yoyambira yowerengera kukana (\(R\)) mu kondakitala yokhala ndi kutalika (\(L\)) ndi dera lopingasa (\(A\)) ndi iyi:
\[R = \rho \frac{L}{A} \]
Mafunso ndi Kukambirana Zitsanzo
Chitsanzo cha Funso 1:
Popeza waya wamkuwa ndi wautali mamita awiri ndi malo opingasa a 0,5 mm\(^2\). Kukana kwapadera kwa mkuwa ndi \(1.68 \times 10^{-8} \; \Omega \cdot m\). Werengani kukana kwa waya.
Kukambirana:
1. Sinthani dera lopingasa kuchokera ku mm\(^2\) kukhala m\(^2\):
\[ 0.5 \; \text{mm}^2 = 0.5 \times 10^{-6} \; \text{m}^2 \]
2. Gwiritsani ntchito fomula \( R = \rho \frac{L}{A} \):
\[ R = (1.68 \nthawi 10^{-8}) \frac{2}{0.5 \nthawi 10^{-6}} \]
\[ R = (1.68 \nthawi 10^{-8}) \nthawi (4 \nthawi 10^{6}) \]
\[ R = 6.72 \nthawi 10^{-2} \; \Omega\]
Kotero, kukana kwa waya wamkuwa ndi 0.0672 Ω.
Chitsanzo cha Funso 2:
Waya wa aluminiyamu uli ndi kukana kwa \(2.82 \times 10^{-8} \; \Omega \cdot m\). Ngati kutalika kwa waya ndi mamita 10 ndipo kuli kukana kwa 0.0564 Ω, kodi dera lopingasa la waya ndi lotani?
Kukambirana:
1. Zimadziwika kuti:
– Kukana kwapadera, \(\rho = 2.82 \times 10^{-8} \; \Omega \cdot m\)
– Kutalika, \( L = 10 \; \text{m} \)
– Kukana \( R = 0.0564 \; \Omega \)
2. Gwiritsani ntchito fomula \( R = \rho \frac{L}{A} \) kuti mupeze dera lopingasa:
\[R = \rho \frac{L}{A} \]
\[ 0.0564 = 2.82 \nthawi 10^{-8} \frac{10}{A} \]
\[ 0.0564 = 2.82 \nthawi 10^{-7} \frac{1}{A} \]
\[ A = \frac{2.82 \times 10^{-7}}{0.0564} \]
\[ A = 5 \nthawi 10^{-6} \; \malemba{m}^2 \]
Kotero, dera lozungulira la waya wa aluminiyamu ndi \(5 \times 10^{-6} \; \text{m}^2\).
Chitsanzo cha Funso 3:
Nanga bwanji ngati titalumikiza mawaya awiri osiyana a conductor motsatizana komanso motsatizana, kodi zotsatira zake zimakhala zotani pa kukana konse ndipo tingakuwerengere bwanji? Tiyerekeze kuti tili ndi waya wamkuwa ndi waya wa aluminiyamu, iliyonse ili ndi kutalika kwa mamita 5 ndi dera lopingasa la 1 mm\(^2\). Kukana kwapadera kwa mkuwa ndi \(1.68 \times 10^{-8} \; \Omega \cdot m\) ndipo aluminiyamu ndi \(2.82 \times 10^{-8} \; \Omega \cdot m\).
Kukambirana:
1. Werengani kukana kwa waya uliwonse.
- Waya wa mkuwa:
\[ R_{\text{copper}} = \rho \frac{L}{A} = (1.68 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{copper}} = 8.4 \times 10^{-2} \; \Omega \]
- Waya wa aluminiyamu:
\[ R_{\text{aluminium}} = \rho \frac{L}{A} = (2.82 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{aluminium}} = 1.41 \times 10^{-1} \; \Omega\]
2. Ngati zalumikizidwa motsatizana:
\[ R_{\text{total}} = R_{\text{copper}} + R_{\text{aluminium}} \]
\[ R_{\text{total}} = 8.4 \times 10^{-2} + 1.41 \times 10^{-1} \]
\[ R_{\text{total}} = 0.224 \; \Omega\]
3. Ngati zalumikizidwa motsatizana:
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{copper}}} + \frac{1}{R_{\text{aluminium}}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{8.4 \times 10^{-2}} + \frac{1}{1.41 \times 10^{-1}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{0.084} + \frac{1}{0.141} \]
\[ \frac{1}{R_{\text{total}}} = 11.905 + 7.092 \]
\[ \frac{1}{R_{\text{total}}} = 18.997 \]
\[ R_{\text{total}} = \frac{1}{18.997} \]
\[ R_{\text{total}} \pafupifupi 0.0526 \; \Omega\]
Kotero, kukana konse pamene mawaya awiri alumikizidwa motsatizana ndi 0.224 Ω ndipo pamene alumikizidwa motsatizana ndi 0.0526 Ω.
Mapeto
Kukana kwa chinthu n'kofunika kwambiri podziwa kukana konse kwa kondakitala. Podziwa kukana, kutalika, ndi dera lodutsa, titha kuwerengera kukana kwa chinthu pogwiritsa ntchito njira yosavuta. Zitsanzo zomwe zili pamwambapa zikuwonetsa kuti kumvetsetsa ndi kuwerengera kukana kumachita gawo lofunika kwambiri pakupanga ndi kusanthula mabwalo amagetsi. Ndi machitidwe, kumvetsetsa kwathu lingaliro la kukana kudzakula ndikugwiritsidwa ntchito m'malo osiyanasiyana.
Kukana mphamvu ndi kuwerengera komwe kumagwirizana nako ndikofunikira kwambiri pakugwiritsa ntchito zinthu zambiri zothandiza mu uinjiniya ndi sayansi ya sayansi. Chifukwa chake, kumvetsetsa bwino lingaliro ili ndikofunikira kwa aliyense amene akuchita nawo magawo awa.
