Isibonelo Semibuzo Yengxoxo Ngezinhlobo Zokumelana
Ukumelana nogesi kuwumqondo oyisisekelo ku-electromagnetism futhi kuyingxenye ebalulekile yokutadisha i-physics, ikakhulukazi kumasekethe kagesi. Lesi sihloko sizoxoxa ngezibonelo eziningana zezinkinga zokumelana, eziphelele ngezincazelo nezixazululo.
Luyini Uhlobo Lwesithiyo?
Ukumelana (\(\rho\)) kuyisilinganiso sempahla yento enquma ukuthi iphazamisa kangakanani ukuhamba kwamandla kagesi. Ukumelana kukalwa ngama-ohm-meters (Ω·m). Uma ukumelana kwento kuphakeme, kuba nzima kakhulu ukuthi amandla kagesi adlule kuyo.
Ifomula eyisisekelo yokubala ukumelana (\(R\)) kumqhubi onobude (\(L\)) kanye nendawo enqamulayo (\(A\)) yile:
\[ R = \rho \frac{L}{A} \]
Imibuzo Eyisibonelo Nengxoxo
Isibonelo Sombuzo 1:
Uma unikezwe ucingo lwethusi olunobude obungamamitha ama-2 kanye nendawo enqamulayo engu-0,5 mm\(^2\). Ukumelana okuqondile kwethusi kungu-\(1.68 \times 10^{-8} \; \Omega \cdot m\). Bala ukumelana kwentambo.
Ingxoxo:
1. Guqula indawo enqamulayo kusuka ku-mm\(^2\) kuya ku-m\(^2\):
\[ 0.5 \; \umbhalo{mm}^2 = 0.5 \izikhathi ezingu-10^{-6} \; \umbhalo{m}^2 \]
2. Sebenzisa ifomula \( R = \rho \frac{L}{A} \):
\[ R = (1.68 \izikhathi ezingu-10^{-8}) \frac{2}{0.5 \izikhathi ezingu-10^{-6}} \]
\[ R = (1.68 \izikhathi ezingu-10^{-8}) \izikhathi (4 \izikhathi ezingu-10^{6}) \]
\[ R = 6.72 \izikhathi ezingu-10^{-2} \; \Omega\]
Ngakho-ke, ukumelana kwentambo yethusi kungu-0.0672 Ω.
Isibonelo Sombuzo 2:
Intambo ye-aluminium inokumelana okungu-\(2.82 \times 10^{-8} \; \Omega \cdot m\). Uma ubude bentambo bungamamitha ayi-10 futhi bunokumelana okungu-0.0564 Ω, iyini indawo yentambo enqamulayo?
Ingxoxo:
1. Kuyaziwa:
– Ukumelana okuqondile, \(\rho = 2.82 \times 10^{-8} \; \Omega \cdot m\)
– Ubude, \( L = 10 \; \text{m} \)
– Ukumelana \( R = 0.0564 \; \Omega \)
2. Sebenzisa ifomula \( R = \rho \frac{L}{A} \) ukuthola indawo enqamulayo:
\[ R = \rho \frac{L}{A} \]
\[ 0.0564 = 2.82 \izikhathi ezingu-10^{-8} \frac{10}{A} \]
\[ 0.0564 = 2.82 \izikhathi ezingu-10^{-7} \frac{1}{A} \]
\[ A = \frac{2.82 \times 10^{-7}}{0.0564} \]
\[ A = 5 \izikhathi 10^{-6} \; \umbhalo{m}^2 \]
Ngakho-ke, indawo enqamula ingxenye yentambo ye-aluminiyamu ingu-\(5 \times 10^{-6} \; \text{m}^2\).
Isibonelo Sombuzo 3:
Kuthiwani uma sixhuma izintambo ezimbili ezihlukene zomqhubi ngochungechunge nangokuhambisana, uyini umphumela ekumelaneni okuphelele nokuthi singakubala kanjani? Ake sithi sinentambo yethusi kanye nentambo ye-aluminiyamu, ngayinye inobude obungamamitha ama-5 kanye nendawo enqamulayo engu-1 mm\(^2\). Ukumelana okuqondile kwethusi kungu-\(1.68 \times 10^{-8} \; \Omega \cdot m\) kanti i-aluminiyamu ingu-\(2.82 \times 10^{-8} \; \Omega \cdot m\).
Ingxoxo:
1. Bala ukumelana kwentambo ngayinye.
– Ucingo lwethusi:
\[ R_{\text{copper}} = \rho \frac{L}{A} = (1.68 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{copper}} = 8.4 \times 10^{-2} \; \Omega \]
– Ucingo lwe-aluminium:
\[ R_{\text{aluminium}} = \rho \frac{L}{A} = (2.82 \times 10^{-8}) \frac{5}{1 \times 10^{-6}} \]
\[ R_{\text{aluminium}} = 1.41 \times 10^{-1} \; \Omega\]
2. Uma kuxhunywe ochungechungeni:
\[ R_{\text{total}} = R_{\text{copper}} + R_{\text{aluminium}} \]
\[ R_{\text{total}} = 8.4 \times 10^{-2} + 1.41 \times 10^{-1} \]
\[ R_{\text{total}} = 0.224 \; \Omega\]
3. Uma kuxhunywe ngokuhambisana:
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{copper}}} + \frac{1}{R_{\text{aluminium}}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{8.4 \times 10^{-2}} + \frac{1}{1.41 \times 10^{-1}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{0.084} + \frac{1}{0.141} \]
\[ \frac{1}{R_{\text{total}}} = 11.905 + 7.092 \]
\[ \frac{1}{R_{\text{total}}} = 18.997 \]
\[ R_{\text{total}} = \frac{1}{18.997} \]
\[ R_{\text{total}} \cishe 0.0526 \; \Omega\]
Ngakho-ke, ukumelana okuphelele lapho izintambo ezimbili zixhunywe ochungechungeni kungu-0.224 Ω kanti uma zixhunywe ngokuhambisana kungu-0.0526 Ω.
Isiphetho
Ukumelana kwezinto kubalulekile ekunqumeni ukumelana okuphelele komqhubi. Ngokwazi ukumelana, ubude, kanye nendawo enqamulayo, singabala ukumelana kwezinto sisebenzisa ifomula elula. Izibonelo ezingenhla zibonisa ukuthi ukuqonda nokubala ukumelana kudlala indima ebalulekile ekwakhiweni nasekuhlaziyweni kwezifunda zikagesi. Ngokuzijwayeza, ukuqonda kwethu umqondo wokumelana kuzojula futhi kusebenze ezimweni ezahlukene.
Ukumelana kanye nokubala okuhambisana nakho kubalulekile ekusetshenzisweni okuningi okusebenzayo kobunjiniyela kanye nefiziksi. Ngakho-ke, ukuqonda okuqinile kwalomqondo kubalulekile kunoma ubani ohilelekile kule mikhakha.
