Tusaale Su'aalaha Doodda ee ku saabsan Noocyada Iska caabinta
Iska caabintu waa fikrad aasaasi ah oo ku jirta electromagnetism waana qayb muhiim ah oo ka mid ah daraasadda fiisigiska, gaar ahaan wareegyada korontada. Maqaalkani wuxuu ka hadli doonaa dhowr tusaale oo ku saabsan dhibaatooyinka iska caabinta, oo ay ku jiraan sharraxaad iyo xalal.
Waa maxay Nooca Caqabadda?
Iska caabinta (\(\rho\)) waa cabbir lagu cabbiro hantida walaxda taasoo go'aamisa inta ay carqaladeynayso socodka qulqulka korantada. Iska caabinta waxaa lagu cabbiraa mitirrada ohm (Ω·m). Inta uu le'eg yahay iska caabinta walaxda, ayay sii adkaanaysaa in qulqulka korontada uu dhex maro.
Qaacidada aasaasiga ah ee lagu xisaabinayo iska caabbinta (\(R\)) ee ku jirta koronto-wade dhererkiisu yahay (\(L\)) iyo aagga isgoyska (\(A\)) waa:
\[ R = \rho \frac{L}{A} \]
Su'aalo iyo Doodo Tusaale ah
Su'aal Tusaale 1aad:
Iyada oo la siinayo silig naxaas ah oo dhererkiisu yahay 2 mitir iyo aag isgoys ah oo ah 0,5 mm\(^2\). Iska caabbinta gaarka ah ee naxaasta waa \(1.68 \jeer 10^{-8} \; \Omega \cdot m\). Xisaabi iska caabbinta siligga.
Dood:
1. Bedka isgoyska laga bilaabo mm\(^2\) una beddel m\(^2\):
\[ 0.5 \; \qoraal{mm}^2 = 0.5 \jeer 10^{-6} \; \qoraal{m}^2 \]
2. Isticmaal qaacidada \( R = \rho \frac{L}{A} \):
\[ R = (1.68 \jeer 10^{-8}) \frac{2}{0.5 \jeer 10^{-6}} \]
\[ R = (1.68 \jeer 10^{-8}) \jeer (4 \jeer 10^{6}) \]
\[ R = 6.72 \jeer 10^{-2} \; \Omega\]
Markaa, iska caabbinta fiilada naxaasta ah waa 0.0672 Ω.
Su'aal Tusaale 2aad:
Fiilada aluminiumku waxay leedahay iska caabin dhan \(2.82 \ jeer 10^{-8} \; \Omega \cdot m\). Haddii dhererka siliggu yahay 10 mitir oo uu leeyahay iska caabin dhan 0.0564 Ω, waa maxay aagga isgoyska ee siligga?
Dood:
1. Waa la yaqaan:
– Iska caabin gaar ah, \(\rho = 2.82 \times 10^{-8} \; \Omega \cdot m\)
– Dhererka, \( L = 10 \; \qoraalka{m} \)
– Iska caabinta \( R = 0.0564 \; \Omega \)
2. Adeegso qaacidada \( R = \rho \frac{L}{A} \) si aad u hesho aagga isgoyska ah:
\[ R = \rho \frac{L}{A} \]
\[ 0.0564 = 2.82 \jeer 10^{-8} \frac{10}{A} \]
\[ 0.0564 = 2.82 \jeer 10^{-7} \frac{1}{A} \]
\[ A = \frac{2.82 \jeer 10^{-7}}{0.0564} \]
\[ A = 5 jeer 10^{-6} \; \qoraalka{m}^2 \]
Markaa, aagga isgoyska ee fiilada aluminiumku waa \(5 \times 10^{-6} \; \text{m}^2\).
Su'aal Tusaale 3aad:
Ka warran haddii aan isku xirno laba fiilooyin oo kala duwan oo taxane ah iyo kuwo is barbar socda, maxay tahay saameynta iska caabbinta guud iyo sida loo xisaabiyo? Bal aan ka soo qaadno inaan haysanno silig naxaas ah iyo silig aluminium ah, mid walbana dhererkiisu yahay 5 mitir iyo aag isgoys ah oo ah 1 mm\(^2\). Iska caabbinta gaarka ah ee naxaasta waa \(1.68 \times 10^{-8} \; \Omega \cdot m\) iyo aluminium waa \(2.82 \times 10^{-8} \; \Omega \cdot m\).
Dood:
1. Xisaabi iska caabinta silig kasta.
– Silig naxaas ah:
\[ R_{\text{copper}} = \rho \frac{L}{A} = (1.68 \jeer 10^{-8}) \frac{5}{1 \jeer 10^{-6}} \]
\[ R_{\text{copper}} = 8.4 \jeer 10^{-2} \; \Omega \]
– Fiilo aluminium ah:
\[ R_{\text{aluminium}} = \rho \frac{L}{A} = (2.82 \jeer 10^{-8}) \frac{5}{1 \jeer 10^{-6}} \]
\[ R_{\text{aluminium}} = 1.41 \jeer 10^{-1} \; \Omega\]
2. Haddii si taxane ah loogu xidho:
\[ R_{\text{total}} = R_{\text{copper}} + R_{\text{aluminium}} \]
\[ R_{\text{wadarta}} = 8.4 \jeer 10^{-2} + 1.41 \jeer 10^{-1} \]
\[ R_{\text{total}} = 0.224 \; \Omega\]
3. Haddii isku xiran yahay si is barbar socda:
\[ \frac{1}{R_{\text{total}}} = \frac{1}{R_{\text{copper}}} + \frac{1}{R_{\text{aluminum}}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{8.4 \jeer 10^{-2}} + \frac{1}{1.41 \jeer 10^{-1}} \]
\[ \frac{1}{R_{\text{total}}} = \frac{1}{0.084} + \frac{1}{0.141} \]
\[ \frac{1}{R_{\text{total}}} = 11.905 + 7.092 \]
\[ \frac{1}{R_{\text{total}}} = 18.997 \]
\[ R_{\text{total}} = \frac{1}{18.997} \]
\[ R_{\text{total}} \qiyaastii 0.0526 \; \Omega\]
Markaa, iska caabbinta guud marka laba fiilooyin isku xiran yihiin waa 0.224 Ω marka isku xiran yihiinna waa 0.0526 Ω.
Gabagabo
Iska caabbinta walaxdu waa muhiim marka la go'aaminayo iska caabbinta guud ee koontaroolaha. Marka la ogaado iska caabbinta, dhererka, iyo aagga isgoyska ah, waxaan xisaabin karnaa iska caabbinta walax iyadoo la adeegsanayo qaacido fudud. Tusaalooyinka kor ku xusan waxay muujinayaan in fahamka iyo xisaabinta iska caabbinta ay door muhiim ah ka ciyaaraan naqshadeynta iyo falanqaynta wareegyada korantada. Iyadoo la adeegsanayo ku dhaqanka, fahamkeenna fikradda iska caabbinta ayaa sii qoto dheeraan doonta oo noqon doonta mid khuseeya xaalado kala duwan.
Iska caabinta iyo xisaabinteeda la xiriirta ayaa aasaas u ah codsiyo badan oo wax ku ool ah oo ku saabsan injineernimada iyo fiisigiska. Sidaa darteed, faham adag oo ku saabsan fikraddan ayaa lagama maarmaan u ah qof kasta oo ku lug leh meelahan.
