Mehlala ea Lipotso Tse Buisanang ka Li-Capacitor tsa Parallel Plate
Pendahuluan
Li-capacitor ke likarolo tsa bohlokoa tsa elektroniki tse bolokang le ho lokolla matla ka mokhoa oa tjhaja ea motlakase. Li-capacitor tsa parallel-plate ke mofuta o bonolo ka ho fetisisa le o sebelisoang haholo. Sengoloa sena se tla akaretsa mehlala e 'maloa le lipuisano tse amanang le li-capacitor tsa parallel-plate ho fana ka kutloisiso e tebileng ea mohopolo le lits'ebetso tsa tsona.
Ho Utloisisa Li-Capacitors tsa Parallel Plate
Capacitor ea poleiti e tšoanang e na le lipoleiti tse peli tse tsamaisang motlakase tse arotsoeng ke dielectric, e leng thepa e sireletsang mocheso e eketsang bokhoni ba ho boloka tjhaja ea motlakase. Capacitance (C) ea capacitor ea poleiti e tšoanang e ka baloa ho sebelisoa mokhoa o latelang:
\[ C = \frac{\varepsilon A}{d} \]
Di mana:
– \( \varepsilon \) ke tumello ea thepa ea dielectric,
– \( A \) ke sebaka se ka holimo sa puck,
– \( d \) ke sebaka se pakeng tsa dikotwana tse pedi.
Foromo ena e bonts'a hore capacitance ea capacitor ea poleiti e tsamaeang ka tsela e ts'oanang e lekana ka ho toba le sebaka sa poleiti le permittivity ea dielectric, 'me e lekana ka tsela e fapaneng le sebaka se pakeng tsa lipoleiti.
Lipotso tsa Mehlala le Puisano
Mohlala oa Potso ea 1: Ho Bala Bokhoni
Potso:
Lipoleiti tse peli tsa tšepe ka 'ngoe tse nang le sebaka sa bokaholimo ba 0.02 m² li arotsoe ka sebaka sa 0.001 m ho sebelisoa moea e le dielectric (permittivity \(\varepsilon_{0} = 8.85 \times 10^{-12} \, F/m\)). Bala capacitance ea capacitor.
Puisano:
Sebelisa foromo ea capacitance bakeng sa capacitor ea poleiti e bapileng.
\[ C = \frac{\varepsilon_{0} A}{d} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ \varepsilon_{0} = 8.85 \makgetlo a 10^{-12} \, F/m \]
\[ A = 0.02 \, m² \]
\[d = 0.001 \, m \]
\[ C = \frac{(8.85 \times 10^{-12} \, F/m) \times 0.02 \, m²}{0.001 \, m} \]
\[ C = \frac{1.77 \makgetlo a 10^{-13} \, F}{0.001 \, m} \]
\[ C = 1.77 \makgetlo a 10^{-10} \, F \]
Kahoo, capacitance ea capacitor ea poleiti e tšoanang ke \( 1.77 \times 10^{-10} \, F \) kapa 177 pF (picofarads).
Mohlala oa Potso ea 2: Ho Bala Matla a Bolokiloeng
Potso:
Haeba capacitor ho tsoa ho Mohlala oa Potso ea 1 e tjhajwa ho fihlela ho 50 V, ke matla a makae a bolokiloeng ka har'a capacitor?
Puisano:
Matla (\(U\)) a bolokiloeng ka har'a capacitor a ka baloa ho sebelisoa foromo:
\[ U = \frac{1}{2} CV^2 \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ C = 1.77 \makgetlo a 10^{-10} \, F \]
\[ V = 50 \, V \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times (50 \, V)^2 \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times 2500 \, V^2 \]
\[ U = \frac{1.77 \times 10^{-10} \, F \times 2500 \, V^2}{2} \]
\[ U = \frac{4.425 \makgetlo a 10^{-7} \, J}{2} \]
\[ U = 2.2125 \makgetlo a 10^{-7} \, J \]
Kahoo, matla a bolokiloeng ka har'a capacitor ke \( 2.2125 \times 10^{-7} \, J \) kapa 221.25 nJ (nanoujoule).
Mohlala oa 3: Ho Bala Phetoho ea Bokhoni
Potso:
Capacitor ea poleiti e bapileng e na le sebaka sa poleiti sa 0.01 m² 'me e arotsoe ka sebaka sa 0.002 m. Thepa ea dielectric e sebelisitsoeng ke mica e nang le tumello ea \( \varepsilon = 6 \times \varepsilon_{0} \). Bala capacitance ea capacitor.
Puisano:
Tumello ea thepa ea dielectric ea mica ke:
\[ \varepsilon = 6 \ linako \varepsilon_{0} \]
Sebelisa foromo ea capacitance bakeng sa capacitor ea poleiti e tšoanang:
\[ C = \frac{\varepsilon A}{d} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ \varepsilon_{0} = 8.85 \makgetlo a 10^{-12} \, F/m \]
\[ A = 0.01 \, m² \]
\[d = 0.002 \, m \]
\[ \varepsilon = 6 \ka makhetlo a 8.85 \ka makhetlo a 10^{-12} \, F/m = 53.1 \ka makhetlo a 10^{-12} \, F/m \]
\[ C = \frac{53.1 \times 10^{-12} \, F/m \times 0.01 \, m²}{0.002 \, m} \]
\[ C = \frac{5.31 \makgetlo a 10^{-13} \, F}{0.002 \, m} \]
\[ C = 2.655 \makgetlo a 10^{-10} \, F \]
Kahoo, capacitance ea capacitor e nang le mica e le thepa ea dielectric ke \( 2.655 \times 10^{-10} \, F \) kapa 265.5 pF.
Mohlala oa Potso ea 4: Ho Bala Bokhoni ba Kopano
Potso:
Li-capacitor tse peli tsa poleiti tse bapileng, e 'ngoe le e 'ngoe e nang le capacitance ea 100 pF le 200 pF, li hokahane ka tatellano. Capacitance eohle ke efe?
Puisano:
Foromo e felletseng ea capacitance bakeng sa li-capacitor tse hokahantsoeng ka letoto ke:
\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
Kenya mekhoa e tsebahalang sebakeng sa eona:
\[ C_1 = 100 \, pF = 100 \makgetlo a 10^{-12} \, F \]
\[ C_2 = 200 \, pF = 200 \makgetlo a 10^{-12} \, F \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2}{200 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2 + 1}{200 \makgetlo a 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{3}{200 \makgetlo a 10^{-12}} \]
\[ C_{\text{total}} = \frac{200 \times 10^{-12}}{3} \]
\[ C_{\text{total}} = 66.67 \makgetlo a 10^{-12} \, F \]
Kahoo, kakaretso ea capacitance ea li-capacitor tse peli tse hokahantsoeng ka letoto ke \( 66.67 \times 10^{-12} \, F \) kapa 66.67 pF.
Qetello
Sehloohong sena, re akaretse mathata a 'maloa a mehlala le lipuisano tse amanang le li-capacitor tsa parallel-plate. Re akaretse ho bala capacitance, matla a bolokiloeng, le capacitance eohle ea li-capacitor tse hokahantsoeng ka tatellano. Ho utloisisa melao-motheo ea motheo le mokhoa oa ho bala liparamente tsena tse fapaneng ho bohlokoa bakeng sa lits'ebetso tse sebetsang tsa elektroniki. Re tšepa hore puisano ena e tla u thusa ho utloisisa le ho sebelisa likhopolo tseo u ithutileng tsona hamolemo.
