Fa'ata'ita'iga o Fesili e Talanoaina ai Capacitors o le Parallel Plate
Pendahuluan
O capacitors o vaega eletise taua ia e teuina ma faʻasaʻoloto le malosi i le tulaga o le eletise. O capacitors parallel-plate o le ituaiga faigofie ma sili ona faʻaaogaina lautele. O lenei tusiga o le a aofia ai ni faʻataʻitaʻiga ma talanoaga e fesoʻotaʻi ma capacitors parallel-plate e tuʻuina atu ai se malamalamaga loloto i o latou manatu ma faʻaoga.
Malamalama i Capacitors o Plate Parallel
O le capacitor parallel plate e aofia ai ni papatusi fa'aeletise se lua e vaeluaina e se dielectric, o se mea e fa'ateleina ai le gafatia e teu ai le eletise. E mafai ona fuafuaina le capacitance (C) o se capacitor parallel plate e fa'aaoga ai le fua fa'atatau lenei:
\[ C = \frac{\varepsilon A}{d} \]
O fea:
– \( \varepsilon \) o le permittivity o le dielectric material,
– \( A \) o le lautele o le pito i luga o le pak,
– \( d \) o le mamao i le va o vaega e lua.
O lenei fua fa'atatau e fa'aalia ai o le capacitance o se parallel plate capacitor e tutusa lelei ma le area o le plate ma le dielectric permittivity, ma e fa'afeagai fo'i ma le mamao i le va o plates.
Fesili Fa'ata'ita'i ma Talanoaga
Faʻataʻitaʻiga Fesili 1: Fuafuaina o le Malosiaga
Fesili:
E lua ni papa u'amea e tofu ma le lautele o le fogaeleele e 0.02 m² e vaeluaina i se mamao e 0.001 m e fa'aaoga ai le ea e fai ma dielectric (permittivity \(\varepsilon_{0} = 8.85 \times 10^{-12} \, F/m\)). Fa'atatau le capacitance o le capacitor.
Talanoaga:
Faaaoga le fua fa'atatau o le capacitance mo se capacitor o le parallel plate.
\[ C = \frac{\varepsilon_{0} A}{d} \]
Suitulaga i tau ua iloa:
\[ \varepsilon_{0} = 8.85 \times 10^{-12} \, F/m \]
\[ A = 0.02 \, m² \]
\[ d = 0.001 \, m \]
\[ C = \frac{(8.85 \times 10^{-12} \, F/m) \times 0.02 \, m²}{0.001 \, m} \]
\[ C = \frac{1.77 \times 10^{-13} \, F}{0.001 \, m} \]
\[ C = 1.77 \times 10^{-10} \, F \]
O lea la, o le capacitance o se parallel plate capacitor e \( 1.77 \times 10^{-10} \, F \) po'o le 177 pF (picofarads).
Faʻataʻitaʻiga Fesili 2: Fuafuaina o le Malosiaga Faʻasaoina
Fesili:
Afai o le capacitor mai le Fa'ata'ita'iga Fesili 1 ua fa'atumuina i se gafatia e 50 V, o le a le tele o le malosiaga o lo'o teuina i totonu o le capacitor?
Talanoaga:
E mafai ona fuafuaina le malosi (\(U\)) o loʻo teuina i totonu o se capacitor e faʻaaoga ai le fua faʻatatau:
\[ U = \frac{1}{2} CV^2 \]
Suitulaga i tau ua iloa:
\[ C = 1.77 \times 10^{-10} \, F \]
\[ V = 50 \, V \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times (50 \, V)^2 \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times 2500 \, V^2 \]
\[ U = \frac{1.77 \times 10^{-10} \, F \times 2500 \, V^2}{2} \]
\[ U = \frac{4.425 \times 10^{-7} \, J}{2} \]
\[ U = 2.2125 \times 10^{-7} \, J \]
O lea la, o le malosiaga o loʻo teuina i totonu o le capacitor e \( 2.2125 \times 10^{-7} \, J \) poʻo le 221.25 nJ (nanoujoules).
Faataitaiga 3: Fuafuaina o le Suiga o le Malosiaga
Fesili:
O le capacitor parallel plate e 0.01 m² le lautele o le plate ma e 0.002 m le mamao e vaeluaina ai. O le mea dielectric e fa'aaogaina o le mica ma le permittivity o le \( \varepsilon = 6 \times \varepsilon_{0} \). Fa'atatau le capacitance o le capacitor.
Talanoaga:
O le permittivity o le mica dielectric material e:
\[ \varepsilon = 6 \times \varepsilon_{0} \]
Faaaoga le fua fa'atatau o le capacitance mo se capacitor parallel plate:
\[ C = \frac{\varepsilon A}{d} \]
Suitulaga i tau ua iloa:
\[ \varepsilon_{0} = 8.85 \times 10^{-12} \, F/m \]
\[ A = 0.01 \, m² \]
\[ d = 0.002 \, m \]
\[ \varepsilon = 6 \times 8.85 \times 10^{-12} \, F/m = 53.1 \times 10^{-12} \, F/m \]
\[ C = \frac{53.1 \times 10^{-12} \, F/m \times 0.01 \, m²}{0.002 \, m} \]
\[ C = \frac{5.31 \times 10^{-13} \, F}{0.002 \, m} \]
\[ C = 2.655 \times 10^{-10} \, F \]
O lea la, o le capacitance o se capacitor ma le mica o le dielectric material e \( 2.655 \times 10^{-10} \, F \) po'o le 265.5 pF.
Fa'ata'ita'iga Fesili 4: Fuafuaina o le Malosiaga o le Iuni
Fesili:
E lua capacitors parallel plate, e tofu le capacitance ma le 100 pF ma le 200 pF, e feso'ota'i fa'asolosolo. O le a le aofa'i atoa o le capacitance?
Talanoaga:
O le fua fa'atatau o le capacitance atoa mo capacitors ua feso'ota'i fa'asolosolo e fa'apea:
\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
Suitulaga i tau ua iloa:
\[ C_1 = 100 \, pF = 100 \times 10^{-12} \, F \]
\[ C_2 = 200 \, pF = 200 \times 10^{-12} \, F \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2}{200 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2 + 1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{3}{200 \times 10^{-12}} \]
\[ C_{\text{total}} = \frac{200 \times 10^{-12}}{3} \]
\[ C_{\text{total}} = 66.67 \times 10^{-12} \, F \]
O lea la, o le aofaʻi atoa o le capacitance o capacitors e lua ua fesoʻotaʻi faʻasolosolo e \( 66.67 \times 10^{-12} \, F \) poʻo le 66.67 pF.
I'uga
I totonu o lenei tusiga, ua matou talanoaina ai ni faʻataʻitaʻiga o faʻafitauli ma talanoaga e fesoʻotaʻi ma capacitors parallel-plate. Ua matou talanoaina le fuafuaina o le capacitance, le malosi teuina, ma le aofaʻi atoa o capacitors ua fesoʻotaʻi faʻasolosolo. O le malamalama i mataupu faavae autu ma le auala e fuafua ai nei parakalafa eseese e taua tele mo faʻaoga aoga i mea faʻaeletoronika. Matou te faʻamoemoe o lenei talanoaga e fesoasoani ia te oe e malamalama atili ai ma faʻaaoga manatu ua e aʻoaʻoina.
