Fesili Fa'ata'ita'i o le Capacitor
O le capacitor o se vaega eletise e mafai ona teuina le malosi i le tulaga o se fanua eletise. E tele fa'aoga o capacitor i matagaluega eletise, e pei o faamama, teuina o le malosi le tumau, ma fa'atupu fa'ailo. O lenei tusiga o le a talanoaina ai ni fa'ata'ita'iga o fa'afitauli o capacitor, fa'atasi ai ma fofo ma fa'amatalaga, e fesoasoani e malamalama ai i le manatu autu o capacitor i le fisiki.
1. Malosiaga o le Capacitor
Fa'ata'ita'iga Fesili 1:
O le capacitor o se laulau mafolafola e iai le lautele o le laulau \(A = 2 \, m^2\) ma le mamao i le va o laulau \(d = 0.01 \, m\). Afai o le dielectric constant o le ea \(\epsilon_0 = 8.85 \times 10^{-12} \, F/m\), fuafua le capacitance o le capacitor.
Tali:
E mafai ona fuafuaina le gafatia (C) o se capacitor flat plate e faʻaaoga ai le fua faʻatatau:
\[
C = \frac{\epsilon_0 A}{d}
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
C = \frac{(8.85 \times 10^{-12} \, F/m) \times 2 \, m^2}{0.01 \, m}
\]
\[
= \frac{17.7 \times 10^{-12} \, F}{0.01}
\]
\[
= 1.77 \times 10^{-9} \, F
\]
\[
= 1.77 \, nF
\]
O lea la, o le gafatia o le capacitor e 1.77 nanofarads (nF).
2. Malosiaga o loʻo teuina i totonu o se Capacitor
Fa'ata'ita'iga Fesili 2:
O se capacitor e iai lona gafatia e \(C = 5 \, \mu F\) ua feso'ota'i i se puna voltage e \(V = 12 \, V\). Fa'atatau le malosiaga o lo'o teuina i totonu o le capacitor.
Tali:
E mafai ona fuafuaina le malosi (E) o loʻo teuina i totonu o se capacitor e faʻaaoga ai le fua faʻatatau:
\[
E = \frac{1}{2} CV^2
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
E = \frac{1}{2} \times 5 \times 10^{-6} \, F \times (12 \, V)^2
\]
\[
= \frac{1}{2} \times 5 \times 10^{-6} \times 144
\]
\[
= 2.5 \times 10^{-6} \times 144
\]
\[
= 360 \times 10^{-6} \, J
\]
\[
= 0.36 \, mJ
\]
O lea la, o le malosiaga o loʻo teuina i totonu o le capacitor e 0.36 millijoules (mJ).
3. Capacitors i Matagaluega Fa'asolosolo ma Fa'atusatusa
Fa'ata'ita'iga Fesili 3:
E tolu capacitors, e tofu ma capacitances \(C_1 = 2 \, \mu F\), \(C_2 = 3 \, \mu F\), ma le \(C_3 = 6 \, \mu F\), e feso'ota'i i se matagaluega:
a) Faasologa
b) Fa'alava
Fuafua le gafatia tutusa mo faʻatulagaga uma e lua.
Tali:
a) Matagaluega Fa'asolosolo:
Mo capacitors ua feso'ota'i fa'asolosolo, e mafai ona fuafuaina le capacitance tutusa (\(C_{series}\)) e fa'aaoga ai le fua fa'atatau:
\[
\frac{1}{C_{series}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
\frac{1}{C_{series}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6}
\]
\[
\frac{1}{C_{series}} = \frac{3}{6} + \frac{2}{6} + \frac{1}{6}
\]
\[
\frac{1}{C_{series}} = 1
\]
\[
C_{faasologa} = 1 \, \mu F
\]
O lea la, o le capacitance tutusa mo le faʻatulagaga faʻasologa e 1 microfarad (\(\mu F\)).
b) Matagaluega Fa'alava:
Mo capacitors ua feso'ota'i fa'atasi, e mafai ona fuafuaina le capacitance tutusa (\(C_{parallel}\)) e fa'aaoga ai le fua fa'atatau:
\[
C_{parallel} = C_1 + C_2 + C_3
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
C_{parallel} = 2 + 3 + 6
\]
\[
C_{parallel} = 11 \, \mu F
\]
O lea la, o le capacitance tutusa mo le fa'atulagaga tutusa e 11 microfarads (\(\mu F\)).
4. Capacitor ma le Dielectric
Fa'ata'ita'iga Fesili 4:
O se capacitor laulau mafolafola e iai le capacitance \(C_0 = 8 \, pF\) ua fa'atumuina i se mea dielectric e iai le dielectric constant \(k = 4\). Fa'atatau le capacitance fou o le capacitor.
Tali:
E mafai ona fuafuaina le gafatia fou (C) o se capacitor ma se dielectric e faʻaaoga ai le fua faʻatatau:
\[
C = k \times C_0
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
C = 4 x 8 pF
\]
\[
= 32 \, pF
\]
O lea la, o le gafatia fou o le capacitor e 32 picofarads (pF).
5. Fa'atumuina ma Fa'ate'aina o Capacitors
Fa'ata'ita'iga Fesili 5:
O se capacitor e iai le capacitance o le \(C = 10 \, \mu F\) ua feso'ota'i i se resistor o le \(R = 2 \, k\Omega\) i totonu o se matagaluega fa'atumu. Fa'atatau le taimi e mana'omia e fa'atumu ai le capacitor i le 63% o lona voltage maualuga.
Tali:
O le taimi e manaʻomia e faʻatumu ai le capacitor i le 63% o le voltage maualuga e taʻua o le time constant (τ), lea e mafai ona fuafuaina e faʻaaoga ai le fua faʻatatau:
\[
\tau = R \times C
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
\tau = 2 \times 10^3 \, \Omega \times 10 \times 10^{-6} \, F
\]
\[
= 2 \times 10^{-2} \, s
\]
\[
= 20 \, ms
\]
O lea la, o le taimi e manaʻomia e faʻatumu ai le capacitor i le 63% o le voltage maualuga e 20 milliseconds (ms).
6. Capacitors i Matāgaluega AC
Fa'ata'ita'iga Fesili 6:
O se capacitor e iai lona gafatia e \(C = 5 \, \mu F\) ua feso'ota'i i se puna voltage AC e iai lona televave e \(f = 50 \, Hz\). Fa'atatau le capacitive reactance o le capacitor.
Tali:
E mafai ona fuafuaina le capacitive reactance (X_C) e faʻaaoga ai le fua faʻatatau:
\[
X_C = \frac{1}{2 \pi f C}
\]
Suitulaga i tau o loʻo tuʻuina atu:
\[
X_C = \frac{1}{2 \pi \times 50 \times 5 \times 10^{-6}}
\]
\[
= \frac{1}{2 \pi \times 250 \times 10^{-6}}
\]
\[
= \frac{1}{1.57 \times 250 \times 10^{-6}}
\]
\[
= \frac{1}{392.5 \times 10^{-6}}
\]
\[
= 2550 \, \Omega
\]
O lea la, o le capacitive reactance o le capacitor e 2550 ohms (\(\Omega\)).
I'uga
I totonu o lenei tusiga, ua matou talanoaina ni faʻataʻitaʻiga o faʻafitauli e aofia ai capacitors i faʻatulagaga ma tulaga eseese, mai le capacitance faavae, teuina o le malosi, faʻatulagaga faʻasolosolo ma faʻatusatusa, le faatosinaga o mea dielectric, i le tali atu o capacitors i matagaluega AC. O le malamalama i manatu ma faʻatusatusaga e fesoʻotaʻi ma capacitors e taua tele i le eletise ma le fisiki, aua o vaega taua ia i le tele o faʻaoga. E faʻamoemoe o nei faʻataʻitaʻiga o faʻafitauli o le a fesoasoani ia te oe e malamalama atili ai i le manatu o capacitors.
