Mafunso a Chitsanzo cha Capacitor
Capacitor ndi gawo lamagetsi lomwe lingasunge mphamvu mu mawonekedwe a mphamvu zamagetsi. Ma capacitor ali ndi ntchito zosiyanasiyana m'mabwalo amagetsi, monga zosefera, kusungira mphamvu kwakanthawi, ndi ma signal generator. Nkhaniyi ikambirana zitsanzo zingapo za mavuto a capacitor, pamodzi ndi mayankho ndi mafotokozedwe, kuti athandize kumvetsetsa lingaliro loyambira la ma capacitor mu fizikisi.
1. Kutha kwa Capacitor
Chitsanzo cha Funso 1:
Kachipangizo ka flat plate kali ndi malo a mbale \(A = 2 \, m^2 \) ndi mtunda pakati pa mbale \(d = 0.01 \, m\). Ngati mpweya uli ndi dielectric constant \(\epsilon_0 = 8.85 \times 10^{-12} \, F/m\), werengerani capacitance ya capacitor.
Yankho:
Mphamvu (C) ya capacitor ya flat plate ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[
C = \frac{\epsilon_0 A}{d}
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
C = \frac{(8.85 \times 10^{-12} \, F/m) \times 2 \, m^2}{0.01 \, m}
\]
\[
= \frac{17.7 \times 10^{-12} \, F}{0.01}
\]
\[
= 1.77 \nthawi 10^{-9} \, F
\]
\[
= 1.77 \, nF
\]
Kotero, mphamvu ya capacitor ndi 1.77 nanofarads (nF).
2. Mphamvu Zosungidwa mu Capacitor
Chitsanzo cha Funso 2:
Kachipangizo kokhala ndi mphamvu ya \(C = 5 \, \mu F\) kamalumikizidwa ku gwero la magetsi la \(V = 12 \, V\). Werengani mphamvu yosungidwa mu kachipangizoko.
Yankho:
Mphamvu (E) yosungidwa mu capacitor ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[
E = \frac{1}{2} CV^2
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
E = \frac{1}{2} \times 5 \times 10^{-6} \, F \times (12 \, V)^2
\]
\[
= \frac{1}{2} \nthawi 5 \nthawi 10^{-6} \nthawi 144
\]
\[
= 2.5 \nthawi 10^{-6} \nthawi 144
\]
\[
= 360 \nthawi 10^{-6} \, J
\]
\[
= 0.36 \, mJ
\]
Kotero, mphamvu yosungidwa mu capacitor ndi 0.36 millijoules (mJ).
3. Ma Capacitor mu Series ndi Parallel Circuits
Chitsanzo cha Funso 3:
Ma capacitor atatu, aliwonse okhala ndi ma capacitance \(C_1 = 2 \, \mu F\), \(C_2 = 3 \, \mu F\), ndi \(C_3 = 6 \, \mu F\), alumikizidwa mu circuit:
a) Mndandanda
b) Kufanana
Werengerani mphamvu yofanana ya makonzedwe onse awiri.
Yankho:
a) Mzere wa Dera:
Pa ma capacitor olumikizidwa mu mndandanda, capacitance yofanana (\(C_{series}\)) ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[
\frac{1}{C_{series}} = \frac{1}{C_1} + \frac{1}{C_2} + \frac{1}{C_3}
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
\frac{1}{C_{series}} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6}
\]
\[
\frac{1}{C_{series}} = \frac{3}{6} + \frac{2}{6} + \frac{1}{6}
\]
\[
\frac{1}{C_{series}} = 1
\]
\[
C_{series} = 1 \, \mu F
\]
Motero, capacitance yofanana ya kasinthidwe ka mndandanda ndi 1 microfarad (\(\mu F\)).
b) Dera Lofanana:
Pa ma capacitor olumikizidwa motsatizana, capacitance yofanana (\(C_{parallel}\)) ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[
C_{parallel} = C_1 + C_2 + C_3
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
C_{parallel} = 2 + 3 + 6
\]
\[
C_{parallel} = 11 \, \mu F
\]
Motero, capacitance yofanana ya kasinthidwe kofanana ndi 11 microfarads (\(\mu F\)).
4. Capacitor yokhala ndi Dielectric
Chitsanzo cha Funso 4:
Kachipangizo ka flat plate komwe kali ndi capacitance \(C_0 = 8 \, pF\) kamadzazidwa ndi zinthu za dielectric zomwe zili ndi dielectric constant \(k = 4\). Werengani capacitance yatsopano ya capacitor.
Yankho:
Mphamvu yatsopano (C) ya capacitor yokhala ndi dielectric ikhoza kuwerengedwa pogwiritsa ntchito fomula iyi:
\[
C = k \nthawi C_0
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
C = 4 \ nthawi 8 \, pF
\]
\[
= 32 \, pF
\]
Kotero, mphamvu yatsopano ya capacitor ndi 32 picofarads (pF).
5. Ma Capacitor Ochaja ndi Kutulutsa Mphamvu
Chitsanzo cha Funso 5:
Kachipangizo kamene kali ndi mphamvu ya \(C = 10 \, \mu F\) kamalumikizidwa ndi choletsa cha \(R = 2 \, k\Omega\) mu circuit yochajira. Werengani nthawi yofunikira kuti muchajire kachipangizocho kufika pa 63% ya mphamvu yake yayikulu.
Yankho:
Nthawi yofunikira kuti capacitor ipereke mphamvu mpaka 63% ya mphamvu yayikulu imatchedwa nthawi yosasintha (τ), yomwe ingawerengedwe pogwiritsa ntchito fomula iyi:
\[
\tau = R \nthawi C
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
\tau = 2 \nthawi 10^3 \, \Omega \nthawi 10 \nthawi 10^{-6} \, F
\]
\[
= 2 \nthawi 10^{-2} \, s
\]
\[
= 20 \, ms
\]
Kotero, nthawi yofunikira kuti capacitor ija ikwane 63% ya mphamvu yayikulu yamagetsi ndi 20 milliseconds (ms).
6. Ma capacitor mu AC Circuits
Chitsanzo cha Funso 6:
Kachipangizo kamene kali ndi mphamvu ya \(C = 5 \, \mu F\) kamalumikizidwa ku gwero la magetsi a AC lomwe lili ndi mafupipafupi a \(f = 50 \, Hz\). Werengani kuchuluka kwa mphamvu ya kachipangizo kamene kali ndi mphamvu ya kachipangizo kamene kali ndi mphamvu ya \(C = 5 \, \mu F\) .
Yankho:
Kuyankha kwa capacitive (X_C) kungawerengedwe pogwiritsa ntchito fomula iyi:
\[
X_C = \frac{1}{2 \pi f C}
\]
M'malo mwa mfundo zomwe zaperekedwa:
\[
X_C = \frac{1}{2 \pi \nthawi 50 \nthawi 5 \nthawi 10^{-6}}
\]
\[
= \frac{1}{2 \pi \times 250 \times 10^{-6}}
\]
\[
= \frac{1}{1.57 \times 250 \times 10^{-6}}
\]
\[
= \frac{1}{392.5 \times 10^{-6}}
\]
\[
= 2550 \, \Omega
\]
Kotero, capacitor reactance ya capacitor ndi 2550 ohms (\(\Omega\)).
Mapeto
Munkhaniyi, takambirana mavuto angapo okhudzana ndi ma capacitor m'makonzedwe ndi mikhalidwe yosiyanasiyana, kuyambira pa capacitance yoyambira, kusungira mphamvu, makonzedwe otsatizana ndi ofanana, mphamvu ya zinthu zamagetsi, mpaka momwe ma capacitor amayankhira mu ma AC circuits. Kumvetsetsa malingaliro ndi mawerengedwe okhudzana ndi ma capacitor ndikofunikira kwambiri mu zamagetsi ndi fizikisi, chifukwa ndi zigawo zofunika kwambiri pa ntchito zambiri. Tikukhulupirira kuti mavuto awa akuthandizani kumvetsetsa bwino lingaliro la ma capacitor.
