Cov Lus Nug Piv Txwv Sib Tham Txog Cov Capacitors Phaj Sib Npaug
Pendahuluuan
Cov capacitors yog cov khoom siv hluav taws xob tseem ceeb uas khaws cia thiab tso tawm lub zog hauv daim ntawv ntawm cov nqi hluav taws xob. Cov capacitors parallel-plate yog hom yooj yim tshaj plaws thiab siv dav tshaj plaws. Tsab xov xwm no yuav tham txog ntau qhov piv txwv thiab kev sib tham ntsig txog cov capacitors parallel-plate kom muab kev nkag siab tob dua txog lawv lub tswv yim thiab kev siv.
Kev Nkag Siab Txog Cov Capacitors Phaj Sib Nqus
Ib lub capacitor phaj sib luag muaj ob lub phaj conducting sib cais los ntawm dielectric, ib qho khoom siv insulating uas ua rau muaj peev xwm khaws cov nqi hluav taws xob ntau dua. Lub capacitance (C) ntawm lub capacitor phaj sib luag tuaj yeem suav nrog siv cov qauv hauv qab no:
\[ C = \frac{\varepsilon A}{d} \]
Qhov twg:
- \( \varepsilon \) yog qhov permittivity ntawm cov khoom siv dielectric,
- \( A \) yog thaj tsam ntawm lub puck,
- \( d \) yog qhov deb ntawm ob daim.
Cov mis no qhia tau hais tias lub peev xwm ntawm lub capacitor phaj sib luag yog ncaj qha proportional rau thaj tsam phaj thiab dielectric permittivity, thiab inversely proportional rau qhov deb ntawm cov phaj.
Cov Lus Nug Piv Txwv thiab Kev Sib Tham
Piv txwv lus nug 1: Xam qhov Capacitance
Lo lus nug:
Ob lub phaj hlau uas muaj thaj tsam ntawm 0.02 m² raug sib cais los ntawm qhov deb ntawm 0.001 m siv cua ua dielectric (permittivity \(\varepsilon_{0} = 8.85 \times 10^{-12} \, F/m\)). Xam qhov capacitance ntawm lub capacitor.
Kev Sib Tham:
Siv cov mis capacitance rau lub capacitor parallel plate.
\[ C = \frac{\varepsilon_{0} A}{d} \]
Hloov cov nqi uas paub lawm:
\[ \varepsilon_{0} = 8.85 \times 10^{-12} \, F/m \]
\[ A = 0.02 \, m² \]
\[ d = 0.001 \, m \]
\[ C = \frac{(8.85 \times 10^{-12} \, F/m) \times 0.02 \, m²}{0.001 \, m} \]
\[ C = \frac{1.77 \times 10^{-13} \, F}{0.001 \, m} \]
\[ C = 1.77 \times 10^{-10} \, F \]
Yog li, lub capacitance ntawm lub parallel plate capacitor yog 1.77 \times 10^{-10} \, F \) lossis 177 pF (picofarads).
Piv Txwv Lo Lus Nug 2: Xam Lub Zog Khaws Cia
Lo lus nug:
Yog tias lub capacitor los ntawm Piv Txwv Lo Lus Nug 1 raug them rau lub zog ntawm 50 V, muaj pes tsawg lub zog khaws cia rau hauv lub capacitor?
Kev Sib Tham:
Lub zog (U) uas khaws cia rau hauv lub capacitor tuaj yeem suav los ntawm kev siv cov mis:
\[ U = \frac{1}{2} CV^2 \]
Hloov cov nqi uas paub lawm:
\[ C = 1.77 \times 10^{-10} \, F \]
\[ V = 50 \, V \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times (50 \, V)^2 \]
\[ U = \frac{1}{2} \times 1.77 \times 10^{-10} \, F \times 2500 \, V^2 \]
\[ U = \frac{1.77 \times 10^{-10} \, F \times 2500 \, V^2}{2} \]
\[ U = \frac{4.425 \times 10^{-7} \, J}{2} \]
\[ U = 2.2125 \times 10^{-7} \, J \]
Yog li, lub zog khaws cia rau hauv lub capacitor yog ∑(2.2125 \times 10^{-7} \, J \) lossis 221.25 nJ (nanoujoules).
Piv txwv 3: Xam Kev Hloov Pauv Hauv Capacitance
Lo lus nug:
Ib lub capacitor phaj sib luag muaj thaj tsam phaj ntawm 0.01 m² thiab sib cais los ntawm qhov deb ntawm 0.002 m. Cov khoom siv dielectric siv yog mica nrog permittivity ntawm \( \varepsilon = 6 \times \varepsilon_{0} \). Xam qhov capacitance ntawm lub capacitor.
Kev Sib Tham:
Qhov permittivity ntawm mica dielectric khoom yog:
\[ \varepsilon = 6 \times \varepsilon_{0} \]
Siv cov mis capacitance rau lub capacitor parallel plate:
\[ C = \frac{\varepsilon A}{d} \]
Hloov cov nqi uas paub lawm:
\[ \varepsilon_{0} = 8.85 \times 10^{-12} \, F/m \]
\[ A = 0.01 \, m² \]
\[ d = 0.002 \, m \]
\[ \varepsilon = 6 \times 8.85 \times 10^{-12} \, F/m = 53.1 \times 10^{-12} \, F/m \]
\[ C = \frac{53.1 \times 10^{-12} \, F/m \times 0.01 \, m²}{0.002 \, m} \]
\[ C = \frac{5.31 \times 10^{-13} \, F}{0.002 \, m} \]
\[ C = 2.655 \times 10^{-10} \, F \]
Yog li, lub capacitance ntawm lub capacitor nrog mica ua cov khoom siv dielectric yog 2.655 lub sijhawm 10^{-10} F los yog 265.5 pF.
Piv txwv lus nug 4: Xam qhov peev xwm ntawm lub koom haum
Lo lus nug:
Ob lub capacitors phaj sib luag, txhua lub muaj capacitance ntawm 100 pF thiab 200 pF, tau txuas ua ke. Tag nrho capacitance yog dab tsi?
Kev Sib Tham:
Cov mis ntawm tag nrho cov capacitance rau cov capacitors txuas nrog hauv series yog:
\[ \frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} \]
Hloov cov nqi uas paub lawm:
\[ C_1 = 100 \, pF = 100 \times 10^{-12} \, F \]
\[ C_2 = 200 \, pF = 200 \times 10^{-12} \, F \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{1}{100 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2}{200 \times 10^{-12}} + \frac{1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{2 + 1}{200 \times 10^{-12}} \]
\[ \frac{1}{C_{\text{total}}} = \frac{3}{200 \times 10^{-12}} \]
\[ C_{\text{total}} = \frac{200 \times 10^{-12}}{3} \]
\[ C_{\text{total}} = 66.67 \times 10^{-12} \, F \]
Yog li, tag nrho cov capacitance ntawm ob lub capacitors txuas nrog hauv series yog 66.67 \times 10^{-12} \, F \) lossis 66.67 pF.
Xaus
Hauv tsab xov xwm no, peb tau tham txog ntau yam piv txwv teeb meem thiab kev sib tham txog cov capacitors parallel-plate. Peb tau tham txog kev xam capacitance, lub zog khaws cia, thiab tag nrho cov capacitance ntawm cov capacitors txuas nrog hauv series. Kev nkag siab txog cov ntsiab cai yooj yim thiab yuav ua li cas xam cov kev ntsuas sib txawv no yog qhov tseem ceeb rau kev siv hauv kev siv hluav taws xob. Peb vam tias qhov kev sib tham no yuav pab koj nkag siab zoo dua thiab siv cov ntsiab lus uas koj tau kawm.
