Tauira o ngā Pātai Kōrero mō te Pūnga
Pendahuluan
He wāhanga hiko te pūnga hiko e penapena ana i te pūngao i roto i te āhua o te papa hiko. He mea nui te mārama ki ngā pūngao i roto i te hiko, nā te mea e whakamahia ana i roto i te whānuitanga o ngā tono, mai i ngā ara iahiko tātari ki te rokiroki pūngao. I roto i tēnei tuhinga, ka matapakihia e mātou ētahi tauira raruraru pūngao me ō rātou whakamārama hei āwhina i a koe ki te mārama ake ki te ariā me te mahi a ngā pūngao.
Te Ariā Taketake o ngā Pūnga
I mua i te urunga atu ki ngā tauira raruraru, me arotake poto te ariā taketake o ngā pūnga hiko. Ko te pūnga hiko he mea hanga mai i ngā pereti e rua e kawe ana i te hiko e wehea ana e te dielectric. Ina honoa te pūnga hiko ki tētahi pūtake ngaohiko, ka rongoatia he utu hiko ki runga i ngā pereti. Ko te kaha, te āheinga rānei o te pūnga hiko ki te rongoa utu, ka inehia i roto i ngā farad (F).
Ko te tauira taketake o te pūnga ko:
\[
Q = C \whakanuia te V
\]
Kei hea:
– Ko te utu hiko i roto i ngā coulomb (C) ko \( Q \)
– Ko te capacitance i roto i ngā farad (F) ko \( C \)
– Ko te ngaohiko i roto i ngā volts (V) ko \( V \)
Tauira Pātai 1: Te Tatau i te Utu i runga i te Pūnga
Pātai:
Kua honoa tētahi pūnga hiko me te kaha o te 4 µF ki tētahi pūtake ngaohiko 12 V. Tātaihia te utu hiko kua rongoatia i roto i te pūnga hiko.
Kōrero:
Mā te whakamahi i te tātai pūnga taketake \( Q = C \times V \):
\[
Q = 4 \times 10^{-6} F \times 12 V = 48 \times 10^{-6} C = 48 µC
\]
Nō reira, ko te utu e rongoatia ana i roto i te pūnga hiko he 48 µC.
Tauira Pātai 2: Te Tatau i te Pūngao e Penapenahia ana i roto i te Pūngao
Pātai:
Ka utaina he pūngao 10 µF kia tae rā anō te ngaohiko ki te 5 V. E hia te kaha e rongoa ana i roto i te pūngao?
Kōrero:
Ka taea te tatau i te pūngao e rongoatia ana i roto i te pūngao mā te whakamahi i te tātai:
\[
E = \frac{1}{2} CV^2
\]
Kei hea:
– Ko te pūngao i roto i ngā joule (J) ko \( E \)
– Ko te capacitance i roto i ngā farad (F) ko \( C \)
– Ko te ngaohiko i roto i ngā volts (V) ko \( V \)
\[
E = \frac{1}{2} \times 10 \times 10^{-6} F \times (5 V)^2 = \frac{1}{2} \times 10 \times 10^{-6} \times 25 = 0.000125 J = 125 µJ
\]
Nō reira, ko te pūngao e rongoatia ana i roto i te pūngao he 125 µJ.
Tauira 3: Porowhita Pūnga Raupapa
Pātai:
E rua ngā pūnga iahiko, he 6 µF te kaha o ia pūnga, he 8 µF hoki te kaha. Tātaihia te kaha katoa o te ara iahiko.
Kōrero:
Mō ngā pūnga iahiko e honoa ana i roto i te raupapa, ka taea te tatau i te kaha katoa \( C_{total} \) mā te whakamahi i te tātai:
\[
\frac{1}{C_{tapeke}} = \frac{1}{C_1} + \frac{1}{C_2}
\]
\[
\frac{1}{C_{katoa}} = \frac{1}{6 \times 10^{-6} F} + \frac{1}{8 \times 10^{-6} F} = \frac{1}{6} + \frac{1}{8} = \frac{8 + 6}{48} = \frac{14}{48} = \frac{7}{24}
\]
\[
C_{katoa} = \frac{24}{7} \times 10^{-6} F = 3.43 µF
\]
Nō reira, ko te kaha katoa o ngā pūnga hiko e rua e honoa raupapa ana ko 3.43 µF.
Tauira 4: Porowhita Pūnga Whakarara
Pātai:
E toru ngā pūnga hiko me ngā kaha o te 2 µF, 4 µF, me te 6 µF e honoa ana i te taha whakarara. Tātaihia te kaha katoa o te ara iahiko.
Kōrero:
Mō ngā pūnga iahiko e whakaritea ana i te taha whakarara, ka taea te tatau i te kaha katoa \( C_{total} \) mā te tāpiri i ngā kaha o ia pūnga iahiko:
\[
C_{katoa} = C_1 + C_2 + C_3
\]
\[
C_{katoa} = 2 \times 10^{-6} F + 4 \times 10^{-6} F + 6 \times 10^{-6} F = 12 \times 10^{-6} F = 12 µF
\]
Nō reira, ko te kaha katoa o ngā kaha e toru e honoa whakarara ana he 12 µF.
Tauira Pātai 5: Te Pūngao me te Rauemi Hiko-ā-Irahiko
Pātai:
Ko te kaha tīmatanga o te pūnga hiko he 5 µF. Mēnā ka whakaurua he rauemi ārai hiko me te pūmau ārai hiko (\(k \)) o te 3 ki waenganui i ngā pereti pūnga hiko, he aha te kaha hou?
Kōrero:
Ka taea te tatau i te kaha o te pūnga me te rauemi dielectric mā te whakamahi i te tātai:
\[
C' = k \whakanuia ki te C
\]
Kei hea:
– Ko te capacitance hou ko \( C' \)
– Ko te pūmau ārai-hiko te \( k \)
– Ko te capacitance tuatahi ko \( C \)
\[
C' = 3 \times 5 \times 10^{-6} F = 15 \times 10^{-6} F = 15 µF
\]
Nō reira, ina whakaurua he rauemi ārai-hiko me te pūmau ārai-hiko o te 3, ko te kaha hou he 15 µF.
Tauira Pātai 6: Ngā Pūnga i roto i ngā Ara Iahiko RC
Pātai:
He ara iahiko RC kei roto he ātete 10 kΩ me te pūnga 20 µF. Mēnā ka pāngia tēnei ara iahiko e te ngaohiko, kia pēhea te roa ka utua e te pūnga ki te 63% o tōna ngaohiko mōrahi?
Kōrero:
Ko te wā e hiahiatia ana mō te pūnga ki te utu ki te 63% o tōna ngaohiko mōrahi he rite ki te pūmau kotahi wā \( \tau \) (tau), e tatauhia ana e te tātai:
\[
\tau = R \times C
\]
Kei hea:
– He pūmau wā a \( \tau \)
– Ko te ātete i roto i ngā ohm (Ω) ko \( R \)
– Ko te capacitance i roto i ngā farad (F) ko \( C \)
\[
\tau = 10 \times 10^3 \times 20 \times 10^{-6} = 0.2 hēkona
\]
Nō reira, ko te wā e hiahiatia ana kia utua ai e te pūnga hiko ki te 63% o te ngaohiko mōrahi he 0.2 hēkona.
Whakamutunga
He taahiraa nui te matapaki i ngā raruraru pūngao hei mārama ki ngā ariā me ngā whakamahinga taketake o ngā pūngao i roto i ngā ara iahiko hiko. Mai i te tatau i te utu, te pūngao, te pūngao katoa i roto i ngā ara iahiko raupapa me te ara iahiko whakarara, tae atu ki te whai huatanga o ngā dielectrics i roto i ngā pūngao, ka whakaratohia e ia tauira raruraru he tirohanga hōhonu ki te mahi a ngā pūngao. Ko te tumanako, mā ēnei tauira raruraru koe e āwhina ki te ako me te mārama ake mō ngā pūngao.
