Tauira o ngā Pātai Pūngao Pūmanawa Hiko
1. Ka whakaterea te tere o tētahi irahiko mai i te okioki mā roto i tētahi rerekētanga pūmanawa o te 12 volts. He aha te panonitanga o te pūngao pūmanawa o te irahiko?
Kōrero
E mōhiotia ana:
Utaina 1 irahiko (e) = -1,60 x 10-19 Coulomb
Rerekētanga pūmanawa hiko = ngaohiko hiko (V) = 12 Volts
I pātaihia: Te huringa o te pūngao pūmanawa irahiko (ΔEP)
Whakautu:
ΔEP = q V = (-1,60 x 10-19 C)(12 V) = -19,2 x 10-19 Joule
Ko te tohu kino te tikanga pūngao pūmanawa hiko ka heke. Ina tata ki te pereti utu kino, ka eke te kaha hiko o te irahiko ki tōna taumata teitei. I muri i te taenga ki te pereti utu pai, ka eke te kaha hiko o te irahiko ki tōna taumata iti rawa.
2. E rua ngā pereti whakarara e utaina ana ki te taha pai, ki te taha kino hoki. Ko te āpure hiko i waenganui i ngā pereti e rua he 500 Volts/mita. Ko te tawhiti i waenganui i ngā pereti e rua he 2 cm. Tātaihia te huringa o te pūngao pūmanawa o te porotini ina neke mai i te pereti utu pai ki te pereti utu kino!
Kōrero
E mōhiotia ana:
Mara hiko i waenganui i ngā pereti e rua (E) = 500 Volts/mita
Te tawhiti i waenganui i ngā pereti e rua = 2 cm = 0,02 mita
Te utunga pūwero = +1,60 x 10-19 Coulomb
I pātaihia: Te huringa o te pūngao pūmanawa hiko (ΔEP)
Whakautu:
Tātaihia tuatahi te rerekētanga pūmanawa, te ngaohiko hiko :
V = E s
V = (500 Volts/mita)(0,02 mita)
V = 10 Ngāohiko
Ngā panonitanga o te pūngao pūmanawa hiko:
ΔEP = q V
ΔEP = (1,60 x 10-19 C)(10 V)
ΔEP = 16 x 10-19 Joule
ΔEP = 1,6 x 10-18 Joule
Ina tata ki te pereti utu pai, ka eke te kaha hiko o te porotana ki tōna taumata teitei. Ina tae ki te pereti utu kino, ka eke te kaha hiko o te porotana ki tōna taumata iti. Nō reira, ina neke atu i te pereti utu pai ki te pereti utu kino, ka heke te kaha hiko o te porotana.
3. E rua ngā utu e whakaritea ana e ai ki te pikitia i raro nei. Ko te utu i A he +9 μC, ā, ko te utu i B he -4 μC. Ko te pūmau o Coulomb (k) = 9 x 109 Nm2C-2, 1 μC = 10-6 C. E hia te nui o te panonitanga o te pūngao hiko o te utu B mēnā ka neke ki te utu A?
Kōrero
E mōhiotia ana:
Utu A (q1) = +9 μC = +9 x 10-6 C
Utu B (q1) = -4 μC = -4 x 10-6 C
Te pūmau o Coulomb (k) = 9 x 109 Nm2C-2
Ko te tawhiti i waenganui i ngā utu A me B (r) = 10 cm = 0,1 mita = 10-1 mita
I pātaihia: Te huringa o te pūngao pūmanawa hiko o te utu B mēnā ka neke ki te utu A
Whakautu:
Ka neke te utu B ki te utu A kia heke ai tōna pūngao pūmanawa hiko mā te 2,4 Joule.
He rite tēnei ki tētahi mea papatipu e neke ana ki raro ki te whenua, ā, ka heke tōna teitei me te pūngao pūmanawa ā-papa.
4. Kei roto i tētahi papa hiko he \( q = 5 \times 10^{-6} \) C te utu, ā, ko tōna pūmanawa he \( V = 300 \) V. He aha te kaha pūmanawa hiko o te matūriki?
Kōrero:
Ko te pūngao pūmanawa hiko e homai ana e:
\[ U = q \whakanuia te V \]
\[ U = 5 \times 10^{-6} \times 300 \]
\[ U = 1.5 \times 10^{-3} \] J
5. Ka whakanohoia he irahiko ki roto i tētahi papa hiko me te pūmanawa o te 500 V. He aha te pūngao pūmanawa hiko o te irahiko?
Kōrero:
Te utunga irahiko \( q = -1.6 \times 10^{-19} \) C.
\[ U = q \whakanuia te V \]
\[ U = -1.6 \times 10^{-19} \times 500 \]
\[ U = -8 \times 10^{-17} \] J
6. Ka neke te pūrotene mai i te pūmanawa o te 100 V ki te 200 V. He aha te panonitanga o tōna pūngao pūmanawa?
Kōrero:
Te utunga porotana \( q = 1.6 \times 10^{-19} \) C.
\[ \Delta U = q \times \Delta V \]
\[ \Delta U = 1.6 \times 10^{-19} \times (200 – 100) \]
\[ \Delta U = 1.6 \times 10^{-17} \] J
7. E rua ngā mea he utu ā rāua \( q_1 = 2 \times 10^{-6} \) C me \( q_2 = -3 \times 10^{-6} \) C kua whakanohoia ki roto i tētahi papa hiko me te pūmanawa o \( V = 400 \) V. He aha te pūngao pūmanawa katoa o ngā mea e rua?
Kōrero:
\[ U_1 = q_1 \whakareatia ki te V \]
\[ U_2 = q_2 \whakareatia ki te V \]
\[ U_{katoa} = U_1 + U_2 \]
\[ U_{katoa} = (2 \times 10^{-6} + (-3 \times 10^{-6})) \times 400 \]
\[ U_{katoa} = -4 \times 10^{-3} \] J
8. Kei roto i tētahi āpure hiko he katote he utu \( q = 4e \) (ko \( e \) te utu taketake) he āpure hiko he pūmanawa \( V = 250 \) V. He aha te kaha pūmanawa hiko o te katote?
Kōrero:
\[ U = q \whakanuia te V \]
\[ U = 4 \times 1.6 \times 10^{-19} \times 250 \]
\[ U = 1.6 \times 10^{-16} \] J
9. E mōhiotia ana ko te pūngao pūmanawa o tētahi matūriki he \( q = -7 \times 10^{-5} \) C he \( 2 \times 10^{-2} \) J. He aha te pūmanawa o te papa hiko kei reira te matūriki?
Kōrero:
\[ U = q \whakanuia te V \]
\[ V = \frac{U}{q} \]
\[ V = \frac{2 \times 10^{-2}}{-7 \times 10^{-5}} \]
\[ V = -285.71 \] V
10. E rua ngā mea he utu ā rāua \( q_1 = 5e \) me \( q_2 = -2e \) kei roto i tētahi papa hiko me te pūmanawa o \( V = 300 \) V. He aha te pūngao pūmanawa katoa o ngā mea e rua?
Kōrero:
\[ U_1 = q_1 \whakareatia ki te V \]
\[ U_2 = q_2 \whakareatia ki te V \]
\[ U_{katoa} = U_1 + U_2 \]
\[ U_{katoa} = (5 \times 1.6 \times 10^{-19} – 2 \times 1.6 \times 10^{-19}) \times 300 \]
\[ U_{katoa} = 1.44 \times 10^{-16} \] J
11. Ko te kaha pūmanawa o tētahi katote he utu \( q = -3e \) he \( -9.6 \times 10^{-19} \) J. He aha te kaha pūmanawa o te papa hiko kei reira te katote?
Kōrero:
\[ U = q \whakanuia te V \]
\[ V = \frac{U}{q} \]
\[ V = \frac{-9.6 \times 10^{-19}}{-3 \times 1.6 \times 10^{-19}} \]
\[ V = 200 \] V
12. E mōhiotia ana ko te pūngao pūmanawa hiko o tētahi utu \( q \) i roto i tētahi mara hiko me te pūmanawa \( V = 450 \) V ko \( 9 \times 10^{-18} \) J. He aha te utu \( q \)?
Kōrero:
\[ U = q \whakanuia te V \]
\[ q = \frac{U}{V} \]
\[ q = \frac{9 \times 10^{-18}}{450} \]
\[ q = 2 \times 10^{-20} \] C
13. Ka nekehia he utu pai \( q = 1.5 \times 10^{-19} \) C mai i tētahi pūwāhi me te pūmanawa \( V_1 = 100 \) V ki \( V_2 = 500 \) V. He aha te huringa o te pūngao pūmanawa?
Kōrero:
\[ \Delta U = q \times \Delta V \]
\[ \Delta U = 1.5 \times 10^{-19} \times (500 – 100) \]
\[ \Delta U = 6 \times 10^{-17} \] J
