25 Pūngao hiko – ngā raruraru me ngā otinga
1. E 30 meneti te roa o te whakamahinga o tētahi rama hiko 220 V – 5. E hia te kaha e hiahiatia ana?
Rongoā:
Ngaohiko (V) = 220 Ngaohiko
Iahiko hiko (I) = 5 Ampere
Wā (t) = 30 meneti = 30 x 60 hēkona = 1800 hēkona
Mana hiko (P):
P = VI = (220 Volt)(5 Ampere) = 1100 Volt Ampere = 1100 Watt = 1100 Joule/hekona
Pūngao hiko = Mana hiko x wā = (1100 Joule/hēkona)(1800 hēkona)
Pūngao hiko = 1,980,000 Joules = 1,980 kiroJoules
2. E 4 meneti te roa o te whakamahi i tētahi rino tūhono 220 V – 60 W. E hia te kaha e hiahiatia ana?
Mōhiotia:
Mana (P) = 60 Watts = 60 Joules/hēkona
Ngaohiko (V) = 220 Ngaohiko
Wā (t) = 4 meneti = 4 x 60 hēkona = 240 hēkona
E hiahiatia ana: Mana hiko
Rongoā:
Ko te tikanga o te 220 Volt – 60 Watt he pai te mahi a te tūhono hiko mēnā he 220 volts te rerekētanga pūmanawa, te ngaohiko rānei, ā, ko tōna mana he 60 Watt = 60 Joules/hekona, ko te tikanga ka whakamahia e te tūhono hiko te pūngao o te 60 Joules ia hekona.
Pūngao hiko = mana hiko x wā = (60 Joule/hēkona)(240 hēkona) = 14,400 Joule.
3. Ko te pūngao e whakamahia ana e te rino mō te 1 meneti he 33 kJ, i te ngaohiko o te 220 volts. Te nui o te iahiko i roto i te rino.
Mōhiotia:
Wā wā (t) = 1 meneti = 60 hēkona
Pungao (W) = 33 kiroJoules = 33,000 Joules
Ngaohiko (V) = 220 Ngaohiko
E hiahiatia ana: Te au hiko (I)
Rongoā:
Ko te mana hiko ko te pūngao hiko e whakamahia ana i roto i tētahi wā kua whakaritea.
P = W / t = 33,000 Joules / 60 hēkona
P = 550 Wāti
Te au hiko:
I = P / V = 550 / 220 = 2.5 Āmperes
4. E ono hāora te roa o te mātakitaki pouaka whakaata a tetahi i te rā. E hono ana te pouaka whakaata ki te hiko 220 Volt, ā, ko te iahiko e rere ana i roto i te pouaka whakaata he 0.5 Amperes. Mēnā he $0.092 te utu a te kamupene hiko mō ia kWh, ko te utu mō te whakamahi i te hiko mō te pouaka whakaata mō te 1 marama (30 rā) ko…
Mōhiotia:
Wā whakatā = 6 hāora x 30 = 180 hāora
Ngaohiko (V) = 220 Ngaohiko
Iahiko hiko (I) = 0.5 Ampere
E hiahiatia ana: Te utu mō ia marama
Rongoā:
Te mana o te pouaka whakaata:
P = VI = (220 Volt)(0.5 Ampere) = 110 Volt Ampere = 110 Watt
Pūngao hiko = mana hiko x wā
Pūngao hiko o te pouaka whakaata = 110 Watt x 180 hāora = 19800 Watt hāora = 19.8 kiro Watt hāora = 19.8 kiro Watt hāora = 19.8 kWh
Te utu mō te whakamahi i te hiko mō te pouaka whakaata mō te 1 marama:
19.8 kWh x $0.092/kWh = $1.8216
5. I roto i tētahi whare e 4 ngā rama 20 Watt, e 2 ngā rama 10 Watt, e 3 ngā rama 40 Watt, e whakamahia ana mō ngā hāora e 5 i ia rā. Mena ko te utu a te kamupene hiko he 0.092 ia kWh, ko te utu mō te whakamahi i te hiko mō te 1 marama (30 rā) ko ….
Mōhiotia:
4 ngā rama 20 Watts = 4 x 20 Watts = 80 Watts
2 ngā rama 10 Watts = 2 x 10 Watts = 20 Watts
3 ngā rama 40 Watts = 3 x 40 Watts = 120 Watts
Mana katoa (W) = 80 Watts + 20 Watts + 120 Watts = 220 Watts
Wā wā (t) = 5 hāora x 30 = 150 hāora
E hiahiatia ana: Te utu mō te whakamahi i te hiko mō te 1 marama (30 rā)
Rongoā:
Pūngao hiko = mana hiko x wā = 220 Watt x 150 hāora = 33,000 Watt hāora = 33 kiro Watt hāora = 33 kiro Watt hāora = 33 kWh
Te utu mō te whakamahi i te hiko mō te 1 marama (30 rā)
(33 kWh)(0.092/kWh) = $3.036
6. Ko te ātete o tētahi ara iahiko he \(5\Omega\) me te iahiko he \(2A\). Kimihia te mana hiko.
Otinga: \( P = IV = 2A \whakareatia ki te 5\Omega = 10W \)
7. Kua honoa he pākahiko \(10V\) ki tētahi ātete \(2\Omega\). Tātaihia te iahiko.
Otinga: \( I = \frac{V}{R} = \frac{10V}{2\Omega} = 5A \)
8. He pūrama rama e 60W te whakatauranga e mahi ana i runga i te pūtake hiko 120V. Kimihia te ātete.
Otinga: \( R = \frac{V^2}{P} = \frac{120^2}{60} = 240\Omega \)
9. Tātaihia te pūngao e pau ana i te pūangi \(100W\) i roto i \(2\) hāora.
Otinga: \( E = Pt = 100W \whakanuia 2h = 200Wh = 0.2kWh \)
10. Ka utaina he pūngao \(20\mu F\) ki te \(50V\). Kimihia te pūngao kua rongoatia.
Otinga: \( E = \frac{1}{2} CV^2 = \frac{1}{2} \times 20 \times 10^{-6}F \times 50^2 = 25mJ \)
11. Tātaihia te iahiko i roto i te inductor \(10mH\) ina ko te tere o te huringa o te iahiko he \(5A/s\).
Otinga: \( V = L\frac{di}{dt} = 10 \times 10^{-3}H \times 5A/s = 50mV \)
12. Kimihia te ngaronga hiko i roto i tētahi raina tuku hiko me te ātete o te \(8\Omega\) me te iahiko o te \(3A\).
Otinga: \( P = I^2R = 3^2 \whakareatia e 8\Omega = 72W \)
13. Ko te ngaohiko tuatahi o te whakawhiti hiko he 120V, ā, ko te ngaohiko tuarua he 240V. Mena ko te iahiko tuatahi he 2A, kimihia te iahiko tuarua.
Otinga: Iahiko tuarua = \( \frac{{\text{{Ngaohiko tuatahi}}}}{{\text{{Ngaohiko tuarua}}}} \times \text{{Iahiko tuatahi}} = \frac{{120V}}{{240V}} \times 2A = 1A \)
14. Tātaihia te tauhohenga o tētahi inductor \(50Hz\), \(0.2H\).
Otinga: \(
15. Kimihia te kaha katoa o ngā pūnga hiko e toru (10µF) e honoa raupapa ana.
Otinga: \( \frac{1}{{C_{\text{{total}}}} = \frac{1}{{C_1}} + \frac{1}{{C_2}} + \frac{1}{{C_3}} = \frac{1}{10} + \frac{1}{10} + \frac{1}{10} = \frac{3}{10}, C_{\text{{total}}} = \frac{10}{3} \mu F \approx 3.33\mu F \)
16. Ka utaina he pūngao nui \(0.1F\) ki \(5V\). Kimihia te pūngao kua rongoatia.
Otinga: \( E = \frac{1}{2} CV^2 = \frac{1}{2} \times 0.1 \times 5^2 = 1.25J \)
17. Tātaihia te tauwehenga mana o tētahi ara iahiko me te mana tūturu o te \(60W\) me te mana āhua o te \(75VA\).
Otinga: Tauwehenga mana = \( \frac{{\text{{Mana Tūturu}}}}{{\text{{Mana Āhua}}}} = \frac{{60W}}{{75VA}} \approx 0.8 \)
18. Kimihia te ātete ōrite o ngā ātete e rua e whakarara ana.
Otinga: \( \frac{1}{{R_{\text{{eq}}}}} = \frac{1}{{R_1}} + \frac{1}{{R_2}} = \frac{1}{4} + \frac{1}{4} = \frac{1}{2}, R_{\text{{eq}}} = 2\Omega \)
19. Whakatauhia te aukati o tētahi ara iahiko me te ātete o te \(5\Omega\) me te tauhohenga o te \(12\Omega\).
Otinga: \( Z = \sqrt{R^2 + X^2} = \sqrt{5^2 + 12^2} \approx 13.34\Omega \)
15. Tātaihia te uara RMS o te ngaohiko sinusoidal me te uara tihi o \(120V\).
Otinga: \( V_{\text{{RMS}}} = \frac{{V_{\text{{peak}}}}}{\sqrt{2}} \approx 84.85V \)
16. Kimihia te mana i marara i roto i tētahi ātete \(5\Omega\) me te iahiko o \(4A\).
Otinga: \( P = I^2R = 4^2 \whakareatia e 5\Omega = 80W \)
17. Tātaihia te auau o tētahi inductor \(25mH\) me te tauhohenga o \(50\Omega\).
Otinga: \( f = \frac{{X_L}}{{2\pi L}} = \frac{50}{{2\pi \times 25 \times 10^{-3}}} \approx 31.83Hz \)
18. Tātaihia te iahiko i roto i tētahi ātete \(20\Omega\) me te pūhiko \(100V\).
Otinga: \( I = \frac{V}{R} = \frac{100V}{20\Omega} = 5A \)
19. Kimihia te tapeke o te inductors o ngā inductors e rua e honoa ana i te taha whakarara.
Otinga: \( \frac{1}{{L_{\text{{total}}}}} = \frac{1}{{L_1}} + \frac{1}{{L_2}} = \frac{1}{10} + \frac{1}{10} = \frac{1}{5}, L_{\text{{total}}} = 5mH \)
20. Tātaihia te pūngao e pau ana i te rino \(1500W\) i whakamahia mō \(0.5\) hāora.
Otinga: \( E = Pt = 1500W \whakanuia 0.5h = 750Wh = 0.75kWh \)
