25 Lùth dealain – duilgheadasan agus fuasglaidhean
1. Tha lampa dealain 220 V – 5 A air a chleachdadh airson 30 mionaid. Dè an ìre lùtha a dh’fheumas e?
fuasgladh:
bholtaids (V) = 220 Volt
Sruth dealain (I) = 5 Amperes
Ùine (t) = 30 mionaid = 30 x 60 diogan = 1800 diogan
Cumhachd dealain (P) :
P = VI = (220 Volt)(5 Ampere) = 1100 Volt Ampere = 1100 Watt = 1100 Joule / diog
Cumhachd dealain = Cumhachd dealain x ùine = (1100 Joules/diog)(1800 diogan)
Lùth dealain = 1,980,000 Joules = 1,980 kiloJoules
2. Tha iarann-tàthaidh 220 V – 60 W air a chleachdadh airson 4 mionaidean. Dè an ìre lùtha a dh’ fheumas e.
Aithnichte:
Cumhachd (P) = 60 Watts = 60 Joules/diog
Bholtaids (V) = 220 Volt
Ùine (t) = 4 mionaid = 4 x 60 diogan = 240 diogan
Ag iarraidh: Cumhachd dealain
fuasgladh:
220 Volt – Tha 60 Watt a’ ciallachadh gu bheil an t-sàdair dealain ag obair gu math ma tha an diofar comasach no bholtaids 220 bholt agus ma tha cumhachd 60 Watt = 60 Joules/diog aige, a’ ciallachadh gu bheil an t-sàdair dealain a’ cleachdadh lùth 60 Joules gach diog.
Lùth dealain = cumhachd dealain x eadar-ama = (60 Joules/diog)(240 diogan) = 14,400 Joules.
3. Is e 33 kJ an lùth a bhios an iarann a’ cleachdadh airson 1 mionaid, aig bholtaids de 220 bholt. Dè cho mòr ‘s a tha an sruth san iarann.
Aithnichte:
Eadar-ama (t) = 1 mionaid = 60 diogan
Lùth (W) = 33 kiloJoules = 33,000 Joule
Bholtaids (V) = 220 Volt
A dhìth: Sruth dealain (I)
fuasgladh:
Is e cumhachd dealain an lùth dealain a thathar a’ cleachdadh rè ùine sònraichte.
P = W / t = 33,000 Joules / 60 diogan
P = 550 Watt
Sruth dealain:
I = P / V = 550 / 220 = 2.5 Amperes
4. Bidh cuideigin a’ coimhead Tbh airson 6 uairean a thìde san latha air a’ chuibheasachd. Tha an Tbh ceangailte ri bholtaids 220 Volt agus mar sin tha an sruth dealain a’ sruthadh tron Tbh aig 0.5 Amperes. Ma chosgas a’ chompanaidh dealain $0.092 gach kWh, is e cosgais lùth dealain a chleachdadh airson Tbh airson 1 mìos (30 latha)…
Aithnichte:
Eadar-ama = 6 uairean x 30 = 180 uairean
Bholtaids (V) = 220 Volt
Sruth dealain (I) = 0.5 Ampere
A dhìth: A’ chosgais gach mìos
fuasgladh:
Cumhachd an telebhisean:
P = VI = (220 Volt)(0.5 Ampere) = 110 bholta ampere = 110 watt
Lùth dealain = cumhachd dealain x eadar-ama
Lùth dealain an TBh = 110 Watt x 180 uair = 19800 Watt uairean = 19.8 kilo Watt uairean = 19.8 kilo Watt uairean = 19.8 kWh
Cosgais a bhith a’ cleachdadh lùth dealain airson Tbh airson 1 mìos:
19.8 kWh x $0.092/kWh = $1.8216
5. Ann an taigh tha 4 lampaichean 20 Watt, 2 lampa 10 Watt, 3 lampaichean 40 Watt, air an cleachdadh 5 uairean a thìde gach latha. Ma tha cosgais a’ chompanaidh dealain 0.092 gach kWh, is e cosgais cleachdadh lùth dealain airson 1 mìos (30 latha) ….
Aithnichte:
4 lampaichean 20 Watt = 4 x 20 Watt = 80 Watt
2 lampaichean 10 Watt = 2 x 10 Watt = 20 Watt
3 lampaichean 40 Watt = 3 x 40 Watt = 120 Watt
Cumhachd iomlan (W) = 80 Watts + 20 Watts + 120 Watts = 220 Watts
Eadar-ama (t) = 5 uairean x 30 = 150 uairean
A dhìth: Cosgais cleachdadh lùth dealain airson 1 mìos (30 latha)
fuasgladh:
Lùth dealain = cumhachd dealain x eadar-ama = 220 Watt x 150 uair = 33,000 Watt uair = 33 cileavat uair = 33 cileavat uair = 33 kWh
Cosgais cleachdadh lùth dealain airson 1 mìos (30 latha)
(33 kWh)(0.092/kWh) = $3.036
6. Tha strì an aghaidh 5 Omega agus sruth 2 A aig cuairt. Lorg an cumhachd dealain.
Fuasgladh: (P = IV = 2A x 5 Omega = 10W)
7. Tha bataraidh \(10V\) ceangailte ri resistor \(2\Omega\). Obraich a-mach an sruth.
Fuasgladh: (I = \frac{V}{R} = \frac{10V}{2\Omega} = 5A)
8. Bidh bulb solais aig a bheil rangachadh de 60W ag obair air solar 120V. Lorg an aghaidh.
Fuasgladh: (R = \frac{V^2}{P} = \frac{120^2}{60} = 240Ω)
9. Obraich a-mach an lùth a bhios bulb \(100W) a’ caitheamh ann an \(2) uair a thìde.
Fuasgladh: (E = Pt = 100W x 2h = 200Wh = 0.2kWh)
10. Tha comasair 20 mu F air a ghearradh gu 50 V. Lorg an lùth a tha air a stòradh.
Fuasgladh: (E = \frac{1}{2} CV^2 = \frac{1}{2} \times 20 \times 10^{-6}F \times 50^2 = 25mJ)
11. Obraich a-mach an sruth ann an inductor \(10mH\) nuair a tha an ìre atharrachaidh srutha \(5A/s\).
Fuasgladh: (V = Ldi/dt = 10 × 10⁻³ H × 5A/s = 50mV)
12. Lorg an call cumhachd ann an loidhne-tar-chuir le strì an aghaidh Ω(8Ω) agus sruth Ω(3A).
Fuasgladh: (P = I²R = 3² × 8 Omega = 72W)
13. Tha bholtaids phrìomhach de 120V agus bholtaids àrd-sgoile de 240V aig claochladair. Ma tha an sruth prìomhach de 2A, lorg an sruth àrd-sgoile.
Fuasgladh: Sruth àrd-sgoile = ( \frac{{\text{{Bholtadh prìomhach}}}}{{\text{{Bholtadh àrd-sgoile}}}} × \text{{Sruth prìomhach}} = \frac{{120V}}{{240V}} × 2A = 1A)
14. Obraich a-mach ath-bhualadh inductor \(50Hz\), \(0.2H\).
Fuasgladh: \(
15. Lorg comas iomlan trì comasairean \(10\mu F\) ceangailte ann an sreath.
Fuasgladh: ( \frac{1}{{C_{\text{{iomlan}}}} = \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{{iomlan}}} = \frac{10}{3} μF \approx 3.33\muF \)
16. Tha supercomasair \(0.1F\) air a ghearradh gu \(5V\). Lorg an lùth stòraichte.
Fuasgladh: (E = 1/2 CV² = 1/2 × 0.1 × 5² = 1.25J)
17. Obraich a-mach factar cumhachd cuairte le fìor chumhachd de 60W agus cumhachd follaiseach de 75VA.
Fuasgladh: Factar cumhachd = (\frac{{\text{{Fìor Chumhachd}}}}{{\text{{Cumhachd Choltach}}}} = \frac{{60W}}{{75VA} \approx 0.8 \)
18. Lorg an aghaidh co-ionann aig dà aghaidh \(4\Omega\) ann an co-shìnte.
Fuasgladh: (\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. Obraich a-mach impedance cuairte le strì de ≤ 5 Omega agus ath-bhualadh de ≤ 12 Omega.
Fuasgladh: (Z = R² + X² = 5² + 12² = timcheall air 13.34 Omega)
15. Obraich a-mach luach RMS bholtaids sinusoidal le luach as àirde de 120V.
Fuasgladh: (V_{RMS}}} = \frac{{V_{{peak}}}}{\sqrt{2}} \approx 84.85V \)
16. Lorg an cumhachd a thèid a sgaoileadh ann an resistor 5 Omega le sruth de 4 A.
Fuasgladh: (P = I²R = 4² × 5 Omega = 80W)
17. Obraich a-mach tricead inductor 25mH le ath-bhualadh de 50Ω.
Fuasgladh: (f = \frac{{X_L}}{{2πL}} = \frac{50}{{2π \× 25 \× 10^{-3}}} \timcheall air 31.83Hz)
18. Obraich a-mach an sruth ann an resistor 20 Omega le solar 100V.
Fuasgladh: (I = \frac{V}{R} = \frac{100V}{20\Omega} = 5A)
19. Lorg an ionduchtachd iomlan aig dà ionduchtair \(10mH\) ceangailte ann an co-shìnte.
Fuasgladh: (\frac{1}{{L_{\text{{iomlan}}}}} = \frac{1}{{L_1}} + \frac{1}{{L_2}} = \frac{1}{10} + \frac{1}{10} = \frac{1}{5}, L_{\text{{iomlan}}} = 5mH)
20. Obraich a-mach an lùth a bhios iarann \(1500W) a’ caitheamh airson \(0.5) uairean.
Fuasgladh: (E = Pt = 1500W x 0.5h = 750Wh = 0.75kWh)
