Ihe Nlereanya nke Nsogbu Ndị Na-ekwu Maka Mgbanwe Nha nhata Ugbu A
Pendahuluan
Ọwa eletriki ọzọ (AC) bụ ụdị ọkụ eletrik nke nwere ike ịgbanwe ntụziaka mgbe ụfọdụ. N'adịghị ka ọkụ eletrik kpọmkwem (DC), nke na-aga n'otu ụzọ, AC nwere ụdị ebili mmiri sinusoidal ma dị oke mkpa n'ọtụtụ ngwa kwa ụbọchị, site n'ezinụlọ ruo n'ụlọ ọrụ mmepụta ihe. Ịmara otu esi arụ ọrụ na nha nha ọkụ eletrik dị oke mkpa iji ghọta ọtụtụ akụkụ dị mkpa nke eletrọniki na ọkụ eletrik. Isiokwu a ga-atụle ọtụtụ nsogbu na ngwọta iji mee ka echiche nke nha nha ọkụ eletrik ọzọ doo anya.
Nhazi Izugbe nke Ugbu a Na-agbanwe Agbanwe
A na-egosipụtakarị mgbanwe ọkụ eletrik site na nha sinusoidal:
\[ i(t) = Abụ m \sin(\omega t + \phi) \]
Ebe:
– \(i(t) \) bụ ọkụ eletrik ozugbo dịka ọrụ oge si dị.
– \( I_m \) bụ uru kachasị elu (kachasị) nke ugbu a.
– \( \omega \) bụ ọsọ angular, ya na nkeji nke radians kwa sekọnd.
– \( t \) bụ oge.
– \( \phi \) bụ usoro mbụ nke ugbu a.
Ajụjụ Ihe atụ nke 1: Ịchọpụta Ugbu a n'Oge A Kpọrọ
Ajụjụ:
E nyere nha nha ugbu a nke na-agbanwe agbanwe \( i(t) = 10 \sin(100\pi t + \pi/3) \). Chọpụta oke nke ugbu a n'oge \(t = 0.01 \) sekọnd.
Azịza:
A maara:
\[ M_m = 10 \, \ederede{A} \]
\[ \omega = 100\pi \, \text{rad/s} \]
\[ \phi = \pi/3 \]
\[ t = 0.01 \, \ederede{sekọnd} \]
Tinye ụkpụrụ ndị a n'ime usoro dị ugbu a:
\[ i(0.01) = 10 \sin(100\pi \ugboro 0.01 + \pi/3) \]
\[ i (0.01) = 10 \ sin(\pi + \ pi/3) \]
\[ i (0.01) = 10 \ mmehie (4\pi/3) \]
Ekwuru na:
\[ \ sin(4\pi/3) = -\ sin(\pi/3) \]
\[ \ sin(\pi/3) = \sqrt{3}/2 \]
Ya mere:
\[ \ sin(4\pi/3) = -\sqrt{3}/2 \]
\[ i(0.01) = 10 \ugboro -\sqrt{3}/2 \]
\[ i(0.01) = -5\sqrt{3} \]
\[ i(0.01) \ihe dịka -8.66 \, \ederede{A} \]
Ya mere, oke nke ugbu a n'oge \(t = 0.01 \) sekọnd dị ihe dị ka \(-8.66 \, \text{A} \).
Ajụjụ Ihe Nlereanya nke 2: Ịchọpụta Ọsọ na Ugboro Angular
Ajụjụ:
Maka ọkụ eletrik na-agbanwe agbanwe nke e gosipụtara site na nha anya \( i(t) = 5 \cos(200\pi t – \pi/4) \), chọpụta ọsọ angular (ω) na ugboro (f) nke ọkụ eletrik.
Azịza:
E nyere:
\[ i(t) = 5 \cos(200\pi t – \pi/4) \]
Ọsọ angular (\( \omega \)) bụ ọnụọgụ nke \( t \) na arụmụka cosine, nke bụ \( 200 \pi \).
\[ \omega = 200\pi \, \text{rad/s} \]
Enwere ike nweta ugboro ugboro (f) site na iji mmekọrịta ahụ:
\[ \omega = 2\pi f \]
\[f = \frac{\omega}{2\pi} \]
Dochie uru ọsọ angular:
\[f = \frac{200\pi}{2\pi} \]
\[f = 100 \, \ederede{Hz} \]
Ya mere, ọsọ nke ugbu a bụ \( 200\pi \, \text{rad/s} \) na ugboro nke ugbu a bụ \( 100 \, \text{Hz} \).
Ajụjụ Ihe Nlereanya nke 3: Ịchọpụta Uru RMS
Ajụjụ:
Maka ọkụ eletrik nke a na-agbanwe agbanwe nke \(i(t) = 7 \sin(50t) \ nyere), chọpụta uru RMS (mkpụrụedemede mgbọrọgwụ nkezi square).
Azịza:
A maara:
\[ i(t) = 7 \sin(50t) \]
Uru RMS maka ugbu a sinusoidal bụ:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
ebe \(I_m \) bụ uru kachasị elu nke ugbu a.
Uru kachasị elu nke ugbu a \(I_m \) bụ 7 A.
Ya mere:
\[ I_{\text{RMS}} = \frac{7}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{7 \sqrt{2}}{2} \]
\[ I_{\text{RMS}} \ihe dị ka 4.95 \, \text{A} \]
Ya mere, uru RMS maka ugbu a bụ ihe dịka 4.95 A.
Ihe atụ Ajụjụ nke 4: Ịgbakọ Ike nkezi
Ajụjụ:
Sekit eletriki nwere resistor 10 ohm ma nwee ọkụ eletrik na-agbanwe agbanwe \( i(t) = 6 \sin(120\pi t) \). Gbakọọ ike nkezi nke resistor na-eri.
Azịza:
N'ihi ugbu a:
\[ i(t) = 6 \sin(120\pi t) \]
Uru kachasị elu nke ugbu a (\( I_m \)) bụ 6 A.
Uru RMS nke ugbu a bụ:
\[ I_{\text{RMS}} = \frac{I_m}{\sqrt{2}} \]
\[ I_{\text{RMS}} = \frac{6}{\sqrt{2}} \]
\[ I_{\text{RMS}} = 3\sqrt{2} \]
Nguzogide (\( R \)) = 10 ohms.
Enwere ike ịgbakọ ike nkezi (\(P \)) na resistor site na:
\[ P = I_{\text{RMS}}^2 \times R \]
\[ P = (3\sqrt{2})^2 \ugboro 10 \]
\[ P = 18 \ugboro 10 \]
\[ P = 180 \, \ederede{W} \]
Ya mere, ike nkezi nke resistor na-eji bụ 180 W.
Penutup
N'isiokwu a, anyị ekpuchila ọtụtụ nsogbu atụ ma tụlee nha nhata maka mgbanwe ọkụ eletrik. Ịmara otu esi agbakọ oge ugbu a kwa nkeji, ọsọ angular, ugboro ole, uru RMS, na ike nkezi dị oke mkpa maka ịghọta mgbanwe ọkụ eletrik na ojiji ya na ndụ kwa ụbọchị. Ịghọta echiche ndị a na-enyere anyị aka ịmepụta ma nyochaa sekit eletriki dị iche iche nke na-eji mgbanwe ọkụ eletrik.
