Eisimpleir de Cheistean Deasbaid Cuairt RLC
'S e seòrsa de chuairt dealain a th' ann an cuairt RLC anns a bheil resistor (R), inductor (L), agus capacitor (C) ceangailte ann an sreath no co-shìnte. Tha cuairtean RLC air an cleachdadh gu farsaing ann an grunn thagraidhean dealanach, nam measg ann an sìoltachain tonn, oscillators, measgachadh chomharran, agus barrachd. Tha tuigse air mar a nì thu sgrùdadh agus fuasgladh air duilgheadasan anns na cuairtean sin na sgile chudromach do dh'oileanaich innleadaireachd dealain agus proifeiseantaich san raon.
San artaigil seo, bruidhnidh sinn air grunn eisimpleirean de dhuilgheadasan agus na fuasglaidhean aca a tha co-cheangailte ri mion-sgrùdadh chuairtean RLC. Tha na duilgheadasan seo air an dealbhadh gus do chuideachadh le bhith a’ tuigsinn nam prionnsapalan bunaiteach agus nan tagraidhean a tha aig cuairtean RLC.
Eisimpleir de Dhuilgheadas 1: Cuairt Sreath RLC
Ceist:
Ma tha cuairt sreath againn anns a bheil resistor le strì an aghaidh (R = 10, Omega), inductor le inductance (L = 0.1, H), agus capacitor le comas (C = 100, µF). Tha bholtaids sinusoidal (V(t) = 100 sin(1000 t) V) air a thoirt don chuairt seo. Obraich a-mach:
1. Ath-bhualadh ionduchtach \(X_L \) agus ath-bhualadh comasach \(X_C \).
2. Impedance iomlan a’ chuairt.
3. An sruth as àirde \( I_{max} \).
4. Am bholtaids as àirde air gach pàirt.
Deasbad:
1. Freagairt Ion-ghluasadach \(X_L \) agus Freagairt Chomasachail \(X_C \)
Tha ath-bhualadh ionduchtach \( X_L \) air a thomhas leis an fhoirmle:
[X_L = Ω L]
le (omega = 1000, rad/s) agus (L = 0.1, H),
[X_L = 1000 × 0.1 = 100, Omega]
Tha an ath-bhualadh comasach \( X_C \) air a thomhas leis an fhoirmle:
[X_C = \frac{1}{\omega C} \]
le (C = 100, μF = 100 × 10⁻⁶, F),
\[
2. Impedance Iomlan a’ Chuairteachaidh
Is e an impedance iomlan \(Z \) airson cuairt RLC sreath:
[Z = \sqrt{R^2 + (X_L – X_C)^2}]
Cuir na luachan an àite:
\[ Z = \ sqrt{10^2 + (100 – 10)^2} = \ sqrt{10^2 + 90^2} = \ sqrt{100 + 8100} = \ sqrt{8200} = 90.55 \, \ Omega \]
3. An sruth as àirde \( I_{max} \)
Faodar an sruth as àirde obrachadh a-mach le bhith a’ cleachdadh lagh Ohm:
[ I_{max} = \frac{V_{max}}{Z} \]
le (V_{max} = 100, V) agus (Z = 90.55, Omega):
[I_{max} = \frac{100}{90.55} = 1.104 \, A \]
4. Am bholtaids as àirde air gach pàirt
Bholtaids air an resistor:
[V_R = I_{max} \times R = 1.104 \times 10 = 11.04 \, V \]
Bholtaids air an inductor:
[V_L = I_{max} × X_L = 1.104 × 100 = 110.4, V]
Bholtaids air a’ chomasair:
[V_C = I_{max} × X_C = 1.104 × 10 = 11.04, V]
Eisimpleir Ceist 2: Cuairt RLC Co-shìnte
Ceist:
Ma tha cuairt co-shìnte ann, anns a bheil resistor le strì an aghaidh (R = 50, Omega), inductor le inductance (L = 0.5, H), agus capacitor le comas (C = 10, µF). Tha an stòr bholtaids sinusoidal le bholtaids (V(t) = 200 cos(2000 t), V). Obraich a-mach:
1. Ath-bhualadh ionduchtach \(X_L \) agus ath-bhualadh comasach \(X_C \).
2. Cead a-steach iomlan na cuairte.
3. An sruth as àirde \( I_{max} \).
Deasbad:
1. Freagairt Ion-ghluasadach \(X_L \) agus Freagairt Chomasachail \(X_C \)
Tha ath-bhualadh ionduchtach \( X_L \) air a thomhas leis an fhoirmle:
[X_L = Ω L]
le (omega = 2000, rad/s) agus (L = 0.5, H),
[X_L = 2000 × 0.5 = 1000, Omega]
Tha an ath-bhualadh comasach \( X_C \) air a thomhas leis an fhoirmle:
[X_C = \frac{1}{\omega C} \]
le (C = 10, μF = 10 × 10⁻⁶, F),
\[
2. Cead a-steach iomlan na cuairte
Is e an admittance \(Y \) co-ionannachd an impedance. Airson cuairt RLC co-shìnte:
[Y = \sqrt{G^2 + (B_L – B_C)^2}]
far a bheil G = 1/R,
[G = \frac{1}{50} = 0.02 \, S \]
Glacadh ionduchtach \( B_L \):
[B_L = \frac{1}{X_L} = \frac{1}{1000} = 0.001 \, S \]
Gabhailteachd comasach \( B_C \):
[B_C = \frac{1}{X_C} = \frac{1}{50} = 0.02 \, S]
Cuir na luachan uile an àite na foirmle:
\[ Y = \sqrt{0.02^2 + (0.001 – 0.02)^2} = \ sqrt{0.0004 + 0.000361} = \sqrt{0.000761} = 0.0276 \, S \]
Is e an impedance iomlan \( Z \) co-ionann ri co-phàirteach an admittance:
[Z = \frac{1}{Y} = \frac{1}{0.0276} = 36.23 \, Omega \]
3. An sruth as àirde \( I_{max} \)
[ I_{max} = \frac{V_{max}}{Z} \]
le (V_{max} = 200, V) agus (Z = 36.23, Omega):
[I_{max} = \frac{200}{36.23} \approx 5.52 \, A \]
Co-dhùnadh
Tha e deatamach tuigse fhaighinn air mar a nì thu obrachadh a-mach ath-bhualadh, admittance, impedance, agus sruth ann an cuairt RLC airson tagraidhean ann an innleadaireachd dealain. Le cleachdadh cunbhalach tro dhiofar eisimpleirean mar an fheadhainn air an do bhruidhinn sinn, bidh do thuigse air mion-sgrùdadh cuairt RLC a’ dol nas doimhne. Cuidichidh cleachdadh leantainneach le bhith a’ leasachadh do sgilean fuasgladh-cheistean agus dealbhadh san àm ri teachd de chuairtean dealain iom-fhillte.
