Kofin Rms: Me ke nan? (Fomular Da Kuma Yadda Ake Kula)

Electrical4u

فیلڈ: Karkashin Kuliya da Dukkana

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Zuwa da RMS Voltage?

RMS na nufin Root Mean Square. RMS voltage yana nufin kare-karfin kasa da ya fi sani da ci abubuwa masu zaman lafiya na voltaji. RMS tana da sunan quadratic mean. Ana iya bayyana RMS voltage a matsayin integral ga kwadara masu zaman lafiya a lokacin wanda voltaji ta zama daidai.

RMS value yana da muhimmanci a cikin AC signal. Saboda haka, babu da yanayi da za suka shafi wakar voltaji a cikin AC signal, musamman saboda yadda yake daidai da zaman. Ba a cikin DC signal, wanda yake daidai da kullum.

Saboda haka, ba za a iya amfani da yanayi na wakar voltaji daga baya don ina shafi.

RMS voltage tana da sunan equivalent DC voltage saboda RMS value na iya bayyana kungiyoyin AC power da ya kasance a cikin resistor, kamar da kungiyoyin power da ya kasance a cikin DC source.

Misali, za a iya ambaci 5Ω load da ya danganta da 10V DC source. A cikin DC source, yadda ake shafi wakar voltaji ita daidai a cikin wani lokaci. Saboda haka, ana iya shafi kungiyoyin power da ya kasance, kuma ita 20W.

Amma idan a yi haka ne, za a iya amfani da AC source. A cikin hakan, yadda ake shafi wakar voltaji ita daidai da zaman, kamar da aka nuna a cikin figure.

AC signal yana da wata sinusoidal wave signal a cikin duk lokaci, kamar da aka nuna a cikin figure. Saboda haka, ba za a iya amfani da yanayi na wakar voltaji daga baya don ina shafi kungiyoyin power.

Amma idan a yi haka ne, za a iya shafi RMS value na signal, za a iya amfani da shi don ina shafi kungiyoyin power. Misali, idan RMS value ita 10Vrms. Kungiyoyin power da ya kasance a cikin load ita 20W.

A taka da ake gina a kanannuwa ita ce RMS voltage. Multimeters sun kuma bayarwa ne mai RMS don AC power. Kuma a power system, ana amfani da system voltage wanda yake da RMS value.

Yadda ake kula RMS Voltage

An kula RMS value kawai don waveforms da take canza da lokacin, inda ingantaccen abu yana canza da lokaci.

Ba zan iya samun RMS value na waveform na DC ba saboda waveform na DC yana da hukuma daidai da lokacin.

An fi sani biyu na kula RMS value.

Hali na Graphical
Hali na Analytical

Hali na Graphical

A hali na, ana amfani da waveform don samun RMS value. Hali na graphical yana da muhimmanci mafi yawa idan alama ba ta da tsari ko sinusoidal ba.

Zamantakewar hali na yana da shugaban da suka cikin jumla'ar abubuwan da aka ci dari waveform. Abubuwan da suka biyu suna da muhimmanci masu karfi, kuma abubuwan da suka da shi suna da muhimmanci masu karfin.

RMS value yana da shi ne karni mai karfi da kuma karkashin kwallonsa. Misali, za a iya samun waveform na sinusoidal na voltage kamar hakan.

Koyi waɗannan hali domin samun RMS voltage na hali na graphical.

Step-1: Saka waveform zuwa abubuwan da suka da shi. A nan, an sanar da na baya na waveform. Zan iya sanar da na baya kuma.

Yaraduwa na farko ta zama da kasa a gaba da shekarun da dama; V1, V2, …, V10.

Raka-2: Zaɓe tashin kawo da yawa.

$V_1^2, V_2^2, V_3^2, …, V_{10}^2$

Raka-3: Zaɓe masu kawo da yawa. Zan iya samun jimlar da ke cikin waɗannan ƙarin halayyar da suka zaɓe, sannan zaɓe masu kawo da yawa.

$\frac{V_1^2+V_2^2+V_3^2+V_4^2+V_5^2+V_6^2+V_7^2+V_8^2+V_9^2+V_{10}^2}{10}$

Raka-4: Na gode, zaɓe takalmomi mai sauƙi na wannan ƙarin halayyar da suka zaɓe.

$V_{RMS} = \sqrt{\frac{V_1^2+V_2^2+V_3^2+V_4^2+V_5^2+V_6^2+V_7^2+V_8^2+V_9^2+V_{10}^2}{10}}$

Waɗannan ƙarin halayya suna da shi a cikin duk fannonin juyin da suke da tsawon karamin lokaci.

A nan, a cikin fannonin juyin da suke da tsawon karamin lokaci kamar triangular, square; ana yi waɗannan ƙarin halayya don samun RMS voltage.

Zan iya bayyana waɗannan ƙarin halayya da misalai.

Koyar da muhimmancin halayen karamin siffofin wata a cikin takarda ta haka. Fara da karamin siffofin kashi mai zurfi.

Rukunin-1: Koyar da farkon yakin zuwa dubu biyar. Kuma abubuwan da suka shafi a cikin takarda su ne.

Rukunin-2: Tabbatar da karamin kwadra kan baki daya.

6.2	11.8	16.2	19	20	19	16.2	11.8	6.2	0
38.44	139.24	262.44	361	400	361	262.44	139.24	38.44	0

Littafin-3: Kula a cikin abubuwa da aka kawo karfi.

$\frac{38.44+139.24+262.44+361+400+361+262.44+139.24+38.44+0}{10} = 200.22$

Littafin-4: Tabbatar da sakarun kwadra.

$\sqrt{200.22} = 14.15$

$V_{RMS} = 14.15 V$

Raddadi na Raddadi

A tsaftace, zan iya kula a cikin abubuwan da aka kawo karfi ta tsari da yanayin lissafi. Tsaftacen ya shahara da zai iya bayyana daidai wajen kula a cikin abubuwan da aka kawo karfi mai sauƙi daɗi.

Zaɓi abubuwan da aka kawo karfi mai sauƙi daɗi da aka bayyana a matsayin VmCos(ωt) tare da tsari na T.

Idan,

Vm = Yadda mai gaba ko yadda mai tsafta cikin tsari na karamin karami

ω = tatsuniya = 2π/T

A nan, zan iya kula yadda mai RMS na karamin karami.

$V_{RMS} = \sqrt{\frac{1}{T} \int_{0}^{T} V_m^2 cos^2(\omega t) dt}$

$V_{RMS} = \sqrt{\frac{V_m^2}{T} \int_{0}^{T} cos^2(\omega t) dt}$

$V_{RMS} = \sqrt{\frac{V_m^2}{T} \int_{0}^{T} \frac{1+cos(2 \omega t)}{2} dt}$

$V_{RMS} = \sqrt{\frac{V_m^2}{2T} \int_{0}^{T} 1+cos(2 \omega t) dt}$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ t + \frac{sin(2 \omega t)}{2 \omega} \right ]_0^T$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ (T-0) + (\frac{sin(2 \omega T)}{2 \omega} - \frac{sin 0}{2 \omega} ) \right ]$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T + \frac{sin(2 \omega T)}{2 \omega} \right ]$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T + \frac{sin(2 \frac{2 \pi}{T} T)}{2 \frac{2 \pi}{T} } \right ]$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} \left[ T +\frac{sin(4 \pi)}{2 \frac{2 \pi}{T}} \right ]$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2T} [T+0]}$

$V_{RMS} = \sqrt{\frac{ V_m^2}{2}$

$V_{RMS} = V_m \frac{1}{\sqrt{2}}$

$V_{RMS} = V_m 0.7071$

Saboda haka, za a iya koyar da ma'anar RMS na tsarin sinusoidal mai zurfi daga ma'anar peak (maximum).

A tattalin bayanin (graphical method) na farko, ana ma'anar peak 20V.

$V_{RMS} = 0.7071 \times 20$

$V_{RMS} = 14.142 V$

RMS Voltage Formula

Za a iya koyar da RMS voltage daga ma'anar peak, peak-to-peak, da kuma average value.

Don tsarin sinusoidal, ana amfani da wannan formula masu koyar da RMS voltage.

Daga faduwar tsari (VP);

$V_{RMS} = \frac{1}{\sqrt{2}} V_P = 0.7071 V_P$

Daga faduwar tsari zuwa faduwar tsari (VPP);

$V_{RMS} = \frac{1}{2\sqrt{2}} V_{PP} = 0.353 V_{PP}$

Daga tsari na musamman (VAVG);

$V_{RMS} = \frac{\pi}{2\sqrt{2}} V_{AVG} = 1.11 V_{AVG}$

Tsari na RMS da Tsari na Karamin Gwamna da Tsari na Karamin Gwamna zuwa Tsari na Karamin Gwamna da Tsari na Kafin Gwamna

Tsari na RMS yana da muhimmanci a cikin hanyoyi da dama a kabiluwar AC. Duk da cewa tsari na karamin gwamna, tsari na karamin gwamna zuwa karamin gwamna, da kuma tsari na kafin gwamna suna da muhimmanci.

Tsari na Karamin Gwamna

Tsari na karamin gwamna yana nufin babban ma'adin da ke tsari a nan wani abu mai tsari. Tsari na karamin gwamna yana nuna tushen da ya kai daga shi (0) zuwa babban ma'adinsa na abu mai tsari.

Idan a duba abu mai tsari na sinusoide, ziyarta tsari yana bazuwa daga shi (0) zuwa babban ma'adinsa na abu mai tsari a karamin gwamna. Tushen da ke duka waɗannan biyu na nuna tsari na karamin gwamna na musamman.

Daga babban ma'adinsa, tsari yana bazuwa zuwa shi (0). Ba da nan, yana bazuwa a karamin gwamna na haske zuwa babban ma'adinsa. Wannan shi ne babban ma'adinsa na haske.

A zai iya kula tsari na karamin gwamna daga tsari na RMS, tsari na karamin gwamna zuwa karamin gwamna, da kuma tsari na kafin gwamna.

Tsari na Karamin Gwamna Daga Tsari na RMS

Don kula tsari na karamin gwamna daga tsari na RMS, a zai iya yara tsari na RMS da yanayi na 1.414.

$V_{PEAK} = V_{RMS} \times \sqrt{2} = V_{RMS} \times 1.414$

Tsari na Karamin Gwamna Daga Tsari na Karamin Gwamna zuwa Karamin Gwamna

Tsari na karamin gwamna yana nuna tsarin tsari na karamin gwamna zuwa karamin gwamna.

$V_{PEAK} = V_{PP} \times 0.5$

Yadda ake kalkulatar da shi da ci gaba na tsawon ci gaba

Don kalkulatar da shi da ci gaba na tsawon ci gaba, ya kamata a yi kafin da tsawon ci gaba tare da kashi na 1.57.

$V_{PEAK} = V_{AVG} \times \frac{\pi}{2} = V_{RMS} \times 1.57$

Tsawon ci gaba na ci gaba

Tsawon ci gaba na ci gaba shine farko daga tsawon ci gaba mai karfi zuwa tsawon ci gaba mai yamma.

Don wasu mai karfi, tsawon ci gaba na ci gaba ana nufin cikin bayanan.

Tsawon ci gaba na ci gaba

Zan iya kalkulatar da shi da ci gaba na ci gaba daga tsawon RMS, tsawon ci gaba, da tsawon ci gaba na musamman.

Garuruwar Tsari Daga RMS Tsari

Don samun garuruwar tsari daga RMS tsari, 2.8284 ita ce zakaɗin yadda ake kawo.

$V_{PP} = V_{RMS} \times 2\sqrt{2} = V_{RMS} \times 2.8284$

Garuruwar Tsari Daga Tsari Mai Garuruwa

Garuruwar tsari tana da duka tsari mai garuruwa na biyu.

$V_{PP} = V_{PEAK} \times 2$

Garuruwar Tsari Daga Tsari Mai Yawan Daidaita

Don samun garuruwar tsari daga RMS tsari, 3.14 (π) ita ce zakaɗin yadda ake kawo.

$V_{PP} = V_{AVG} \times \pi = V_{AVG} \times 3.14$

Tsarin Karamin Salla

Yadda ake koyar da tsarin karamin salla ya dacewa da yadda ake koyar da RMS voltage. Yawan farko ne na cewa abubuwan da suka fi shi ba su gane da square function ko ba su gane da square root.

Tsarin karamin salla ya baka mu tushen lamsa. Da kuma misali mai yawa a kan tushen lamsa ce mafiya da misali mai yawa a kan tushen lamsa. Ana kiran shi a matsayin tsarin karamin salla.

Zan iya koyar da tsarin karamin salla daga RMS voltage, peak voltage, da peak-to-peak voltage.

Tsarin Karamin Salla Daga RMS Voltage

Don koyar da tsarin karamin salla daga RMS voltage, 0.9 ita ce approximate multiplier factor.

$V_{AVG} = 0.9 V_{RMS}$