Matsayin Hadisar Millman

Teorema na Millman ya zama da sunan daga fili mai karatu na kimiyya na inganci JACOB MILLMAN wanda ya bayar fikirin wannan teorem. Teorema ta Millman yana aiki a matsayin alama mai yawa a lokacin da aka yi gudanar da abubuwa mai yawa na cikakken kimiyya. Wannan teorem ba shi ne musamman yadda kan Teorema na Thevenin da Teorema na Norton. Yana taimakawa a gudanar da voltage a kan muhimmanci da karamin ruwa a kan muhimmanci. Wannan teorem tana da sunan TEOREMA NA MAKARANTA.
Teorema na Millman yana iya amfani a cikakken kimiyya da ke da voltage sources da suka bai da sauran current sources da suka bai da sauran. Ba na nufin a tafi kan haka.

Cikakken da ke da Voltage Sources Kawai

Ba na iya samun cikakken kimiyya kamar yadda ake nuna a taswirin a cikin fagen a.

A nan V1, V2 da V3 su ne voltage na farkon, na biyu da na uku. R1, R2 da R3 su ne resistance daga baya. IL, RL da VT su ne load current, load resistance da terminal voltage.
A nan za a iya gudanar da wannan cikakken kimiyya mai yawa zuwa cikakken equivalent voltage source da series resistance da take da Teorema na Millman kamar yadda ake nuna a taswirin b.

Yadda ake nufin equivalent voltage VE a cikin Teorema na Millman ya zama –

VE ya zama Thevenin voltage da Thevenin resistance RTH za a iya tabbatar da ita daidai. Saboda haka RTH ya zama

Load current da terminal voltage za su iya samun daidai da

Ba na iya samun fahimta duka cewa a kan Teorema na Millman da tushen misal.

Misali – 1
A cikakken kimiyya ne kamar yadda ake nuna a taswirin c. Samun voltage a kan 2 Ohm resistance da karamin ruwa a kan 2 ohm resistance.

Amsa : Ana iya samun wannan babban maimaitaccen kimiyya da koyarren rike, amma an fara daidai da Teorema na Millman. Cikakken kimiyya ya zama cikakken kamar yadda ake nuna a taswirin d inda equivalent voltage VE ya zama da millman’s theorem da shi ne


Equivalent resistance ko Thevenin resistance ya zama da shorting the voltage sources kamar yadda ake nuna a taswirin e.


Na iya samun karamin ruwa a kan 2 Ohm load resistance da Ohm’s law.

Voltage across load is,

Cikakken da ke da Mixture of Voltage and Current Source

Teorema na Millman yana taimakawa a gudanar da mixture of voltage and current source connected in parallel zuwa single equivalent voltage ko current source. Ba na iya samun cikakken kimiyya kamar yadda ake nuna a taswirin f.

Harshen duka irin letters ya zama ma'ana masu tsari. Cikakken ya zama cikakken kamar yadda ake nuna a taswirin g.

Inda VE wanda ba shi ne Thevenin voltage wanda za a iya tabbatar da ita da Teorema na Millman da shi ne

RTH za a iya tabbatar da ita da current sources with open circuits da voltage sources with short circuits.

Na iya samun load current IL da terminal voltage VT da Ohm’s law.

Ba na iya samun fahimta duka cewa a kan tushen misal.

Misali 2 :

A cikakken kimiyya ne kamar yadda ake nuna a taswirin h. Samun karamin ruwa a kan load resistance inda RL = 8 Ω.

Amsa : Wannan babban maimaitaccen kimiyya na iya zama da mutane da kuma zama da wata, amma ana iya samun shi da wata da Teorema na Millman. Cikakken ya zama cikakken kamar yadda ake nuna a taswirin i. Inda VE ya zama da Teorema na Millman,


Saboda haka, karamin ruwa a kan load resistance 8 Ω ya zama,