Makalu

Physics: Darasi game da resistivity and conductivity

  • A darasinmu na kimiyya da fasaha na gefen ilmin kimiyyar lissafi wato (physics) yau zamu san mene ne resistivity da conductivity, daga nan sai mu koyi yadda ake lissafinsu. A Turance ana defining resistivity ne kamar haka; Resistivity of a material is defined as the resistance per unit length per unit cross sectional area of the material. It’s useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.

    Idan muka duba ainihin tarihin resistivity zamu gane cewa ana amfani da wasu symbols wajen lissafin su, wadanda an samo su ne daga Greek letter (rho,ρ), a Turance ana cewa they are quantitatively equal to the resistance R of a specimen such as a wire, multiplied by its cross-sectional area A, and divided by its length Ɩ; ρ = RA /Ɩ. Yana da kyau ku sani cewa unit din resistance shi ne ohm in the metre-kilogram-second(mks).

    Yanzu zamu fitar da su a matsayin yadda suke a formula sannan mu kawo fassarar kowanne fomula a ciki gasu nan kamar haka:

    Resistivity ρ = RA/ ko kuma yana iya zama , ρ = Rπ r ko kuma ya zama, ρ = Rπd/ 4Ɩ

    Za a iya dubaMene ne elementary projectiles

    Yanzu zamu bada fassarar kowanensu a Turance kamar yadda muka fada a baya kuma hakan zai taimaka ma dalibai wajen samun saukin lissafi da kuma sanin wacce formula ce a cikin ukun ta dace ai amfani da ita bayan mun fitar da data wato abubuwan da aka bayar cikin tambayar. Gasu nan kamar haka:

    ρ = resistivity in Ωm

    R = resistance in Ω

    A = cross sectional area = π r= πd/ 4 in (m)

    Ɩ = length of wire in m

    d = diameter of wire in m2

    r = radius of wire in m2

    Electrical conductivity: A Turance ana defining electrical conductivity ne kamar haka, it’s the measure of the amount of electrical current a material can carry or its ability to carry a current, its also known as specific conductance. bayan wannan definition din na electrical conductivity akan ce masa it’s the reciprocal of resistivity, wanda ana auna shi ne da (Ωm)-1 ko kuma Ω-1m-1

    Yanzu zamu kawo formula electrical conductivity.

    Electrical conductivity = 1/ρ = Ɩ/RA = Ɩ/R × π r= 4Ɩ/R × π d 

    Yana da kyau ku tabbatar cewa kun yi lissafinku in uniform unit of measurement, kada ku yi mixing m2 da cm2 ko kuma m da mm. Yanda aka fiso shine kowanne measurement a dauke shi da S.I unit dinsa. Ga kuma wasu abubuwa da ya kamata mu sani a wannan lissafin:

    1mm = 0.001m or 1×10-3m

    1cm = 0.01m or 1×10-2m

    1mm= 0.000001 or 1×10-6m2

    1cm2 = 0.0001 or 1×10-4m2   

    Yanzu zamu dauko misalai wanda tambayoyi ne da suke fitowa a jarabawar aji shidda ta gama sakandire wato ( WAEC,NECO,JAMB).

    Ku duba: Darasi game da electrical method

    Misali na daya:

    Calculate the resistivity of a wire of length 2m and cross-sectional area 0.004cmif its resistance is 3.0 ohm.                                WAEC 2005

    Amsar tambayar:

    Zamu fara duba abubuwan da aka bamu a tambayar sannan sai mu fitar da su daya bayan daya kamun musan wacce fomula ce ta cancanta muyi amfani da ita a cikin lissafin.

    Data:

    Length, Ɩ = 2m = 200cm; cross sectional area A = 0.004cm2;

    Resistance R = 3.0Ω.

    Idan muka duba abubuwan da aka bamu zamu gane cewa akwa formula mai dauke da R,A,Ɩ da kuma ρ, kenan dai abu daya ne bamu da shi a cikin tambayar, shi ne ana so mu nemo resistivity.

    Ga formula kamar haka; Resistivity, ρ = RA / Ɩ = 3×0.004 / 200 = 0.012 / 200 = 0.00006Ω

    = 6.0 × 10-5Ωcm

    Yanzu zamu dauko resistivity in Ωcm wanda ana converting din shi zuwa Ωm ta hanyar dividing by 100 (100cm = 1m)

    Don haka zai zama 0.00006/100 = 6.0 × 10-7 Ωm

    Misali biyu:

    A constant wire has a cross sectional area of 4 10-8m2 and a resistivity of 1.1  10-6Ωm. If a resistor of resistance 11Ω is to be made from this wire, calculate the length of the wire required.

    Yanzu zamu fitar da abubuwan da aka bamu;

    Data:

    A = 4 10-8m ;   Ɩ = 1.1  10-6Ωm ; R = 11Ω

    Tunda munfitar da data yanzu zamu dauko formula da zamu yi amfani da ita.

    From ρ = RA/Ɩ,

    Length, Ɩ = 11 ×4 × 10-8 / 1.1 10-6 0.4m

    Misali na uku:

    A wire of length 100cm and cross-sectional area 2.0 10-3 cmhas a resistance of 0.10Ω. calculate its electrical conductivity.                             NECO 2009

    Amsar tambayar:

    Idan baku manta ba mun fitar da formula da ake amfani wajan lissafin electrical conductivity,yanzu zamu fitar da data domin musan wacce fomula aciki zamu dauka.

    Data:

    Length, Ɩ = 100cm; cross sectional area = 2.0 10-3 cm; R = 0.10Ω

    Electrical conductivity, σ = 1 / ρ = Ɩ / RA = 100 / 0.1 × 2.0 × 10-3 = 5.0 × 105Ω-1cm-1

    Duba: Darasi game da method of mixtures

    Misali na hudu:

    A 2m wire of resistivity 5.5 × 10-7Ωm has a cross sectional area of 0.50mm2. Calculate its resistance.

    Amsar tambayar:

    Data:

    Ɩ = 2m,

    Resistivity, ρ = 5.5 × 10-7 Ω m;

    Cross sectional area, A = 0.50mm= 0.5×10-6m (1mm= 1×10-6)

    Yanzu zamu dauko formula da zamu yi lissafi da ita

    From ρ = RA / Ɩ, resistance R = ρƖ / A = 5.5 × 10-7 / 0.5×10-6 = 1.1×10-6 / 0.5×10-6 2.2Ω

    Misali na biyar:

    A wire of length 15m made of a material of resistivity 1.8×10-6 Ωm  has a resistance of a0.27Ω. determine the area of the wire . A. 1.5×10-4 m   B. 1.0×10-4 m C. 2.7×10-5 m  D. 7.3×10-6 m    JAMB 2006

    Amsar tambayar: 

    Yanzu zamu fitar da abubuwan da aka bamu domin samun saukin lissafi.

    Data:

    Ɩ = 15m; ρ = 1.8×10-6 Ωm; R = 0.27Ω

    From ρ = RA / Ɩ, area, A = ρƖ / R = 1.8×10-6 ×15 / 0.27 = 2.7×10-5 / 0.27

    1.0×10-4m2 

    Wadannan misalan da duk muka kawo muku yana da kyau ku gwada dauko wasu tambayoyi wanda suka shafi resistivity and conductivity domin hakanne zai sa ku kara kwarewa wajen iya lissafinsu da kuma kara fahimtar makala sosai mun gode.

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