Dimensional formula of electric conductivity of a material
Answers
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Answer:
M^-1 L^-3 T^3 I
Explanation:
Resistivity of a material is given by
ρ= A R / S where A is area of cross section, R is the resistance and S is the length of the conductor,
Conductivity is the reciprocal of resistivity and hence
σ = S/ (AR)
(S/A) has the dimension L^(-1)
We have to find the dimension of R^(-1)
R^(-1)=I / E where E is the potential difference and I is the current.
Multiplying the numerator and denominator by I we get
R^(-1)= I^2/ ( EI) and we know E I is the power and its dimension is
ML^(2 ) T^(-3)
Dimension of R^(-1) is M^(-1) L^(-2 ) T^3 I^2
Dimension of σ is L^(-1)*(M^(-1) L^(-2 ) T^3 I^2
Dimension of σ = M^(-1) L^(-3 ) T^3 I^2
S I unit of conductance is (A^2 s^3 m^(-3) kg^(-1)) = kg^(-1) m^(-3) s^3 A^2 arranging in the order of mass, length time and current.
And one can verify that the above result is correct .