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Question 58 of 73

Q.Unit of specific conductance :

(a) ohm−1ohm^{-1}
(b) ohm−1 m2ohm^{-1}\,m^2
(c) ohm−1 m−1ohm^{-1}\,m^{-1}
(d) ohm mohm\,m
Tamil Nadu DgeTamil Nadu HSC (DGE) Board 2019MCQ· 1mImportance★★★★★
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Specific conductance κ=1/ρ\kappa = 1/\rho (reciprocal of resistivity), and since resistivity has SI unit ohm⋅mohm\cdot m, specific conductance has unit ohm−1 m−1ohm^{-1}\,m^{-1} (equivalently S m−1S\,m^{-1}).

Electrical resistance RR (ohm) of a conductor of length ll and cross-sectional area AA is given by R=ρlAR=\rho \dfrac{l}{A}, so resistivity ρ=RAl\rho = R\dfrac{A}{l} has SI unit ohm ×m2m=ohm⋅m\times \dfrac{m^2}{m} = ohm\cdot m. Specific conductance (conductivity), κ\kappa, is defined as the reciprocal of resistivity, κ=1/ρ\kappa = 1/\rho, so its unit is the reciprocal of ohm⋅mohm\cdot m, i.e. ohm−1 m−1ohm^{-1}\,m^{-1} (also written as siemens per metre, S m−1S\,m^{-1}). ohm−1ohm^{-1} alone (option a) …

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