If R and C denote resistance and capacitance of a material, then the dimension of C R will be :

Step-by-step solution

The dimension of resistance R is given by R = V I . Since V = W q , we have R = W Iq = [ML^2T⁻²] [A][AT] = [ML^2T⁻³A⁻²] . The dimension of capacitance C is given by C = q V . Since V = W q , we have C = q^2 W = [AT]^2 [ML^2T⁻²] = [M⁻¹L⁻²T^4A^2] . The product CR has dimensions [M⁻¹L⁻²T^4A^2] [ML^2T⁻³A⁻²] = [M¹⁻¹L²⁻²T⁴⁻³A²⁻²] = [M^0L^0T^1] . Thus, the dimension of CR is [T] , which corresponds to [M^0L^0T] . Answer: [ M ^0 ~L ^0 ~T ]