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  • Understanding the Dimensions of Electrical Conductivity [M⁻¹L⁻³T³I²]
    The dimension of conductivity is [M⁻¹L⁻³T³I²].

    Here's how we break it down:

    * M: Mass

    * L: Length

    * T: Time

    * I: Electric Current

    Let's derive it from the definition of conductivity:

    * Conductivity (σ) = Current density (J) / Electric field (E)

    Now, let's break down the dimensions of each component:

    * Current density (J): Current per unit area, so its dimension is [I/L²] = [I L⁻²]

    * Electric field (E): Force per unit charge, so its dimension is [M L T⁻² / I T] = [M L T⁻³ I⁻¹]

    Therefore, the dimension of conductivity is:

    σ = [J/E] = [I L⁻² / (M L T⁻³ I⁻¹)] = [M⁻¹L⁻³T³I²]

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