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A physical quantity X is defined as ε0L(ΔV/Δt), where ε0 denotes the permittivity of free space, L is a length, ΔV is a potential difference, and Δt is a time interval. The dimensional formula of X matches that of which of the following?

1. resistance
2. charge
3. potential difference
4. electric current

Correct answer: electric current

Solution

eps0 times a length has the dimensions of capacitance (C = eps0*Area/d ~ eps0*length). Then X = C*(dV/dt) = I, the displacement current, so X has the dimensions of electric current.

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