a quantity `X` is given by `epsilon_(0)L(DeltaV)/(Deltat)` where `in_(0)` is the permittivity of the free space, L is a length, `DeltaV` is a potential difference and `Deltat` is a time interval. The dimensinal formula for `X` is the same as that of

Options

A. charge
B. voltage
C. current
D. Resistance

Answer

C

Explanation

`X=epsi_(0)L(DeltaV)/(Deltat)`
For a paralel plate capacitor `C=(epsi_(0)A)/(d)`
but `[A]=[L^(2)] and [d]=[L]`
`therefore`Dimensions of C
=Dimensions of `epsi_(0)xx("Dimensions of "L^(2))/("Dimensions of L")`
=Dimensions of `epsi_(0)L`
`therefore`Dimensions of X
=dimensions of `Cxx("Dimensions of V")/("Dimensions of Time")`
But `CxxV=Q` for a conductor
`therefore`Dimensions of `X=("dimensions of charge")/("Dimensions of time")`
=Dimensions of time