Dimension of resistance in an elecatrical circuit, in terms of dimension of mass `M`, of length `L`, of time `T`, and of current `I`, would be

Options

A. `[ML^(2)T^(3)I^(-I)]`
B. `[ML^(2)T^(2)]`
C. `[ML^(2)L^(-1)]`
D. `[ML^(2)T^(3)]`

Answer

D

Explanation

Resistance
`R=("potential di fference")/("Current")=V/i=W/(qi)`
(`:.` Potential difference is equal to work done per unit charge)
So, Dimension of `R`
`=(["Dimension of work"])/(["Dimension of charge"]["Dimension of current"])`
`=([ML^(2)T^(-2)])/([IT][I])=[ML^(2)T^(-3)I^(-2)]`