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

Answer

D

Explanation

According to Ohm's law, `V prop I`
and `V = IR`
Resistance, `R =("Potential difference")/("Current") = (V)/(i) =(W)/(qi)`
`({:( :' "Potential difference is equal"),("to the work done per unti charge"):})`
So, dimensions of R
`= ("Dimensions of worl")/("Dimensions of charge" xx "Dimensions of current")`
`= ([ML^(2)T^(-2)])/([IT][I]) = [ML^(2)T^(-3)T^(-2)]`