Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I would be

Question

Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I would be (A) [ML2T-3I-1] (B) [ML2T-2] (C) [ML2T-1I-1] (D) [ML2T-3I-2]

Tardigrade Admin · Accepted Answer

According to Ohmâs law V=IR or R=(V/I) Dimensions of V=(W/q)=([ML2T-2]/[IT]) ∴ Dimensions of R=([ML2T-2/IT]/I) =[ML2T-3I-2]

Q. Dimensions of resistance in an electrical circuit, in terms of dimension of mass $M$ , of length $L$ , of time $T$ and of current $I$ would be

$[M L^{2} T^{- 3} I^{- 1}]$

$[M L^{2} T^{- 2}]$

$[M L^{2} T^{- 1} I^{- 1}]$

$[M L^{2} T^{- 3} I^{- 2}]$

According to Ohm’s law
$V = I R$
or $R = \frac{V}{I}$
Dimensions of $V = \frac{W}{q} = \frac{[ M L ^{2} T ^{- 2} ]}{[ I T ]}$
$∴$ Dimensions of $R = \frac{[ M L ^{2} T ^{- 2} / I T ]}{I}$
$= [M L^{2} T^{- 3} I^{- 2}]$

Q. Dimensions of resistance in an electrical circuit, in terms of dimension of mass M, of length L, of time T and of current I would be

[ML2T−3I−1]

[ML2T−2]

[ML2T−1I−1]

[ML2T−3I−2]