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

Resistance R=( textpotential textdifference/ textcurrent)=(V/i)=(W/qi) ( ∵ Potential difference is equal to work done per unit charge) So, Dimensions of R = ([Dimensions of work]/[Dimensions of charge][Dimensions of current]) =([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

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

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

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

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

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]

Resistance R=currentpotentialdifference​=iV​=qiW​ ( ∵ Potential difference is equal to work done per unit charge) So, Dimensions of R =[Dimensionsofcharge][Dimensionsofcurrent][Dimensionsofwork]​ =[IT][I][ML2T−2]​=[ML2T−3I−2]

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

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

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

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