The physical quantity having the dimensions $[M^{- 1} L^{- 3} T^{3} A^{2}]$ is :

Resistance

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Resistivity

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Electrical conductivity

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Electromotive force

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is D Electrical conductivity
Electrical conductivity is given by : $ρ = R \frac{A}{l}$ = $\frac{{n e}^{2} τ}{m}$
Dimensions of $A$ = $L^{2}$
Dimensions of $l$ = $L^{1}$
Dimensions of $R$ = $M^{- 1} L^{- 4} T^{3} A^{2}$
n $=$ number of electrons per unit volume $= L^{- 3}$
Dimensions of $e = C^{2} = {A T}^{2}$
where, $C =$ coulomb; $A =$ Ampere;
$T =$ time
Dimensions of $τ$ $= T$
Dimension of mass $m = M$
Dimensions of $ρ = \frac{A^{2} T^{2} T^{1}}{M} \times \frac{1}{L^{3}}$ $= M^{- 1} L^{- 3} T^{3} A^{2}$

Hence, option C is correct.

Suggest Corrections

Similar questions

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

1 %, 1.5 %

3 %

[M L^{- 1} T^{- 1}]

2

[L^{a} M^{b} T^{c}]

M^{- 1} L^{- 2} T^{4} A^{2}

Join BYJU'S Learning Program