If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of λ, where ( C / V )=λ ?

Question

If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of λ, where ( C / V )=λ ? (A) [ M -2 L -3 I 2 T 6] (B) [ M -3 L -4 I 3 T 7] (C) [ M -1 L -3 I -2 T -7] (D) [ M -2 L -4 I 3 T 7]

Tardigrade Admin · Accepted Answer

λ=( C / V )=( Q / V / V )=( Q / V 2) V =( text work / Q ) λ=( Q 3/( text work )2)=(( It )3/( F . s )2) =([ I 3 T 3]/[ ML 2 T -2]2)=[ M -2 L -4 I 3 T 7]

Q. If $^{'} C^{'}$ and $^{'} V^{'}$ represent capacity and voltage respectively then what are the dimensions of $λ,$ where $\frac{C}{V} = λ ?$

$[M^{- 2} L^{- 3} I^{2} T^{6}]$

$[M^{- 3} L^{- 4} I^{3} T^{7}]$

$[M^{- 1} L^{- 3} I^{- 2} T^{- 7}]$

$[M^{- 2} L^{- 4} I^{3} T^{7}]$

$λ = \frac{C}{V} = \frac{Q / V}{V} = \frac{Q}{V ^{2}}$
$V = \frac{work}{Q}$
$λ = \frac{Q ^{3}}{( work ) ^{2}} = \frac{( I t ) ^{3}}{( F . s ) ^{2}}$
$= \frac{[ I ^{3} T ^{3} ]}{[ M L ^{2} T ^{- 2} ] ^{2}} = [M^{- 2} L^{- 4} I^{3} T^{7}]$

Q. If ′C′ and ′V′ represent capacity and voltage respectively then what are the dimensions of λ, where VC​=λ?

[M−2L−3I2T6]

[M−3L−4I3T7]

[M−1L−3I−2T−7]

[M−2L−4I3T7]