Question

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

• A. $\left[ M ^{-2} L ^{-3} I ^{2} T ^{6}\right]$
• B. $\left[ M ^{-3} L ^{-4} I ^{3} T ^{7}\right]$
• C. $\left[ M ^{-1} L ^{-3} I ^{-2} T ^{-7}\right]$
• D. $\left[ M ^{-2} L ^{-4} I ^{3} T ^{7}\right]$

Answer 1

Answer: (D)

$\lambda=\frac{ C }{ V }=\frac{ Q / V }{ V }=\frac{ Q }{ V ^{2}}$
$V =\frac{\text { work }}{ Q }$
$\lambda=\frac{ Q ^{3}}{(\text { work })^{2}}=\frac{( It )^{3}}{( F . s )^{2}}$
$=\frac{\left[ I ^{3} T ^{3}\right]}{\left[ ML ^{2} T ^{-2}\right]^{2}}=\left[ M ^{-2} L ^{-4} I ^{3} T ^{7}\right]$