Question

If $C$ and $V$ represent capacitance and voltage respectively then what is the dimension of $\lambda$ where $\lambda =\frac{C}{V}?$

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

Answer 1

The correct option is A $\left[M^{-2}{L}^{-4}{I}^3{T}^7\right]$

We know that,

$V=\frac{w}{q}$ and $C=\frac{q}{V}=\frac{q^2}{w}$

So, $\lambda =\frac{C}{V}=\frac{\frac{q^2}{w}}{\frac{w}{q}}$

$\Rightarrow \lambda =\frac{q^3}{w^2}$

$\Rightarrow \lambda =\frac{I^3{t}^3}{w^2}[\because I=q/t]$

$\Rightarrow \left[\lambda \right]=\left[\frac{I^3{t}^3}{w^2}\right]$

$\Rightarrow \left[\lambda \right]=\left[\frac{I^3{T}^3}{(M{L}^2{T}^{-2}{)}^2}\right]$

$\Rightarrow \left[\lambda \right]=\left[M^{-2}{L}^{-4}{I}^3{T}^7\right]$