Question

If C is the capacity and V is the potential across the condenser, what will be the dimensional representation of $\frac{1}{2}C{V}^2$?

• A. $M{L}^2{T}^{-2}{A}^2$
• B. ${ML}^{-2}{T}^{-2}$
• C. $M{L}^2{T}^{-3}{A}^{-2}$
• D. ${ML}^2{T}^{-2}$

Answer 1

The correct option is D ${ML}^2{T}^{-2}$

Let $X$ be the quantity represented.

$X=\frac{1}{2}C{V}^2$

$X=\frac{1}{2}\frac{Q}{V}\times V^2$

$X=\frac{1}{2}Q.V$

$\left[X\right]=\left[Q\right]\left[V\right]=\left[IT\right]\left[M{L}^2{T}^{-3}{I}^{-1}\right]=\left[M{L}^2{T}^{-2}\right]$