Let $\mathrm{Q}$ denote the charge on the plate of a capacitor of capacitance $\mathrm{C}$. The dimensional…

Let $\mathrm{Q}$ denote the charge on the plate of a capacitor of capacitance $\mathrm{C}$. The dimensional formula for $\frac{\mathrm{Q}^{2}}{\mathrm{C}}$ is
  1. $\left[\mathrm{L}^{2} \mathrm{M}^{2} \mathrm{~T}\right]$
  2. $\left[\mathrm{LMT}^{2}\right]$
  3. $\left[\mathrm{L}^{2} \mathrm{MT}^{-2}\right]$
  4. $\left[\mathrm{L}^{2} \mathrm{M}^{2} \mathrm{~T}^{2}\right]$

Solution

We know that $\frac{\mathrm{Q}^{2}}{2 \mathrm{C}}$ is energy of capacitor, so it represent the dimension of energy $=\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$ .

Asked in: JEE Mains - Units and Dimensions - Chapter Test

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