JEE MAIN - Physics (2025 - 22nd January Evening Shift - No. 4)
Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,
$[\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]$
$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$
$[\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]$
Explanation
$C=\frac{q}{V}=\frac{q \cdot q}{V \cdot q}=\frac{q^2}{W D}=\frac{C^2}{M L L^2 T^{-2}}=C^2 M^{-1} L^{-2} T^2$
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