Question

The dimensional formula for the capacitance of a capacitor is

• A. $\left[A^2{M}^{-1}{L}^{-2}{T}^4\right]$
• B. $\left[A{M}^{-1}{L}^{-2}{T}^4\right]$
• C. $\left[A^2{M}^{-2}{L}^{-2}{T}^4\right]$
• D. $\left[A^0{M}^0{L}^{-2}{T}^4\right]$

Answer 1

Answer: (A)

$U=\frac{q^2}{2C}$
$\therefore$ $C=\frac{q^2}{2U}$
$\therefore$ $\left[C\right]=\frac{{\left(AT\right)}^2}{{\left(ML\right)}^2{T}^{-2}}$
$=\left[A^2{M}^{-1}{L}^{-2}{T}^4\right]$