Question

The dimensional formula of capacitance is ______. Take $Q$ as the dimension formula of charge.

• A. $M^{1} L^{-2} T^{-2} Q^{-2}$
• B. $M^{1} L^{2} T^{-2} Q^{-2}$
• C. $M^{1} L^{-2} T^{2} Q^{2}$
• D. $M^{-1} L^{-2} T^{2} Q^{2}$

Answer 1

Answer: (D)

Capacitance $C=\frac{Q}{V}$
but $V=\frac{W}{Q}$
$C=\frac{Q^{2}}{W}$
$C=\frac{\left[Q^{2}\right]}{\left[M L^{2} T^{-2}\right]}$
$=\left[M^{-1} L^{-2} T^{2} Q^{2}\right]$