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

Question

The dimensional formula of capacitance is . Take Q as the dimension formula of charge. (A) M1 L-2 T-2 Q-2 (B) M1 L2 T-2 Q-2 (C) M1 L-2 T2 Q2 (D) M-1 L-2 T2 Q2

Tardigrade Admin · Accepted Answer

Capacitance C=(Q/V) but V=(W/Q) C=(Q2/W) C=([Q2]/[M L2 T-2]) =[M-1 L-2 T2 Q2]

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

$M^{1} L^{- 2} T^{- 2} Q^{- 2}$

$M^{1} L^{2} T^{- 2} Q^{- 2}$

$M^{1} L^{- 2} T^{2} Q^{2}$

$M^{- 1} L^{- 2} T^{2} Q^{2}$

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

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

M1L−2T−2Q−2

M1L2T−2Q−2

M1L−2T2Q2

M−1L−2T2Q2