The dimensions of capacitance are -displaystyle left- - ML - -2 - Q - -2 - T - 2 - right- displaystyle left- - M - -1 - L - 2 - T - -2 - Q - -2 - right- displaystyle left- - M - -1 - L - 2 - T - -2 - Q - 2 - right- displaystyle left- - M - -1 - L - -2 - T - 2 - Q - 2 - right-

Question

Toppr Admin · Accepted Answer

Capacitance - ChargePotentialdifferenceand potential difference -WorkchargeChargeCapacitance -Charge2Workdone-C-Q2-ML2T-x2212-2-M-x2212-1L-x2212-2T2Q2-

Column I	Column II
a) Angular momentum	g) ${M L}^{2} T^{- 2}$
b) Latent heat	h) ${M L}^{2} Q^{- 2}$
c) Torque	i) ${M L}^{2} T^{- 1}$
d) Capacitane	j) ${M L}^{3} T^{- 1} Q^{- 2}$
e) Inductance	k) $M^{- 1} L^{- 2} T^{2} Q^{2}$
f) Resistivity	l) $L^{2} T^{- 2}$

The dimensions of capacitance are :
$[{M L}^{- 2} Q^{- 2} T^{2}]$
$[M^{- 1} L^{2} T^{- 2} Q^{- 2}]$
$[M^{- 1} L^{2} T^{- 2} Q^{2}]$
$[M^{- 1} L^{- 2} T^{2} Q^{2}]$

Capacitance = $\frac{C h a r g e}{P o t e n t i a l d i f f e r e n c e}$
and potential difference $= \frac{W o r k c h a r g e}{C h a r g e}$
Capacitance $= \frac{{C h a r g e}^{2}}{W o r k d o n e}$
$[C] = \frac{[Q^{2}]}{[{M L}^{2} T^{- 2}]}$
$= [M^{- 1} L^{- 2} T^{2} Q^{2}]$

The dimensions of capacitance are :[ML−2Q−2T2][M−1L2T−2Q−2][M−1L2T−2Q2][M−1L−2T2Q2]

Capacitance = ChargePotentialdifferenceand potential difference =WorkchargeChargeCapacitance =Charge2Workdone[C]=[Q2][ML2T−2]=[M−1L−2T2Q2]

The dimensions of capacitance are :
$[{M L}^{- 2} Q^{- 2} T^{2}]$
$[M^{- 1} L^{2} T^{- 2} Q^{- 2}]$
$[M^{- 1} L^{2} T^{- 2} Q^{2}]$
$[M^{- 1} L^{- 2} T^{2} Q^{2}]$

Capacitance = $\frac{C h a r g e}{P o t e n t i a l d i f f e r e n c e}$
and potential difference $= \frac{W o r k c h a r g e}{C h a r g e}$
Capacitance $= \frac{{C h a r g e}^{2}}{W o r k d o n e}$
$[C] = \frac{[Q^{2}]}{[{M L}^{2} T^{- 2}]}$
$= [M^{- 1} L^{- 2} T^{2} Q^{2}]$