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Capacitance of a Random Conductor

Question

Find the dimensions of capacitance :
$= [M^{- 1} L^{2} T^{4} A^{- 2}]$
$= [M^{- 1} L^{- 1} T^{4} A^{2}]$
$= [M^{- 1} L^{- 2} T^{- 4} A^{2}]$
$= [M^{- 1} L^{- 2} T^{4} A^{2}]$

A

= [M^{- 1} L^{- 1} T^{4} A^{2}]

B

= [M^{- 1} L^{- 2} T^{- 4} A^{2}]

C

= [M^{- 1} L^{- 2} T^{4} A^{2}]

D

= [M^{- 1} L^{2} T^{4} A^{- 2}]

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Solution

Verified by Toppr

From the expression of energy stored in capacitor,
$U = \frac{1}{2} \frac{q^{2}}{C}$
$∴ [C] = [\frac{q^{2}}{U} =] [\frac{A^{2} T^{2}}{M L^{2} T^{-} 2}]$
$= [M^{- 1} L^{- 2} T^{4} A^{2}]$

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