(D) The formula for capacitance $C$ is given by $C = \frac{q}{V}$,where $q$ is charge and $V$ is electric potential.Since $V = \frac{W}{q}$,where $W$

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$[F] = [C^2 M^{-1} L^{-2} T^2]$

(D) The formula for capacitance $C$ is given by $C = \frac{q}{V}$,where $q$ is charge and $V$ is electric potential.Since $V = \frac{W}{q}$,where $W$ is work done,we can write $C = \frac{q^2}{W}$.The dimensional formula for charge $q$ is $[C]$.The dimensional formula for work $W$ is $[M L^2 T^{-2}]$.Substituting these into the formula for capacitance:$[C] = \frac{[C]^2}{[M L^2 T^{-2}]} = [C^2 M^{-1} L^{-2} T^2]$.

Class 12 Physics Electric Potential and Capacitance Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

Medium

Which one of the following is the correct dimensional formula for the capacitance in $F$? $M, L, T$ and $C$ stand for units of mass,length,time,and charge respectively.

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A
$[F] = [C^2 M^{-2} L^2 T^2]$
B
$[F] = [C M^{-2} L^{-2} T^{-2}]$
C
$[F] = [C M^{-1} L^{-2} T^2]$
D
$[F] = [C^2 M^{-1} L^{-2} T^2]$

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Electric Potential and Capacitance

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Basic of Capacitor and type of capacitor (Spherical, Cylindrical)

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Which one of the following is the correct dimensional formula for the capacitance in $F$? $M, L, T$ and $C$ stand for units of mass,length,time,and charge respectively.

Similar Questions

In a spherical condenser, the radius of the outer sphere is $R$. The difference in the radii of the outer and inner sphere is $x$. Its capacity is proportional to:

Eight drops of mercury, each of same radius and same charge, combine to form a bigger drop. The ratio of the capacitance of the bigger drop to that of each smaller drop is: (in $ : 1$)

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air concentrically. $B$ is given a charge $+Q$ and $A$ is grounded. The equivalent capacitance of this system is:

$1000$ small water drops,each of capacitance $C$,join together to form one large spherical drop. The capacitance of the bigger sphere is ......... $C$.

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