Question 136: Electrostats & Capacitance

Question

Which one of the following is the correct dimensional formula for the capacitance in F ? $\mathrm{M}, \mathrm{L}, \mathrm{T}$ and $C$ stand for unit of mass, length, time and charge,

Accepted Answer

The capacitance (in farads) is defined as the ratio of charge to potential difference. Let's go through the steps:
Capacitance is given by:
$$C = \frac{Q}{V}$$
where:
$ Q $ is the charge with dimensional symbol $ C $.
$ V $ is the potential difference.
Voltage (potential difference) is defined as energy per unit charge:
$$V = \frac{W}{Q}$$
where:
$ W $ is energy with dimensions:
$$[W] = [M L^2 T^{-2}]$$
Therefore, the dimensions of voltage are:
$$[V] = \frac{[ML^2T^{-2}]}{[C]}$$
Now, substitute this back into the expression for capacitance:
$$[C] = \frac{[Q]}{[ML^2T^{-2}]/[C]} = \frac{[C]^2}{ML^2T^{-2}}$$
Simplifying gives:
$$[C] = [C^2 M^{-1}L^{-2}T^2]$$
Comparing with the given options, we see that Option C is:
$$[F] = [C^2 M^{-1}L^{-2}T^2]$$
Thus, the correct dimensional formula for the capacitance in farads is given by Option C.

Answer

$[\mathrm{F}]=\left[\mathrm{CM}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$

Answer

$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-2} \mathrm{~L}^2 \mathrm{~T}^2\right]$

Answer

$[\mathrm{F}]=\left[\mathrm{C}^2 \mathrm{M}^{-1} \mathrm{~L}^{-2} \mathrm{~T}^2\right]$

Answer

$[\mathrm{F}]=\left[\mathrm{CM}^{-2} \mathrm{~L}^{-2} \mathrm{~T}^{-2}\right]$

Electrostats & Capacitance

Which one of the following is the correct dimensional formula for the capacitance in F ? \mathrm{M}, \mathrm{L}, \mathrm{T} and C stand for unit of mass, length, time and charge,

Choose the correct answer: