Question

Find the dimensional formulae of the capacitance C

Some of the equations containing these quantities are

Q = It, U = VIt, Q = CV and V = RI;

Where 'I' denote the electric current, 't' is time and 'U' is energy.

Energy has the dimension of Force x displacement

• A. $M^{-1}{L}^{-1}{I}^{-2}{T}^4$
• B. $M^{-1}{L}^{-2}{I}^2{T}^4$
• C. $M{L}^2{I}^{-1}{T}^{-3}$
• D. none of these

Answer 1

The correct option is B

$M^{-1}{L}^{-2}{I}^2{T}^4$

Given, Q = CV -----(i),
U = VIt -----(ii),

from (i) $\Rightarrow C=\frac{Q}{V}$
from (ii) $\Rightarrow V=\frac{U}{It}$

$\Rightarrow C=\frac{Q}{U}\times IT$

[Q] = [I][T]

$\left[U\right]=M{L}^2{T}^{-2}$

$\therefore \left[C\right]=\frac{IT}{M{L}^2{T}^{-2}}IT$

= $M^{-1}{L}^{-2}{I}^2{T}^4$