Question

Choose the correct dimensional formula of $5CV$.
($C$ is capacitance and $V$ is potential difference)

• A. $\left[M^{\circ }{L}^2{T}^3{A}^2\right]$
• B. $\left[M^1{L}^0{T}^1{A}^1\right]$
• C. $\left[M^{\circ }{L}^{\circ }{T}^2{A}^1\right]$
• D. $\left[M^{\circ }{L}^{\circ }{T}^1{A}^1\right]$

Answer 1

The correct option is D $\left[M^{\circ }{L}^{\circ }{T}^1{A}^1\right]$

We have the well known equation

$Q=CV$

And the number $5$ is dimensionless. So, the expression has the same dimensional formula as that of charge.

Electric current is the rate of flow of charge.

$\therefore I=\frac{Q}{t}\Rightarrow Q=It$

The physical quantities current and time are both fundamental units in the SI system.

Therefore, dimensional formula of charge $Q$ will be $\left[A^1{T}^1\right]$ or you can say $\left[M^0{L}^0{T}^1{A}^1\right]$.

Hence, option $\left(c\right)$ is correct.

Key Concept: The relation between charge, potential difference, and capacitance of a capacitor is $Q=CV$.