The dimensional formula of capacitance is:

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The capacitance $C$ is defined as the ratio of charge $Q$ to potential difference $V$,given by $C = \frac{Q}{V}$.Since $V = \frac{W}{Q}$,where $W$

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) The capacitance $C$ is defined as the ratio of charge $Q$ to potential difference $V$,given by $C = \frac{Q}{V}$.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 $[A^1T^1]$.The dimensional formula for work $W$ is $[M^1L^2T^{-2}]$.Substituting these into the formula: $C = \frac{[A^1T^1]^2}{[M^1L^2T^{-2}]} = \frac{[A^2T^2]}{[M^1L^2T^{-2}]}$.Simplifying the expression,we get $[C] = [M^{-1}L^{-2}T^4A^2]$.

Similar Questions

According to Newton,the viscous force acting between liquid layers of area $A$ and velocity gradient $\Delta v/\Delta z$ is given by $F = - \eta A \frac{\Delta v}{\Delta z}$,where $\eta$ is a constant called the coefficient of viscosity. The dimensions of $\eta$ are:

The position of a particle at time $t$ is given by the equation $x(t) = \frac{v_0}{A}(1 - e^{-At})$, where $v_0$ is a constant and $A > 0$. The dimensions of $v_0$ and $A$ respectively are:

What is the dimensional formula for the ratio of angular momentum to linear momentum?

Write the dimensional formula for energy density.

Which of the following physical quantities has a unit but no dimensions?

Vedclass Test Series

Exam Paper Generator

Online Exam Module