Question

Find the dimensions of capacitance.

Answer 1

Answer:

The dimensional formula for capacitance is $M^{-1} L^{-2} T^{4} I^{2}$.

Capacitance can be defined as the ratio of the change in an electric charge to the corresponding change in its electric potential in a system. The SI unit of capacitance is the farad (F). In SI base units = $kg^{-1}$

Answer 2

Dimensions of Capacitance

                          = [$A^{2} T^{3} M^{-1} L^{-2}$ ]

Explanation:

Capacitance is defined as the electric charge storing capacity of a body.

SI unit of capacitance is farad (F).

We will use the relation q = CV

where q = charge in columbs

V = voltage in volts

C = capacitance of a body.

q = I × T

Where I is current in amperes and T is time in seconds.

we know that power = V × I

unit of power = joules per second

V = P÷I

dimensions of joules are [M $L^{2}$ $T^{-2}$]

hence dimensions of voltage = [ M $L^{2}$ $T^{-2}$ $A^{-1}$]

IT = CV

C = I×T÷V

dimension of current = A

Dimensions of C = [ A ] [T][ $M^{-1}$$L^{-2}$ $T^{2}$ A]

                          = [$A^{2} T^{3} M^{-1} L^{-2}$ ]