Question

What is the dimensional formula of capacitance of a capacitor?

(a) M^1L^2T^-4I^-2

(b) M^-1L^-2T^4I^2

(c) M^-1L^-2T^6

(d) M^-2L^2T^4

This question was addressed to me in my homework.

I'd like to ask this question from Capacitors and Capacitance topic in portion Electrostatic Potential and Capacitance of Physics – Class 12

Answer 1

The correct option is (b) M^-1L^-2T^4I^2

For explanation I would say: We know that Capacitance=Charge*(voltage)^-1

Now charge=current*time=[I^1T^1].

voltage=electric field*distance, and electric field=force*(charge)^-1

Since we know the dimensional formula of force is [M^1L^1T^-2], therefore,

Electric field=[M^1L^1T^-2] * [I^1T^1]^-1=[M^1L^1T^-3I^-1].

Finally, voltage becomes=[M^1L^1T^-3I^-1] *L.

Hence, we conclude that dimensional formula of capacitance is [I^1T^1] * ([M^1L^1T^-3I^-1] *L)^-1 that is M^-1L^-2T^4I^2.