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^4This 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

What is the dimensional formula of capacitance of a capacitor?(a) M^1L

1.	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^4This 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» The correct option is (b) M^-1L^-2T^4I^2 For explanation I would say: We know that CAPACITANCE=CHARGE(voltage)^-1 Now charge=currenttime=[I^1T^1]. voltage=electric FIELDdistance, 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.

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