COMEDK Exam 2022 Solved Paper

The capacitance of a conductor is defined as the ratio of the charge given to the rise in the potential of the conductor.
C=

q

V

=

q2

W

(V=

W

q

)
C=

ampere2−second2

kg2−metre2second−2

Hence, dimensionally [M−1L−2T4A2]
From Ohm's law, V=IR,
Hence, R=

V

I

=

Volt

Ampere

=

W

q

×

t

q

R=

F×s×t

q2

=kg

m

s2

×

m×s

A2×s2

=kgm2s−3A−2
Dimesionally, R=[ML2T−3A−2]
Hence, CR=[M−1L−2T4A2][ML2T−3A−2]
=[M0L0T]