COMEDK Exam 2017 Solved Paper

We know that, in L−C−R series resonant circuit, resonance frequency,
‌f=‌

1

2π√LC

‌⇒√LC=‌

1

2πf

‌⇒√LC=‌

1

ω

[ω= angular frequency ]
‌∴‌ Dimension of ‌√LC=‌

1

‌ Dimension of ‌ω

‌⇒‌‌[ω√LC]=‌

1

[ω]

=‌

1

[T−1]

=[T]
Hence, square root of the product of inductance [L] and capacitance [C] has the dimension of time.