First slide

Dimensions of physical quantities

Question

$L. C and R$ represent the physical quantities inductance, capacitance and resistance respectively. The combinations which does not have the dimensions of frequency are

Moderate

A

$\frac{1}{R C}$
B

$\frac{R}{L}$
C

$\frac{1}{\sqrt{L C}}$
D

$\frac{C}{L}$

Solution

$C R and \frac{L}{R}$ both are time constants Their units is second.
$∴ \frac{1}{C R} and \frac{R}{L}$ have the SI unit $(second)^{- 1}$ . Further, resonance frequency $ω = \frac{1}{\sqrt{L C}}$

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