Question

If $C$ denotes the capacitance and $L$ denotes the inductance, then the dimensional formula of $L C$ is

• A. $\left[ M ^{0} L ^{0} T ^{2}\right]$
• B. $\left[ M ^{1} L ^{0} T ^{2}\right]$
• C. $\left[ M ^{1} L ^{1} T ^{2}\right]$
• D. $\left[ M ^{0} L ^{1} T ^{2}\right]$

Answer 1

Answer: (A)

Resonant frequency $f=\frac{1}{\sqrt{L C}}$
$\Rightarrow [L C]=\left[\frac{1}{f^{2}}\right]=\left[ T ^{2}\right]=\left[ M ^{0} L ^{0} T ^{2}\right]$