Question

The dimension of $LC$, where $L$ is the inductance and $C$ is the capacitance, is -

• A. $\left[L\right]$
• B. $\left[L^2\right]$
• C. $\left[T\right]$
• D. $\left[T^2\right]$

Answer 1

The correct option is D $\left[T^2\right]$

We know that, frequency of oscillations of charge in the LC circuit is,

$f=\frac{1}{2\pi \sqrt{LC}}$

So, time period,

$T_0=\frac{1}{f}=2\pi \sqrt{LC}$

Now,

$\left[T_0\right]=\left[2\pi \sqrt{LC}\right]$

$\Rightarrow \left[T_0\right]=\left[\sqrt{LC}\right][\because 2\pi$ is constant$]$

$\Rightarrow \left[LC\right]=\left[T_0^2\right]$

Therefore, $LC$ has dimension $\left[T^2\right]$.

Hence, option $\left(D\right)$ is the correct answer.