If L , C and R denote the inductance, capacitance and resistance...

L

C

and

R

denote the inductance, capacitance and resistance respectively, the dimensional formula for

C^{2} LR

Options

A $[ {ML}^{- 2}T^{- 1}I^{0} ]$
B $\left[M^{0}L^{0}T^{3}\right]$
C $[ M^{- 1}L^{- 2}T^{6}I^{2} ]$
D $[ M^{0}L^{0}T^{2}I^{0} ]$

Correct answer

B. $\left[M^{0}L^{0}T^{3}\right]$

Step-by-step solution

\left[C^{2}LR\right] =\left[C^{2}L^{2}\right] $\times \left[\dfrac{R}{L}\right]$

As $\dfrac{L}{R} and$ \sqrt{LC} $both have the dimensions of time, we get</p><p> \left[C^{2}LR\right] =$ \left[M^{0}L^{0}T^{4}\right]\times \left[M^{0}L^{0}T^{- 1}\right] $=\left[M^{0}L^{0}T^{3}\right]$

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