Question

Dimension of √R/LC , where L is inductance, C is Capacitance & R is resistance

Answer 1

We do not remember the dimensions of R, L and C usually.  But we find the dimensions of R, L and C as follows.

Power = I² R      =>     [ R ] = [ M L² T⁻³ A⁻² ]
Potential Energy  = 1/2 L I²  =>  [ M L² T⁻² A⁻² ]
Potential Energy = 1/2 Q² / C    =>    C = [ A T ]² / [ M L² T⁻² ] = [ M⁻² L⁻² T⁴ A² ]

Now  [ √R / (LC) ] = $[M^{\frac{1}{2}-1+2}] [L^{1 -2+2} ] [T^{-\frac{3}{2}+2-4}] [A^{-1+2-2}]\\\\=[M^{-\frac{3}{2}}][L^{1}][T^{-\frac{7}{2}}][A^{-1}]$