Question

If \(R=\) resistance, \(L=\) inductance, \(C=\) capacitance, then the dimension \([ML^2T^{-4}A^{-2}]\) represents

• A. \(\displaystyle \frac{R}{\sqrt{LC}}\)
• B. \(\displaystyle \frac{1}{R}\sqrt{\frac{L}{C}}\)
• C. \(\displaystyle R\sqrt{LC}\)
• D. \(\displaystyle \sqrt{RLC}\)

Answer 1

The Correct Option is A

Concept: Use dimensional formulas of electrical quantities. \[ [R]=\frac{V}{I}=ML^2T^{-3}A^{-2} \] Also, \[ \omega=\frac{1}{\sqrt{LC}} \] where \(\omega\) is angular frequency. \[ [\omega]=T^{-1} \] Step 1: Dimension of \(\frac{R{\sqrt{LC}}\)} \[ \left[\frac{R}{\sqrt{LC}}\right]=[R]\times T^{-1} \] \[ =(ML^2T^{-3}A^{-2})(T^{-1}) \] \[ =ML^2T^{-4}A^{-2} \] Thus the required expression is \[ \boxed{\frac{R}{\sqrt{LC}}} \]