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  • The dimension of is same as that of<div class='

The dimension of \mathrm{\sqrt{\frac{L}{C}}} is same as that of

Option: 1

time


Option: 2

velocity


Option: 3

capacitance


Option: 4

resistance  


Answers (1)

best_answer

energy stored in the capacitor is \mathrm{=U_E=(1 / 2) C V^2}

The magnetic energy stored in an inductor\mathrm{=U_B=(1 / 2) \mathrm{Li}^2}

Equating these two dimensionally

\mathrm{\begin{aligned} & \frac{1}{2} C V^2=\frac{1}{2} L i^2 \\ & \Rightarrow \frac{V}{i}=\sqrt{\frac{L}{C}} \Rightarrow R=\sqrt{\frac{L}{C}} \end{aligned}}

Therefore \mathrm{\sqrt{\frac{L}{C}}} is equal to resistance R.

 

 

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