Units & Dimensions

JEE Main level, single correct, medium

31 of 149

Question 31 of 149

The dimension of μ0ϵ0\sqrt{\frac{\mu_0}{\epsilon_0}} is equal to that of :
( μ0=\mu_0= Vacuum permeability and ϵ0=\epsilon_0= Vacuum permittivity)

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Answer: (D) Resistance

L=μ0NAℓC=Aϵ0dLC∝μ0ϵ0μ0ϵ0∝LCLC=τR(τ/R)=R2μ0ϵ0=R\begin{aligned} & L=\frac{\mu_0 N A}{\ell} \\ & C=\frac{A \epsilon_0}{d} \\ & \frac{L}{C} \propto \frac{\mu_0}{\epsilon_0} \\ & \sqrt{\frac{\mu_0}{\epsilon_0}} \propto \sqrt{\frac{L}{C}} \\ & \frac{L}{C}=\frac{\tau R}{(\tau / R)}=R^2 \\ & \sqrt{\frac{\mu_0}{\epsilon_0}}=R\end{aligned}

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