The dimension of √μ0/∈0 is equal to that of : (μ0 = Vacuum permeability and ∈0 = Vacuum permittivity)

Question

The dimension of \(\sqrt{\frac{\mu_0}{\in _0}}\) is equal to that of :

(\(\mu_0\) = Vacuum permeability and \(\in _0\) = Vacuum permittivity)

(1) Voltage

(2) Capacitance

(3) Inductance

(4) Resistance

Answer 1

Correct option is : (4) Resistance

\(L = \frac{\mu_0NA}{\ell}\)

\(C = \frac{A\ \in _0}{d}\)

\(\frac{L}{C}\propto \frac{\mu _0}{\in _0}\)

\(\sqrt{\frac{\mu_0}{\in_0} }\propto \sqrt{\frac{L}{C}}\)

\(\frac{L}{C} = \frac{\tau R}{(\tau/R)} = R^2\)

\(\sqrt{\frac{\mu_0}{\in _0}} = R\)