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The intrinsic impedance of air or vacuum is given by :

  • A.\(z_{0} = \sqrt{\mu_{0}\varepsilon_{0}}\)
  • B.\(z_{0} = \sqrt{\frac{1}{\mu_{0}\varepsilon_{0}}}\)
  • C.\(z_{0} = \sqrt{\frac{\varepsilon_{0}}{\mu_{0}}}\)
  • D.\(z_{0} = \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}}\)

Answer: D

The intrinsic impedance is \(z_{0} = \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}}\).

The intrinsic impedance of a medium is the ratio of the electric field to the magnetic field in a plane wave, \(\eta = \sqrt{\mu/\varepsilon}\). For free space:

\[ \begin{aligned} \eta_{0} &= \sqrt{\frac{\mu_{0}}{\varepsilon_{0}}} \\ &\approx 120\pi \approx 377\ \Omega \end{aligned} \]

The other forms are different quantities. \(\frac{1}{\sqrt{\mu_{0}\varepsilon_{0}}}\) is the speed of light \(c\), and \(\sqrt{\mu_{0}\varepsilon_{0}}\) is \(1/c\). \(\sqrt{\varepsilon_{0}/\mu_{0}}\) is the intrinsic admittance, the reciprocal of the impedance.

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