A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given $\mu_0=4\pi\times10^{-7}\,\text{H/m}$ and $\varepsilon_0=\dfrac{10^{-9}}{36\pi}\,\text{F/m}$, the characteristic impedance of the cable is

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33Ω. For a coaxial cable, $Z_0=\dfrac{60}{\sqrt{\varepsilon_r}}\ln(b/a)$, where $a$ and $b$ are the inner and outer radii. Here $a=0.5$ mm and $b=1.2$ mm, so $b/a=2.4$; substituting $\varepsilon_r=10.89$ gives approximately $33\,\Omega$.

A coaxial cable with an inner diameter of 1 mm and outer diameter of 2.4 mm is filled with a dielectric of relative permittivity 10.89. Given \(\mu_0=4\pi\times10^{-7}\,\text{H/m}\) and \(\varepsilon_0=\dfrac{10^{-9}}{36\pi}\,\text{F/m}\), the characteristic impedance of the cable is

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