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For a co-axial cable, inner diameter of outer conductor and diameter of inner conductor are 1 cm and 0.01 cm respectively. If dielectric constant \(\epsilon{_r}\) of the material filling in cable is 4, characteristic impedance of the co-axial cable is_____\(\Omega\)

Use \({\mu _o} = 4\pi \times {10^{ - 7}}H/m,\ \epsilon{_o} = \frac{{{{10}^{ - 9}}}}{{36\pi }}F/m\)


1. 330 ohm
2. 150 ohm
3. 200 ohm
4. 138 ohm
5.

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Correct Answer - Option 4 : 138 ohm

Inner diameter of outer conductor, D = 1 cm

Diameter of inner conductor, d = 0.01 cm

Characteristic impedance of coaxial cable, 

\({Z_0} = \frac{1}{2\pi }\sqrt {\frac{\mu }{\epsilon}} \times ln\left( {\frac{D}{d}} \right) = \frac{{138}}{{\sqrt {{\varepsilon _r}} }}\log \frac{D}{d}\)

\( \Rightarrow {Z_o} = \frac{{138}}{2}\log \frac{1}{{0.01}} = 138\;{\rm{\Omega }}\)

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