GATE EC 2000 Electromagnetics Solution Q 2

GATE EC 2000 Electromagnetics Solution Q 2

The coaxial cables 1 and 2 are filled with different dielectric constants $latex \in_{r_1}and\;\in_{r_2}$ respectively. The ratio of the wavelengths in two cables, $latex (\lambda_1/\lambda_2)$ is

(a) \sqrt{\in_{r_1}/\in_{r_2}}

(b) \sqrt{\in_{r_2}/\in_{r_1}}

(c) \in_{r_1}/\in_{r_2}

(d) \in_{r_2}/\in_{r_1}

Ans : b)

Explanation

v_1=\frac1{\sqrt{\mu_1\in_1}} v_2=\frac1{\sqrt{\mu_2\in_2}} \frac{v_1}{v_2}=\sqrt{\frac{\in_2}{\in_1}}

Now, v=n\lambda where n is the frequency of operation which doesn’t depend on the medium.

\therefore\frac{\lambda_1}{\lambda_2}=\sqrt{\frac{\in_2}{\in_1}}=\sqrt{\frac{\in_0\in_{r_2}}{\in_0\in_{r_1}}}=\sqrt{\frac{\in_{r_2}}{\in_{r_1}}}

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