Question

Two coaxial cables 1 and 2 are filled with different dielectric constants ${ϵ}_{r_1}$ and ${ϵ}_{r_2}$ respectively. The ratio of the wavelengths in the two cables, $\left(\lambda 1/{\lambda }_2\right)$ is

• A. ${ϵ}_{r_1}/{ϵ}_{r_2}$
• B. $\sqrt{{ϵ}_{r_2}/{ϵ}_{r_1}}$
• C. ${ϵ}_{r_2}/{ϵ}_{r_1}$
• D. $\sqrt{{ϵ}_{r_1}/{ϵ}_{r_2}}$

Answer 1

The correct option is B $\sqrt{{ϵ}_{r_2}/{ϵ}_{r_1}}$

Ans : (b)

$V_1=\frac{1}{\sqrt{{\mu }_1{ϵ}_1}}$

$V_2=\frac{1}{\sqrt{{\mu }_2{ϵ}_2}}$

$\frac{v_1}{v_2}=\sqrt{\frac{{ϵ}_2}{{ϵ}_1}}$

$v=f\lambda$

f = frequency of operation

$v\alpha \lambda$

$\therefore \frac{{\lambda }_1}{{\lambda }_2}=\sqrt{\frac{{ϵ}_2}{{ϵ}_1}}=\sqrt{\frac{{ϵ}_0{ϵ}_{r2}}{{ϵ}_0{ϵ}_{r_1}}}=\sqrt{\frac{{ϵ}_{r_2}}{{ϵ}_{r_1}}}$