GATE EC 1999 Electromagnetics Solution Q 5

GATE EC 1999 Electromagnetics Solution Q 5

In air, a lossless transmission line of length 50 cm with L=10μH/m, C = 40pF/m is operated at 25 MHz. Its electrical path length is_____.

(a) 0.5 meters

(b) λ meters

(c) π/2 radians

(d) 180 degrees

Ans :- (c)

Explanation

Path length can be stated in meters or radians which can be transformed from one form to other by knowing

 2\pi(rad)=\lambda(m)

Electrical path length = \beta l

\beta=\frac{2\pi}\lambda v=\frac1{\sqrt{LC}}=\frac1{\sqrt{10\times10^{-6}\times40\times10^{-12}}} =0.5\times10^8 \lambda=\frac vf=\frac{0.5\times10^8}{25\times10^6} \therefore \beta l=\frac{2\pi}\lambda\times l =\frac{2\pi\times0.5\times25\times10^6}{0.5\times10^8}=\frac\pi2rad.

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