GATE EC 2011 Electromagnetics Solution Q 2

GATE EC 2011 Electromagnetics Solution Q 2

A transmission line of characteristic impedance 50Ω is terminated by a 50Ω load. When excited by a sinusoidal voltage source at 10 GHz, the phase difference between two points spaced 2 mm apart on the line is found to be π/4 radians. The phase velocity of the wave along the line is______

(a) 0.8\times10^8\;m/s

(b) 1.2\times10^8\;m/s

(c) 1.6\times10^8\;m/s

(d) 3\times10^8\;m/s

Ans :- (c)

Explanation

Phase difference = \frac{2\pi}\lambda (path difference)

\frac\pi4=\frac{2\pi}\lambda\left(2\times10^{-3}\right) \begin{array}{l}\therefore\lambda=8\times2\times10^{-3}\\=16\times10^{-3}m\end{array} f=10GHz=10\times10^9\;Hz

Hence the phase velocity of wave along the line is given by,

v=f\lambda=10\times10^9\times16\times10^{-3}\;m/sec \therefore v=1.6\times10^8m/s

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