GATE EC 2006 Electromagnetics Solution Q 9

GATE EC 2006 Electromagnetics Solution Q 9

A 30-Volts battery with zero source resistance is connected to a coaxial line of characteristic impedance of 50 Ohms at t = 0 second and terminated in an unknown resistive load. The line length is such that it takes 400μs for an electromagnetic wave to travel from source end to load end and vice-versa. At t = 400μs, the voltage at the load end is found to be 40 Volts.

The load resistance is_____.

(a) 25 Ohms

(b) 50 Ohms

(c) 75 Ohms

(d) 100 Ohms

Ans :- (d)

Explanation

As at the terminal end voltage is found to be 40V, we can say 10V is reflected voltage.

\therefore \Gamma=\frac{V_r}{V_i}=\frac{10}{30}=\frac13 But,\Gamma=\frac{Z_L-Z_0}{Z_L+Z_0} \frac13=\frac{Z_L-50}{Z_L+50} Z_L=100\Omega

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