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GATE 2016 EC – Question 35

Electromagnetics · Transmission Lines · 1 mark · Multiple choice

The propagation constant of a lossy transmission line is $(2 + j5)$ m$^{-1}$ and its characteristic impedance is $(50 + j0)\ \Omega$ at $\omega = 10^6$ rad s$^{-1}$. The values of the line constants L, C, R, G are, respectively,

  1. L = 200 $\mu$H/m, C = 0.1 $\mu$F/m, R = 50 $\Omega$/m, G = 0.02 $\mho$/m
  2. L = 250 $\mu$H/m, C = 0.1 $\mu$F/m, R = 100 $\Omega$/m, G = 0.04 $\mho$/m
  3. L = 200 $\mu$H/m, C = 0.2 $\mu$F/m, R = 100 $\Omega$/m, G = 0.02 $\mho$/m
  4. L = 250 $\mu$H/m, C = 0.2 $\mu$F/m, R = 50 $\Omega$/m, G = 0.04 $\mho$/m

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Correct answer: (B) L = 250 $\mu$H/m, C = 0.1 $\mu$F/m, R = 100 $\Omega$/m, G = 0.04 $\mho$/m

Explanation

For a line, $\gamma Z_0 = R + j\omega L$ and $\frac{\gamma}{Z_0} = G + j\omega C$. Then $\gamma Z_0 = (2 + j5)(50) = 100 + j250$, so $R = 100\ \Omega$/m and $\omega L = 250$, which gives $L = 250\ \mu$H/m. Also $\frac{\gamma}{Z_0} = \frac{2 + j5}{50} = 0.04 + j0.1$, so $G = 0.04$ S/m and $\omega C = 0.1$, which gives $C = 0.1\ \mu$F/m.