Multiple choice

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

The load resistance is

  1. 25 Ohms

  2. 50 Ohms

  3. 75 Ohms

  4. 100 Ohms
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D Correct answer
Explanation

Using transmission line reflection: initial incident voltage V_i = 30V. At load: V_L = V_i + V_r = V_i(1+Γ) = 40V, so Γ = 1/3. Reflection coefficient Γ = (R_L - Z_0)/(R_L + Z_0). Solving (R_L - 50)/(R_L + 50) = 1/3 gives R_L = 100Ω.

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