Correct Answer - Option 1 : Inductive
Concept:
The input impedance of a transmission line is given by:
\({Z_{in}} = {Z_o}\frac{{\left( {{Z_L} + j{Z_0}tanβ l} \right)}}{{\left( {{Z_0} + j{Z_L}tanβ l} \right)}}\) ---(1)
Z0 = Characteristic impedance
ZL = Load impedance
Application:
For l = λ/8
\(β l=\frac{2\pi}{\lambda}\times \frac{\lambda}{8}\)
\(\beta l=\frac{\pi}{4}\)
Putting this Equation (1), we get:
\({Z_{in}} = {Z_o}\frac{{\left( {{Z_L} + j{Z_0}} \right)}}{{\left( {{Z_0} + j{Z_L}} \right)}}\)
For short circuit load (ZL= 0), the input impedance becomes:
\({Z_{in}} = {Z_o}\frac{{\left( {{0} + j{Z_0}} \right)}}{{\left( {{Z_0} + j{0}} \right)}}\)
\({Z_{in}} = j{Z_o}\)
Since Impedance has a positive imaginary part, the transmission line behaves as an inductive Transmission Line.