Many circles are drawn in a Smith chart used for transmission line calculations. The circles shown in Fig. represent

The magnetic field intensity vector of a plane wave is given by
$$\overline H \left( {x,y,z,t} \right) = 10\,\sin \left( {50000t + 0.004x + 30} \right){\mathop a\limits^ \cap _y}$$
Where $${\mathop a\limits^ \cap _y}$$ denotes the unit vector in $$y$$ direction. The wave is propagating with a phase velocity

Characteristic impedance of a transmission line is 50$$\Omega $$. Input impedance of the open-circuited line is $${Z_{oc}} = 100\, + \,j\,\,150\Omega .$$ When the transmission line is short-circuited the value of the input impedance will be

Voltage standing wave pattern in a lossless transmission line with characteristic impedance 50 $$\Omega $$ and a resistive load is shown in Fig. The value of the load resistance is