Let the electric field vector of a plane electromagnetic wave propagating in a homogenous medium be expressed as $$E = \widehat x{E_x}\,{e^{ - j\left( {wt - \beta z} \right)}},$$ , where the propagation constant $$\beta $$ is a function of the angular frequency $$\omega $$. Assume that $$\beta \left( \omega \right)$$ and $${E_x}$$ are known and are real. From the information available, which one of the following CANNOT be determined?

A microwave circuit consisting of lossless transmission lines $$T_1$$ and $$T_2$$ is shown in the figure. The plot shows the magnitude of the input reflection coefficient $$\Gamma $$ as a function of frequency f. The phase velocity of the signal in the transmission lines is $$2\, \times \,{10^8}$$ m/s

A lossless microstrip transmission line consists of a trace of width w. It is drawn over a practically infinite ground plane and is separated by a dielectric slab of thickness 𝑡 and relative permittivity $${\varepsilon _r}\, > \,1$$. The inductance per unit length and the characteristic impedance of this line are L and $$Z_o$$ respectively. Which one of the following inequalities is always satisfied?

Consider the time-varying vector $$I = \,\hat x\,\,15\,\cos \,(\omega \,t) + \,\hat y\,5\,sin(\omega \,t)$$ in Cartesian coordinates, where $$\omega $$ > 0 is a constant. When the vector magnitude $$\left| I \right|$$ is at its minimum value, the angle $$\theta $$ that I makes with the x axis (in degree, such that $$0\, \le \,0 \le \,180$$) is _________________