Consider a uniform plane wave with amplitude $$\left( {{E_0}} \right)$$ of $$10\,\,\,V/m$$ and $$1.1 GHz$$ frequency travelling in air, and incident normally on a dielectric medium with complex relative permittivity $$\left( {{\varepsilon _r}} \right)$$ and permeability $$\left( {{\mu _r}} \right)$$ as shown in the figure.

The magnitude of the transmitted electric field component (in V/m) after it has travelled a distance of $$10$$ cm inside the dielectric region is ________.

The longitudinal component of the magnetic field inside an air-filled rectangular waveguide made of a perfect electric conductor is given by the following expression $${H_z}(x,\,y,\,z,\,t) = \,0.1\,\cos \,(25\,\,\pi \,x)\,\cos \,(30.3\,\pi y)$$ $$\cos \,(12\,\pi \, \times \,{10^9}\,t\, - \beta \,z)(A/m)$$

The cross-sectional dimemsions of the waveguide are given as a = 0.08 m and b = 0.033 m. The mode of propagation inside the waveguide is

The built-in potential of an abrupt p-n junction is 0.75V. If its junction capacitance (C_J) at a reverse bias (V_R) of 1.25V is 5pF, the value of C_J (in pF) when V_R = 7.25V is ___________.

A silicon sample is uniformly doped with donor type impurities with a concentration of $$10^{16}/cm^3$$.The electron and hole mobilities in the sample are $$1200\;cm^2/V-s$$ and $$400\;cm^2/V-s$$ respectively. Assume complete ionization of impurities. The charge of an electron is $$1.6\;\times\;10^{-19}\;C$$.The resistivity of the sample $$\left(in\;\Omega-cm\right)$$ is _____________.