GATE EC 2016 Question Paper (31-Jan-2016) (Shift 1)

A binary communication system makes use of the symbols “zero” and “one”. There are channel errors. Consider the following events:

𝑥₀ : a "zero" is transmitted

𝑥₁: a "one" is transmitted

𝑦₀ : a "zero" is received

𝑦₁ : a "one" is received

The following probabilities are given:

$\mathrm{P}({\mathrm{x}}_0)=\frac{1}{2},\mathrm{P}\left({\mathrm{y}}_0|{\mathrm{x}}_0\right)=\frac{3}{4}\mathrm{and}\mathrm{p}\left({\mathrm{y}}_0|{\mathrm{x}}_1\right)=\frac{1}{2}.$.

The information in bits that you obtain when you learn which symbol has been received (while you know that a “zero” has been transmitted) is ________

The parallel-plate capacitor shown in the figure has movable plates. The capacitor is charged so that the energy stored in it is 𝐸 when the plate separation is 𝑑. The capacitor is then isolated electrically and the plates are moved such that the plate separation becomes 2𝑑.



At this new plate separation, what is the energy stored in the capacitor, neglecting fringing effects?

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 𝜀${}_{\text{r}}$ > 1. The inductance per unit length and the characteristic impedance of this line are 𝐿 and 𝑍₀, respectively.



Which one of the following inequalities is always satisfied?

A microwave circuit consisting of lossless transmission lines T₁ and T₂is shown in the figure. The plot shows the magnitude of the input reflection coefficient Γ as a function of frequency 𝑓. The phase velocity of the signal in the transmission lines is 2 × 10⁸ m/s.



The length 𝐿 (in meters) of T₂ is ________

A positive charge $\mathrm{q}$ is placed at $\mathrm{x}=0$ between two infinite metal plates placed at $\mathrm{x}=-\mathrm{d}$ and at $\mathrm{x}=+\mathrm{d}$ respectively. The metal plates lie in the yz plane.



The charge is at rest at $\mathrm{t}=0$, when a voltage $+\mathrm{V}$ is applied to the plate at $\text{–}\mathrm{d}$ and voltage $-\mathrm{V}$ is applied to the plate at $\mathrm{x}=+\mathrm{d}$. Assume that the quantity of the charge $\mathrm{q}$ is small enough that it does not perturb the field set up by the metal plates. The time that the charge $\mathrm{q}$ takes to reach the right plate is proportional to