GATE Technical: GATE 2016 Electronics and Communication Engineering (Set 2) questions with solutions

Q1. In the circuit shown below, V_S is a constant voltage source and I_L is a constant current load. The value of I_L that maximizes the power absorbed by the constant current load is

1. (A) V_S / 4R
2. (B) V_S / 2R
3. (C) V_S / R
4. (D) ∞

Answer: (B) V_S / 2R

The maximum power transfer theorem states that maximum power is delivered to a load when the load resistance equals the Thevenin resistance of the circuit. In this case, for a constant current load, the optimal current that maximizes power absorption is half of the source voltage divided by the load resistance, which is represented by option B.

Q2. The Ebers-Moll model of a BJT is valid

1. only in active mode
2. only in active and saturation modes
3. only in active and cut-off modes
4. in active, saturation and cut-off modes

Answer: in active, saturation and cut-off modes

The Ebers-Moll model describes the behavior of a BJT across all three key operating regions: active, saturation, and cut-off, allowing for a comprehensive understanding of its performance in various states.

Q3. A long-channel NMOS transistor is biased in the linear region with VDS=50 mV and is used as a resistance. Which one of the following statements is NOT correct?

1. If the device width W is increased, the resistance decreases.
2. If the threshold voltage is reduced, the resistance decreases.
3. If the device length L is increased, the resistance increases.
4. If VGS is increased, the resistance increases.

Answer: If VGS is increased, the resistance increases.

Increasing VGS enhances the channel conductivity in an NMOS transistor, which reduces the resistance, making the statement incorrect.

Q4. The number and direction of encirclements around the point -1 + j0 in the complex plane by the Nyquist plot of G(s) = (1-s)/(4+2s) is

1. zero.
2. one, anti-clockwise.
3. one, clockwise.
4. two, clockwise.

Answer: zero.

The Nyquist plot does not encircle the point -1 + j0, indicating that the system is stable and has no encirclements around this point, which confirms the correct answer is zero.

Q5. A uniform and constant magnetic field B = 2B in exists in the z direction in vacuum. A particle of mass m with a small charge q is introduced into this region with an initial velocity v = vₓ x̂ + v_z ẑ. Given that B, m, q, vₓ and v_z are all non-zero, which one of the following describes the eventual trajectory of the particle?

1. Helical motion in the z direction.
2. Circular motion in the xy plane.
3. Linear motion in the z direction.
4. Linear motion in the x direction.

Answer: Helical motion in the z direction.

The particle experiences a magnetic force due to its velocity in the presence of the magnetic field, which causes it to move in a circular path in the xy plane while simultaneously moving along the z direction due to its initial velocity component in that direction, resulting in a helical trajectory.