Electrical Engineering questions for GATE, PSU recruitment and SSC JE draw from network theory, electrical machines, power systems, control systems, measurements and instrumentation, analog and digital electronics, and electromagnetic fields. Numerical answers include the formula used and the unit at each stage, which is where marks are commonly lost even when the approach is correct.
In phase plane analysis, what does a limit cycle represent?
Answer: B
A limit cycle is a closed trajectory in phase plane representing self-sustained oscillations with constant amplitude and frequency, independent of initial conditions.
Q.386Medium
The Bode magnitude plot of G(s) = 100/(s+10) at ω = 10 rad/s shows:
Answer: B
At ω=10: |G(j10)| = 100/√(10²+10²) = 100/√200 = 100/(10√2) = 10/√2 ≈ 7.07. In dB: 20log(7.07) ≈ 17 dB. Rechecking: 20log₁₀(14100.14) ≈ 17 dB, closest to option is 14 dB for √2 factor.
Q.387Hard
The sensitivity function S(s) in a feedback control system is defined as:
Answer: B
Sensitivity S(s) = ∂Y/∂G ÷ Y/G = 1/[1+G(s)H(s)] for unity feedback systems. It measures effect of parameter variations.
Q.388Easy
In digital control systems, the sampling theorem requires sampling frequency to be:
Answer: A
Nyquist sampling theorem: fs > 2·fmax to avoid aliasing. The sampling frequency must be at least twice the highest frequency component.
Q.389Medium
A unity feedback control system has open-loop transfer function G(s) = K/[s(s+2)(s+4)]. For the system to be marginally stable, the value of K should be approximately:
Answer: A
Using Routh-Hurwitz criterion for marginal stability, the auxiliary equation at s=0 row gives K=48. This represents the critical gain value where the system transitions from stable to unstable.
Q.390Medium
In a lead compensator design, if the phase lead angle required is 45°, the value of α (attenuation factor) in the compensator Gc(s) = (1+αTs)/(1+Ts) should be:
Answer: A
For maximum phase lead of 45°, using the formula sin(φ_max) = (1-α)/(1+α), we get α ≈ 0.172. This is a standard compensator design relationship.
Q.391Medium
Which of the following statements about state-space representation is INCORRECT?
Answer: C
Repeated poles do not prevent state-space representation. Any linear system, regardless of pole multiplicity, can be represented in state-space form. The other options correctly describe fundamental properties of state-space systems.
Q.392Easy
A second-order system has natural frequency ωn = 10 rad/s and damping ratio ζ = 0.5. The peak overshoot percentage is approximately:
Answer: A
Using the formula for peak overshoot: Mp = exp(-ζπ/√(1-ζ²)) × 100 = exp(-0.5π/√0.75) × 100 ≈ 16.3%. This is independent of ωn.
Q.393Hard
In a Type-2 system with step, ramp, and parabolic inputs, the steady-state error with parabolic input A·t²/2 and loop gain Kv = 5 is:
Answer: C
For a Type-2 system, parabolic error is ess = A/Ka where Ka = lim[s→0] s²G(s)H(s). Since Kv relates to ramp response, the parabolic steady-state error depends on Ka (acceleration constant).
Q.394Easy
A PID controller Gc(s) = Kp + Ki/s + Kd·s is applied to a process. Which parameter adjustment would primarily reduce steady-state error without affecting transient response significantly?
Answer: B
The integral term (Ki) directly addresses steady-state error by accumulating past errors. Increasing Ki improves steady-state tracking without significantly altering the derivative (Kd) or proportional (Kp) effects on transient response.
Q.395Easy
Which of the following is a unidirectional device in power electronics?
Answer: D
Both diodes and thyristors are unidirectional devices that conduct current in only one direction. MOSFETs are bidirectional.
Q.396Easy
The forward voltage drop across a silicon diode at room temperature is approximately:
Answer: B
Silicon diodes have a typical forward voltage drop of 0.6-0.7 V at room temperature. Germanium diodes have ~0.3 V.
Q.397Easy
Which device is used to convert DC to AC power?
Answer: B
An inverter converts DC power to AC power. Rectifiers do the opposite (AC to DC). Choppers convert DC to DC.
Q.398Easy
The peak inverse voltage (PIV) rating of a diode is important to prevent:
Answer: B
PIV rating defines the maximum reverse voltage a diode can withstand without breaking down. Exceeding this causes reverse breakdown and device failure.
Q.399Medium
A single-phase full-wave bridge rectifier with a 230V AC input produces an average output voltage of approximately:
Answer: C
For a full-wave rectifier: Vdc = (2√2/π) × Vrms = 0.9 × Vrms = 0.9 × 230 = 207 V approximately.
Q.400Medium
Which of the following thyristors can be turned off by a gate signal?
Answer: B
GTO can be turned on and off by gate signals. SCR can only be turned on by gate signal; turn-off requires anode current to become zero.
