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 a Bode plot, what is the phase margin when the gain crossover frequency equals the phase crossover frequency?
Answer: A
At the gain crossover frequency, magnitude is 0 dB. When this equals phase crossover frequency, the phase is -180°, giving phase margin = -180° - (-180°) = 0°
Q.43Easy
Which of the following transfer functions represents a Type-2 system?
Answer: A
Type of system is determined by the number of poles at origin. Option A has s² in denominator, making it Type-2
Q.44Medium
For a second-order system with ζ = 0.5 and ωn = 4 rad/s, what is the peak overshoot?
In state-space representation, if eigenvalues of A matrix are at s = -1, -2, -3, the system is:
Answer: B
Stability depends only on eigenvalue locations (all in LHP = stable). Controllability requires rank[B AB A²B] = n, which eigenvalues alone don't determine
Q.50Medium
For an underdamped second-order system, the relationship between settling time ts and damping ratio ζ is:
Answer: C
Settling time ts ≈ 4/(ζωn) for 2% criterion, thus ts ∝ 1/(ζωn)
Q.51Medium
Which compensator is preferred for improving steady-state error without significantly affecting transient response?
Answer: B
Lag compensator increases DC gain significantly, improving steady-state error, while its phase lag is restricted to lower frequencies, minimizing transient effects
Q.52Easy
The static error constant for a Type-1 system with G(s) = 20/(s(s+5)(s+10)) is:
For a system to be controllable using state feedback u = -Kx, which condition must be satisfied?
Answer: C
Controllability requires the controllability matrix to have full rank n. This ensures all states can be moved from origin to any desired state
Q.54Medium
A system has poles at -2±j3. The natural frequency and damping ratio are approximately:
Answer: A
ωn = √(4+9) = √13 ≈ 3.6 rad/s, ζ = 2/√13 ≈ 0.55
Q.55Medium
In a unity feedback system, increasing loop gain K generally:
Answer: B
Higher K reduces ess proportionally but shifts root locus rightward, potentially crossing into RHP, thus reducing stability margins
Q.56Easy
The corner frequency of a transfer function H(s) = 1/(1 + s/10) occurs at:
Answer: B
Corner frequency = pole frequency. Rewriting: H(s) = 10/(s+10), so pole at -10, corner frequency = 10 rad/s
Q.57Hard
For improving transient response with minimal steady-state error impact, a lead compensator should be designed to add phase lead at:
Answer: B
Lead compensator adds phase lead at its designed center frequency ωm. For transient improvement, it should coincide with gain crossover frequency to increase phase margin
Q.58Easy
A system with characteristic equation s³ + 6s² + 11s + 6 = 0 has poles at:
Answer: A
Factoring: (s+1)(s+2)(s+3) = 0 gives poles at s = -1, -2, -3. All in LHP, so system is stable
Q.59Medium
In a compensated system, if phase margin PM = 30° and gain margin GM = 8 dB, this indicates:
Answer: C
PM = 30° is acceptable (typically 30-60°), GM = 8 dB (>6 dB threshold) indicates good gain stability. Both margins suggest satisfactory performance
Q.60Easy
A control system has an open-loop transfer function G(s)H(s) = K/[s(s+2)(s+4)]. What is the type of this system?
Answer: B
The type of a system is determined by the number of poles at origin. Here, there is one pole at origin (s term), making it Type 1.
