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.
Which statement is correct regarding the Bode plot of a system?
Answer: B
For minimum phase systems, magnitude and phase are related through the Kramers-Kronig relations. Knowledge of magnitude plot uniquely determines phase plot.
Q.162Medium
A PID controller is used for a plant. If only the derivative gain Kd is increased while keeping Kp and Ki constant, what is the primary effect?
Answer: B
The derivative term acts as damping in the system. Increasing Kd increases damping, which reduces overshoot and oscillations without affecting steady-state error significantly.
Q.163Medium
In frequency response analysis, what does the gain margin represent?
Answer: B
Gain margin is the factor by which the system gain at phase crossover frequency can be increased before the system becomes unstable (phase reaching -180° at unity gain).
Q.164Medium
A lag compensator has the form Gc(s) = K(s+0.1)/(s+0.01). Which characteristic does it primarily improve?
Answer: B
Lag compensator (zero at -0.1, pole at -0.01, with pole closer to origin) adds gain at low frequencies without significantly affecting phase at crossover, improving steady-state accuracy.
Q.165Medium
The characteristic equation of a closed-loop system is s³ + 6s² + 11s + 6 = 0. What are the poles?
Answer: A
The polynomial factors as (s+1)(s+2)(s+3) = 0, giving poles at -1, -2, and -3. All poles are in the left half-plane, making the system stable.
Q.166Medium
For a unity feedback system, if the open-loop DC gain is 100, what is the closed-loop DC gain?
Answer: C
Closed-loop gain = G(s)/(1+G(s)). At DC, this becomes 100/(1+100) = 101100 ≈ 0.99, showing the effect of feedback on reducing overall gain.
Q.167Medium
In the Routh-Hurwitz stability criterion, if the first column has a sign change, what does it indicate?
Answer: C
The number of sign changes in the first column of the Routh array equals the number of poles in the right half-plane. A sign change indicates at least one pole in RHP, making the system unstable.
Q.168Medium
A unity feedback control system has an open-loop transfer function G(s) = 10/(s(s+2)). What is the steady-state error for a unit ramp input?
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.170Medium
For a second-order system with ζ = 0.5 and ωn = 4 rad/s, what is the peak overshoot?
What is the effect of adding a pole at the origin to a stable open-loop system?
Answer: C
Adding a pole at origin adds -90° phase shift at all frequencies, decreasing phase margin. It also reduces high-frequency gain, decreasing gain margin
Q.172Medium
A lead compensator Gc(s) = K(s+a)/(s+b) where b > a provides maximum phase lead at frequency:
Answer: A
For lead compensator, maximum phase lead occurs at ωm = 1/√(τ₁τ₂) where τ₁ = 1/a and τ₂ = 1/b, giving ωm = √(ab)
Q.173Medium
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.174Medium
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.175Medium
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.176Medium
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.177Medium
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.178Medium
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.179Medium
For a unity feedback control system with G(s) = 10/[s(s+5)], the static velocity error constant Kv is:
