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.
What is the steady-state error for a unit step input to a Type 0 system?
Answer: C
For Type 0 system with unit step input, e_ss = 1/(1 + Kp) where Kp is the position error constant.
Q.2Medium
What does the Routh-Hurwitz criterion determine?
Answer: B
Routh-Hurwitz criterion is used to determine the stability of a system by examining the characteristic equation coefficients without calculating poles.
Q.3Medium
The gain margin of a system can be determined from the bode plot as:
Answer: C
Gain margin = 1/|G(jω)| at phase crossover frequency where phase = -180°. It indicates how much gain can be increased before instability.
Q.4Medium
For a second-order system with natural frequency ωn = 2 rad/s and damping ratio ζ = 0.5, the system is:
Answer: B
When ζ < 1 (0.5 < 1), the system is underdamped with oscillatory transient response.
Q.5Medium
The rise time of a second-order underdamped system decreases with:
Answer: A
Rise time tr ≈ (π - cos⁻¹(ζ))/(ωn√(1-ζ²)). It decreases with higher ωn and appropriate ζ value.
Q.6Medium
Which compensation technique is used to improve steady-state accuracy?
Answer: B
Lag compensation increases the system type or gain at low frequencies, improving steady-state accuracy without affecting stability significantly.
Q.7Medium
The Nyquist plot is a mapping of:
Answer: B
Nyquist plot maps the frequency response G(jω)H(jω) in the complex plane by varying ω from 0 to ∞.
Q.8Medium
The overshoot of a second-order system is independent of:
Answer: C
Overshoot = e^(-πζ/√(1-ζ²)) depends only on damping ratio ζ, not on ωn or system gain K.
Q.9Medium
Which of the following is a state-space representation advantage over transfer function?
Answer: B
State-space representation naturally handles MIMO systems, non-linear systems, and time-varying systems better than transfer functions.
Q.10Medium
In a closed-loop control system, the feedback path gain is reduced from 1 to 0.5. How does this affect the system's steady-state error?
Answer: A
Reducing feedback gain reduces the effectiveness of feedback, leading to increased steady-state error for the same input command.
Q.11Medium
For a control system, the gain crossover frequency and phase crossover frequency are equal. What does this indicate about the system's stability margin?
Answer: C
When gain crossover frequency equals phase crossover frequency, the system is at the stability boundary (phase = -180°), indicating marginal stability.
Q.12Medium
A lead compensator has a transfer function Gc(s) = K(s+2)/(s+8). What is the effect of this compensator?
Answer: B
Lead compensator has zero at -2 and pole at -8 (pole further left). This increases bandwidth and adds phase lead, improving transient response.
Q.13Medium
For a system with transfer function G(s)H(s) = 10/(s²(s+2)), the number of asymptotes in the root locus is:
Answer: B
Number of asymptotes = |number of poles - number of zeros| = |3 - 0| = 3. However, for this specific configuration with two poles at origin, effective asymptotes for root locus are 2.
Q.14Medium
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.15Medium
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.16Medium
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.17Medium
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.18Medium
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.19Medium
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.20Medium
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.
