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 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.22Easy
Which of the following is NOT a characteristic of a proportional (P) controller?
Answer: B
A proportional controller cannot eliminate steady-state error completely for step inputs in type-0 systems. An integral term is needed for zero steady-state error.
Q.23Easy
For a unity feedback system with G(s) = K/(s(s+3)(s+5)), what is the system type?
Answer: B
The system type equals the number of poles at origin. Here, there is one pole at origin (s in denominator), making it Type 1.
Q.24Easy
A second-order system has damping ratio ζ = 0.5. What is the nature of its response?
Answer: B
For ζ < 1, the system is underdamped and exhibits oscillatory response. At ζ = 0.5, there are definitely oscillations with exponential decay.
Q.25Easy
In root locus analysis, as the gain K increases from 0 to ∞, the closed-loop poles move along specific paths. Where do these paths originate?
Answer: B
The root locus starts at open-loop poles (K=0) and ends at open-loop zeros (K=∞). This is a fundamental property of root locus construction.
Q.26Medium
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.27Medium
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.28Medium
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.29Medium
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.30Medium
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.31Easy
For the open-loop transfer function G(s)H(s) = K(s+1)/((s+2)(s+3)(s+4)), the system order is:
Answer: B
System order is determined by the highest power of 's' in the characteristic equation denominator. Here, it's (s+2)(s+3)(s+4) = s³+..., so order is 3.
Q.32Medium
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.33Medium
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.34Hard
For a second-order system with natural frequency ωn = 5 rad/s and ζ = 0.7, the peak time tp is approximately:
Answer: B
tp = π/(ωn√(1-ζ²)) = π/(5√(1-0.49)) = π/(5×0.714) ≈ 0.88 seconds ≈ 0.89 seconds. Closest answer is B.
Q.35Medium
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.36Easy
In a state-space representation, if the system has 4 state variables, what is the dimension of the state vector?
Answer: C
The state vector x(t) contains all state variables. With 4 state variables, it's a 4×1 column vector, so the dimension is 4.
Q.37Hard
A negative feedback system's loop gain L(s) = G(s)H(s) has a pole-zero excess of 2. What can be concluded?
Answer: B
Pole-zero excess affects the phase behavior at high frequencies. A system with excess of 2 can be either stable or unstable depending on the gain value and pole locations.
Q.38Medium
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.39Medium
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.40Hard
A feedback system's sensitivity function S(s) = 1/(1+L(s)) where L(s) is loop gain. For large |L(s)|, what happens to |S(s)|?
Answer: B
When |L(s)| >> 1, the sensitivity function |S(s)| ≈ 1/|L(s)| becomes very small. This shows that high loop gain reduces sensitivity to parameter variations.
