Electrical Engg (EEE) - MCQ Practice Questions

Lyapunov's second method directly analyzes stability without solving differential equations. It's applicable to linear and nonlinear systems.

Breakaway/break-in points satisfy dK/ds = 0, derived from the magnitude condition where multiple roots exist on the real axis.

Number of asymptotes = |poles - zeros| = |3 - 1| = 2. Three poles, one zero gives 2 asymptotes.

Kv = lim[s→0] s·Kp·G(s) = lim[s→0] s·10·1/[s(s+2)] = $\frac{10}{2}$ = 5

A limit cycle is a closed trajectory in phase plane representing self-sustained oscillations with constant amplitude and frequency, independent of initial conditions.

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($\frac{100}{14}$.14) ≈ 17 dB, closest to option is 14 dB for √2 factor.

Sensitivity S(s) = ∂Y/∂G ÷ Y/G = 1/[1+G(s)H(s)] for unity feedback systems. It measures effect of parameter variations.

Nyquist sampling theorem: fs > 2·fmax to avoid aliasing. The sampling frequency must be at least twice the highest frequency component.

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.

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.

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.

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.

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).

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.

Both diodes and thyristors are unidirectional devices that conduct current in only one direction. MOSFETs are bidirectional.

Silicon diodes have a typical forward voltage drop of 0.6-0.7 V at room temperature. Germanium diodes have ~0.3 V.

An inverter converts DC power to AC power. Rectifiers do the opposite (AC to DC). Choppers convert DC to DC.

PIV rating defines the maximum reverse voltage a diode can withstand without breaking down. Exceeding this causes reverse breakdown and device failure.

For a full-wave rectifier: Vdc = (2√2/π) × Vrms = 0.9 × Vrms = 0.9 × 230 = 207 V approximately.

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.