GATE EE PYQ Mistake Book: Top Exam Traps

The Trap: Assuming Eddy current loss is always proportional to $f^2$ regardless of supply conditions.

The Reality: - When $V/f = \text{constant}$ (flux density $B_m$ constant): $P_h \propto f$ and $P_e \propto f^2$.
- When $V$ is constant but frequency $f$ varies ($V/f \neq \text{constant}$): $B_m \propto V/f$. Then $P_e \propto B_m^2 f^2 \propto (V/f)^2 f^2 = V^2$ (independent of frequency!), and $P_h \propto B_m^{1.6} f \propto V^{1.6} f^{-0.6}$.

The Trap: Believing over-excitation in a synchronous machine always produces lagging power factor.

The Reality: Generator and motor behaviors are opposites! - Synchronous Generator: Over-excited $\implies$ delivers lagging reactive power (operates at lagging PF).
- Synchronous Motor: Over-excited $\implies$ delivers leading reactive power (operates at LEADING PF, acting as a synchronous condenser!).

The Trap: Using the pre-fault power-angle curve $P_{max1}\sin\delta$ to evaluate the deceleration area after fault clearance.

The Reality: If a faulty line is tripped to clear the fault, the post-fault transfer reactance is HIGHER than pre-fault ($X_{post} > X_{pre}$), meaning $P_{max3} < P_{max1}$. You must integrate the decelerating area against the post-fault curve $P_{max3}\sin\delta$, NOT the pre-fault curve.

The Trap: Omitting the voltage base transformation term when converting transformer or generator per-unit impedance.

The Reality: When both MVA base and kV base change: $$Z_{pu,new} = Z_{pu,old} \times \left(\frac{V_{base,old}}{V_{base,new}}\right)^2 \times \left(\frac{S_{base,new}}{S_{base,old}}\right)$$ Forgetting the squared voltage term $\left(\frac{V_{old}}{V_{new}}\right)^2$ is the #1 NAT mistake in power systems.

The Trap: Adding $+90^\circ$ phase shift for an open-loop zero located in the right-half $s$-plane ($s - z_0$).

The Reality: An RHP zero $(1 - s/z_0)$ increases the magnitude slope by $+20\text{ dB/decade}$, but contributes a NEGATIVE phase shift of $-90^\circ$! It has the magnitude response of a zero, but the phase destabilization of a pole.

The Trap: Forgetting the negative sign in the steady-state transfer function $V_o = -\frac{D}{1-D}V_s$.

The Reality: During switch OFF, the inductor current discharges through the diode into the capacitor from ground upwards, forcing the output terminal to be negative relative to ground. Always verify whether the question asks for magnitude $|V_o|$ or signed potential.

The Trap: Assuming inserting external rotor resistance increases the maximum torque $T_{max}$.

The Reality: Maximum torque $T_{max} \propto \frac{V^2}{2 X_2'}$ is strictly INDEPENDENT of rotor resistance $R_2$! Adding external resistance merely shifts the slip at which maximum torque occurs ($s_m = R_2 / X_2'$), allowing high starting torque at standstill without altering $T_{max}$.

The Trap: Confusing circuit turn-off time $t_c$ with thyristor turn-off time $t_q$.

The Reality: For successful line commutation, the reverse bias duration provided by the AC mains (circuit turn-off time $t_c$) must exceed the manufacturer device turn-off time $t_q$ by a safety margin ($t_c > t_q$). If firing angle $\alpha > 180^\circ - \gamma_{min}$, commutation failure occurs instantly, creating a DC short-circuit.

The Trap: Calculating 3-phase complex power directly as $V_{012}^T I_{012}^*$ without the factor 3.

The Reality: Using standard Fortescue transformation: $S = V_a I_a^* + V_b I_b^* + V_c I_c^* = 3(V_0 I_0^* + V_1 I_1^* + V_2 I_2^*)$. Power invariance only holds without the factor 3 if unitary transformation matrices ($\frac{1}{\sqrt{3}}$ normalization) are used.

The Trap: Equating total 3-phase active power to $(W_1 - W_2)$.

The Reality: - Active Power: $P = W_1 + W_2 = \sqrt{3} V_L I_L \cos\phi$
- Reactive Power: $Q = \sqrt{3}(W_1 - W_2) = \sqrt{3} V_L I_L \sin\phi$
- Power factor: $\tan\phi = \sqrt{3}\frac{W_1 - W_2}{W_1 + W_2}$. When power factor is $0.5$, one wattmeter reads exactly ZERO.