In a network, when using the cut-set method, a cut separates the network into two parts. How many equations are needed for a network with 'b' branches and 'n' nodes to find all branch currents?
Answer: B
Number of independent loop equations needed = b - n + 1 (where b is branches and n is nodes). This represents the circuit's cyclomatic complexity.
Q.5Hard
For a passive linear network, the input impedance looking into terminals is Z(s). If a unit impulse is applied as input, the impulse response h(t) is the:
Answer: C
Impulse response h(t) = L⁻¹[Y(s)] where Y(s) is admittance. For impedance Z(s), admittance Y(s) = 1/Z(s).
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Q.6Hard
For a two-port network, when port 2 is open-circuited (I₂=0), the parameter measured is:
Answer: A
In hybrid (h) parameters: h₁₁ is input impedance with output open (I₂=0). h₁₁ = V₁/I₁|I₂=₀ measured in ohms.
Q.7Hard
The cut-set matrix is used in circuit analysis to:
Answer: B
Cut-set matrix provides a systematic way to write KVL equations for fundamental cut-sets, an alternative to mesh analysis.
Q.8Hard
In a circuit with mutual inductance M between two coils, if the coupling coefficient k = 0.8, L1 = 10H, then L2 is at least:
Answer: A
Coupling coefficient k = M/√(L1·L2). For k=0.8 and L1=10H: 0.8 = M/√(10·L2). Since M ≤ √(L1·L2), we get L2 ≥ (M/k)²/L1 = (10·k²)/k² = L1/k² = 010.64 = 15.625H minimum requires M evaluation, but using k = M/√(L1L2) ≤ 1 gives L2 ≥ 6.25H.
Q.9Hard
A circuit has a loop containing 5V source, 10V source (opposite polarity), 2Ω, and 3Ω resistors. Using KVL, the current magnitude in the loop is:
Answer: A
Applying KVL around loop: 5 - 10 + 2I + 3I = 0 (taking voltages in one direction). This gives -5 + 5I = 0, so I = 1A.
Q.10Hard
In ABCD parameters of a two-port network, parameter C represents:
Answer: B
In ABCD parameters: V1 = AV2 - BI2; I1 = CV2 - DI2. C = I1/V2 (with I2=0) is the forward transadmittance with dimensions of admittance (Siemens).
Q.11Hard
The swing equation in power system stability is given by:
Answer: A
The swing equation relates angular acceleration to net mechanical power (P_m), electrical power (P_e), and damping coefficient (D).
Q.12Hard
The critical clearing time in transient stability refers to:
Answer: A
Critical clearing time is the maximum duration a fault can exist before the system loses synchronism and becomes unstable.
Q.13Hard
The Ferranti effect in long transmission lines is characterized by:
Answer: A
Under light load, capacitive reactance dominates, causing charging current and voltage rise at the receiving end above the sending end voltage.
Q.14Hard
In the Newton-Raphson method for load flow analysis, convergence depends on:
Answer: A
N-R method converges based on good initial guesses (typically 1.0 pu) and the Jacobian matrix representing system sensitivity.
Q.15Hard
The phenomenon of voltage instability leading to voltage collapse occurs primarily due to:
Answer: A
Voltage collapse occurs when reactive power demand exceeds supply, causing progressive voltage reduction that destabilizes the system, as seen in 2012 Indian blackout.
Q.16Hard
Which among the following is the correct formula for calculating bus voltage magnitude in Gauss-Seidel load flow method?
Answer: C
The Gauss-Seidel iterative formula for bus voltage calculation uses the admittance matrix and network equations: V_i = (1/Y_ii)[P_i + jQ_i - Σ(Y_ij*V_j)]
Q.17Hard
In a 500 kV transmission line, if the receiving end voltage drops to 0.9 pu, what type of compensation is most critical?
Answer: C
For severe voltage drop (10%), both series compensation (to reduce voltage drop) and shunt compensation (to support receiving end voltage) are typically required.
Q.18Hard
In transient stability assessment, what does the 'equal area criterion' determine?
Answer: B
Equal area criterion uses the swing equation graph to compare the accelerating area (energy added to rotor) with decelerating area (energy removed), determining stability.
Q.19Hard
In transient stability studies, which machine variable is most critical for assessing first-swing stability?
Answer: A
Speed deviation determines if the generator can maintain synchronism during the first swing after a disturbance. Excessive Δω leads to loss of synchronism.
Q.20Hard
Which FACTS device provides independent control of both voltage magnitude and phase angle?
Answer: C
UPFC can independently control transmission line voltage magnitude, phase angle, and impedance simultaneously using combined series-shunt compensation.
