For Vth = 18 V and Rth = 6 Ω, what load gives maximum power, and how much?
A 3 Ω, 18 W
B 6 Ω, 54 W
C 12 Ω, 6.75 W
D 6 Ω, 13.5 W
Answer: D. 6 Ω, 13.5 W. Maximum transfer requires RL = RTH = 6 Ω; Pmax = 18²/(4 × 6) = 13.5 W.
With 12 V through 2 kΩ, 6 V through 3 kΩ, and 6 kΩ to ground, what is the node voltage?
A 6 V
B 4 V
C 10 V
D 8 V
Answer: D. 8 V. KCL gives (12−V)/2k + (6−V)/3k = V/6k; solving gives 8 V.
For a 3 Ω resistor shared by clockwise meshes I1 and I2, what drop term appears in mesh one?
A 3I2 only
B 3(I1 − I2)
C I1 − 3I2
D 3(I1 + I2)
Answer: B. 3(I1 − I2). Shared current in mesh-one direction is I1 − I2, so the drop is 3(I1 − I2).
During superposition, an inactive independent current source becomes what?
A Open circuit
B Current source
C Short circuit
D Voltage source
Answer: A. Open circuit. Setting an independent current source to zero leaves an open circuit; dependent sources remain active.
When finding Rth with a dependent source present, what method is required?
A Turn off every source
B Short the output
C Use a test source
D Open all branches
Answer: C. Use a test source. Deactivate independent sources, retain dependent sources, and apply a test source to find V/I.
When an ideal voltage source lies between two nonreference nodes, which nodal construct is used?
A Thevenin pair
B Source tree
C Supermesh
D Supernode
Answer: D. Supernode. The two nodes and the source form a supernode; write KCL around its boundary.
What construct handles a current source shared by two meshes?
A Supernode
B Source pair
C Superposition
D Supermesh
Answer: D. Supermesh. A shared current source is handled with a supermesh equation and a current constraint.
In a connected graph with 8 branches and 5 nodes, how many independent loops?
A 8
B 4
C 3
D 5
Answer: B. 4. For a connected graph, loop rank is b − n + 1 = 8 − 5 + 1 = 4.
How many twigs does a spanning tree of 7 nodes contain?
A 8
B 5
C 6
D 7
Answer: C. 6. A spanning tree of n nodes has n − 1 twigs, so it has 6.
Converting three equal 2 Ω star arms gives delta arms of what value?
A 2 Ω each
B 3 Ω each
C 6 Ω each
D 9 Ω each
Answer: C. 6 Ω each. For a balanced star, each delta resistance is three times a star arm: 6 Ω.
Converting three equal 9 Ω delta arms gives star arms of what value?
A 9 Ω each
B 27 Ω each
C 3 Ω each
D 6 Ω each
Answer: C. 3 Ω each. For a balanced delta, each star arm is one third: 3 Ω.
In AC maximum power transfer, what load impedance is required?
A Conjugate of Zth
B Equal to Zth
C Twice Zth
D Zero impedance
Answer: A. Conjugate of Zth. Maximum average power occurs when ZL equals the complex conjugate of ZTH.
With L = 25 mH and C = 10 µF, what is series resonance frequency?
A About 31.8 Hz
B About 1 kHz
C About 318 Hz
D About 3.18 kHz
Answer: C. About 318 Hz. f0 = 1/(2π√LC) ≈ 318 Hz.
For a series RLC with f0 = 1 kHz, L = 10 mH, and R = 10 Ω, what is Q?
A 0.628
B 6.28
C 62.8
D 1.59
Answer: B. 6.28. For series RLC, Q = ω0L/R = 2π(1000)(0.01)/10 ≈ 6.28.
What bandwidth corresponds to f0 = 12 kHz and Q = 8?
A 0.67 kHz
B 96 kHz
C 8 kHz
D 1.5 kHz
Answer: D. 1.5 kHz. Bandwidth is approximately f0/Q = 12/8 = 1.5 kHz.
With R = 6 Ω and net reactance 8 Ω, what is |Z|?
A 10 Ω
B 8 Ω
C 2 Ω
D 14 Ω
Answer: A. 10 Ω. |Z| = √(R² + X²) = √(36 + 64) = 10 Ω.
For a net inductive reactance of 8 Ω and R = 6 Ω, what phase results?
A 53.1° leading
B 53.1° lagging
C 90° lagging
D 36.9° leading
Answer: B. 53.1° lagging. tan⁻¹(X/R) ≈ 53.1°; inductive current lags voltage.
At 100 V RMS, 2 A RMS, and power factor 0.8, what average power is used?
A 80 W
B 250 W
C 160 W
D 200 W
Answer: C. 160 W. P = VRMS IRMS cosφ = 100 × 2 × 0.8 = 160 W.
For a 10 V RC step with τ = 0.1 s, what capacitor voltage occurs at 0.2 s?
A 9.50 V
B 8.65 V
C 1.35 V
D 6.32 V
Answer: B. 8.65 V. Vc = 10(1 − e⁻²) ≈ 8.65 V at two time constants.
If an RL current rises from 2 A to 5 A, what is i after one time constant?
A 3.90 A
B 5.00 A
C 4.10 A
D 2.90 A
Answer: A. 3.90 A. i(τ) = 2 + (5 − 2)(1 − e⁻¹) ≈ 3.90 A.
Given a two-port z21 parameter, what relation is measured?
A I2/V1, V2 = 0
B V2/I1, I2 = 0
C V1/I2, I1 = 0
D I1/V2, I2 = 0
Answer: B. V2/I1, I2 = 0. z21 is V2/I1 with the output port open, so I2 = 0.
What transfer function describes an RC low-pass with output across C?
A 1/(1 + sRC)
B 1/(sRC)
C sRC/(1 + sRC)
D 1 + sRC
Answer: A. 1/(1 + sRC). The divider gives H(s) = ZC/(R + ZC) = 1/(1 + sRC).
When R = 4 Ω, L = 1 H, and C = 0.25 F, what damping occurs?
A Critical damping
B Underdamping
C No damping
D Overdamping
Answer: A. Critical damping. α = R/(2L) = 2 and ω0 = 1/√LC = 2, so damping is critical.
Thevenin and Norton equivalents preserve which circuit property?
A Terminal I–V relation
B Every branch current
C Component count
D Internal topology
Answer: A. Terminal I–V relation. Equivalent two-terminal networks preserve the same external terminal voltage-current behavior.
With 3 Ω and 9 Ω arms adjacent to node A and 6 Ω opposite, what is star arm RA?
A 2 Ω
B 4.5 Ω
C 3 Ω
D 1.5 Ω
Answer: D. 1.5 Ω. RA = (3 × 9)/(3 + 6 + 9) = 27/18 = 1.5 Ω.