FE ELECTRICAL – SIXTH SIMULATION

#1. [Computer Networks] Ignoring loss, TCP throughput with receive window 256 kB and RTT 40 ms is approximately:

61.895 Mb/s

46.433 Mb/s

51.200 Mb/s

57.494 Mb/s

#2. [Power] Ideal transformer with turns ratio Np:Ns=5:1 feeds load 15 Ω on secondary. Reflected primary impedance is:

298.92 Ω

468.73 Ω

416.79 Ω

375.00 Ω

#3. [Linear Systems] For a 2nd-order system with damping ratio ζ=0.5 and ωn=11.25 rad/s, estimate 2% settling time.

0.629 s

0.610 s

0.849 s

0.711 s

#4. [Computer Systems and Software] Which data structure gives O(1) average-time lookup for symbol tables while allowing dynamic insertion?

Linked list

Hash table

Sorted array

Balanced BST

#5. [Circuit Analysis] A branch dissipates 443 W with RMS current 5.59 A. Equivalent resistance is:

15.958

14.177

16.140

11.831

#6. [Circuit Analysis] A current source 11 A feeds two parallel resistors 12 Ω and 6 Ω. Node voltage across them is:

40.027

44.000

46.716

47.532

#7. [Linear Systems] For G(s)=1/(s+6), unit-step response final value is:

0.1369

0.2127

0.1186

0.1667

#8. [Properties of Electrical Materials] A 1.2 mm insulation layer withstands 20527 V. The electric field stress is:

18910550.9 V/m

19806466.7 V/m

17105833.3 V/m

14887826.4 V/m

#9. [Mathematics] A phasor is V = 6 + j2. What is |V|?

5.403

5.253

6.325

7.198

#10. [Power] A balanced 3-phase load consumes 402 kW at 291 V line-line and pf=0.79 lagging. Line current is:

1009.6 A

1070.4 A

944.0 A

890.6 A

#11. [Mathematics] In a fully connected sensor graph with 11 nodes, how many unique undirected links exist?

54

56

66

55

#12. [Power] Transformer no-load secondary voltage is 124 V and full-load is 119 V. Voltage regulation is:

5.1 %

3.4 %

4.2 %

4.7 %

#13. [Properties of Electrical Materials] A package heat spreader has k=127.7 W/m·K, area=0.00e+00 m², thickness=0.026 m, ΔT=34 K. Heat flow is:

0.0 W

#14. [Engineering Economics] A retrofit costs $122,356 now and saves $46,074/year for 8 years. At MARR = 8%, NPV is:

142414.6 USD

112962.2 USD

172480.6 USD

126319.8 USD

#15. [Digital Systems] In unsigned 4-bit arithmetic, adding 1 and 14 sets carry-out flag to:

0

1

undefined

depends on signed interpretation

#16. [Electromagnetics] Transmission line has Z0=63 Ω and load ZL=53 Ω (real). Reflection coefficient Γ is:

-0.086

-0.052

-0.113

-0.100

#17. [Circuit Analysis] A current source 5 A feeds two parallel resistors 7 Ω and 11 Ω. Node voltage across them is:

21.389

23.208

17.373

18.913

#18. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=13, unit-step steady-state error is:

0.087

0.079

0.071

0.078

#19. [Signal Processing] For an ideal 16-bit ADC, quantization-limited SQNR is closest to:

88 dB

90 dB

104 dB

98 dB

#20. [Signal Processing] A tone at 9339 Hz is sampled at fs=10000 Hz. Observed baseband alias frequency is:

661 Hz

870 Hz

393 Hz

1091 Hz

#21. [Signal Processing] For y[n]=0.58y[n-1]+(-0.14)y[n-2]+x[n], which is correct?

Marginally stable (pole on unit circle)

Cannot determine without input specification

BIBO stable (dominant poles inside unit circle)

BIBO unstable (pole outside unit circle)

#22. [Mathematics] In a fully connected sensor graph with 10 nodes, how many unique undirected links exist?

49

44

55

45

#23. [Circuit Analysis] Node A is connected to 18 V through 3 Ω and to 30 V through 3 Ω. What is node voltage VA?

20.7

24.0

27.0

22.1

#24. [Communications] A TDM PCM system multiplexes 18 channels, each sampled at 16000 Hz with 12 bits/sample. Total data rate is:

3.456 Mb/s

3.526 Mb/s

3.974 Mb/s

3.383 Mb/s

#25. [Circuit Analysis] An AC source of 148 Vrms drives impedance Z = 12 + j23 Ω. RMS current magnitude is:

6.949

4.806

4.695

5.705

#26. [Engineering Economics] For a test fixture: fixed cost $140,736, unit price $91, variable cost $44. Breakeven quantity is:

3592 units

3068 units

2830 units

2994 units

#27. [Electromagnetics] For a long straight conductor carrying 88 A, magnetic flux density at radius 0.051 m is:

0.00e+00 T

3.45e-04 T

0.00e+00 T

#28. [Electronics] A BJT in active mode has β=121 and base current 136.4 µA. Collector current is closest to:

18.486 mA

13.985 mA

19.352 mA

16.504 mA

#29. [Circuit Analysis] A Thevenin source Vth=40 V with Rth=3 Ω feeds RL=22 Ω. Load current is:

1.326

1.429

1.600

1.951

#30. [Digital Systems] Pipeline stage has tCQ=1.04 ns, combinational delay=4.48 ns, setup=1.71 ns. Max clock frequency is:

116.6 MHz

169.0 MHz

164.2 MHz

138.3 MHz

#31. [Electronics] Ideal inverting op-amp with Rin=3 kΩ, Rf=30 kΩ, Vin=0.543 V. Output is:

-6.438 V

-4.709 V

-5.430 V

-5.986 V

#32. [Mathematics] Compute the integral ∫_1^3 x^3 dx.

20.0

23.0

15.6

15.8

#33. [Circuit Analysis] In an RL step response with V=40 V, R=32 Ω, L=0.383 H, find i(t) at t=0.019 s.

1.211

1.137

0.994

1.096

#34. [Electromagnetics] If electric field changes at dE/dt=4.64e+06 V/m·s in a dielectric with permittivity ε=0.00e+00 F/m, displacement current density is:

0.00e+00 A/m²

#35. [Linear Systems] For low-pass H(jω)=1/(1+jωτ) with τ=0.627 s, find |H(jω)| at ω=7 rad/s.

0.260

0.267

0.222

0.248

#36. [Properties of Electrical Materials] Estimate skin depth δ for a conductor with σ=2.12e+07 S/m, μr=1, at f=50 Hz.

1.55e-02 m

1.90e-02 m

1.20e-02 m

2.00e-02 m

#37. [Properties of Electrical Materials] A conductor has resistivity 0.00e+00 Ω·m at 20°C and temperature coefficient 0.0033/°C. Estimate resistivity at 78°C.

0.00e+00 Ω·m

#38. [Signal Processing] A first-order analog low-pass has cutoff 5000 Hz. At cutoff frequency, output magnitude relative to passband is:

-6 dB (approximately 0.5 of passband amplitude)

0 dB (full passband amplitude)

-1 dB (approximately 0.89 of passband amplitude)

-3 dB (approximately 0.707 of passband amplitude)

#39. [Digital Systems] Pipeline stage has tCQ=1.89 ns, combinational delay=4.05 ns, setup=0.96 ns. Max clock frequency is:

115.9 MHz

128.6 MHz

144.9 MHz

109.4 MHz

#40. [Ethics and Professional Practice] On a substation relay upgrade, you identify an ungrounded metallic enclosure that poses a shock hazard. The correct professional action is:

Verbally inform a coworker and proceed with the schedule

Document the hazard, notify the authority in responsible charge, and stop affected work until corrected

Note the hazard for the final report and continue working

Apply temporary insulation tape and continue the project

#41. [Electromagnetics] For a lossless medium with εr=2.56 and μr=1.5, intrinsic impedance η is:

313.1 Ω

288.6 Ω

268.5 Ω

322.8 Ω

#42. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(1.02 s).

0.002

#43. [Mathematics] Evaluate Re(e^(j2t)) at t = 0.28 s.

0.625

0.847

0.655

0.947

#44. [Circuit Analysis] A Thevenin source Vth=11 V with Rth=3 Ω feeds RL=25 Ω. Load current is:

0.459

0.453

0.393

0.348

#45. [Probability and Statistics] Assuming normal process variation with mean 103 and std dev 9, what is the 95th percentile?

104.0

117.8

125.3

130.7

#46. [Electronics] Using square-law saturation model Id=0.5k(VGS−VT)^2, find Id for k=0.004 A/V², VGS=3.56 V, VT=0.76 V.

17.756 mA

18.686 mA

18.396 mA

15.680 mA

#47. [Mathematics] For first-order decay dy/dt = -4y with y(0)=1, find y(0.8 s).

0.045

0.041

0.048

0.032

#48. [Communications] Using Shannon capacity C = B log2(1+SNR), with B=5.8 MHz and linear SNR=50, capacity is:

37.090 Mb/s

35.909 Mb/s

38.103 Mb/s

32.900 Mb/s

#49. [Engineering Sciences] A busbar support bracket experiences elastic strain 872 με. Assuming Young’s modulus E = 202.7 GPa, stress is:

163.8 MPa

176.8 MPa

207.6 MPa

200.9 MPa

#50. [Circuit Analysis] An AC source of 211 Vrms drives impedance Z = 14 + j9 Ω. RMS current magnitude is:

14.195

15.029

10.218

12.678

#51. [Control Systems] A loop has crossover ωc=2.3 rad/s and phase margin 58.8°. Which interpretation is correct?

Negative phase margin indicates instability at the crossover frequency

Phase margin has no bearing on closed-loop stability

The system is marginally stable and requires gain reduction

Positive phase margin indicates closed-loop stability with moderate robustness

#52. [Mathematics] A phasor is V = 4 + j2. What is |V|?

4.078

3.779

4.774

4.472

#53. [Mathematics] For f(t) = t^5 – t^2 + 3t, evaluate df/dt at t = 8.

23336

17119

24110

20467

#54. [Power] A component has reactance 0.17 pu on 50 MVA base (same kV base). On 25 MVA base, reactance is:

0.078 pu

0.099 pu

0.073 pu

0.085 pu

#55. [Digital Systems] Pipeline stage has tCQ=2.09 ns, combinational delay=6.4 ns, setup=1.73 ns. Max clock frequency is:

97.8 MHz

119.7 MHz

82.9 MHz

76.8 MHz

#56. [Communications] In M-ary digital modulation, what is the trade-off when increasing the modulation order M?

Increasing M allows more bits per symbol, improving spectral efficiency at the cost of SNR requirement

M-ary modulation reduces bandwidth but has no effect on error rate

Increasing M always improves both spectral efficiency and noise immunity

Higher M reduces the required SNR for a given BER

#57. [Power] At a 22 kV bus with Thevenin reactance 0.284 Ω (line-line basis), 3-phase bolted fault current is:

38119.2 A

44724.3 A

52634.3 A

54431.9 A

#58. [Power] Ideal transformer with turns ratio Np:Ns=3:1 feeds load 23 Ω on secondary. Reflected primary impedance is:

176.28 Ω

207.00 Ω

161.86 Ω

155.61 Ω

#59. [Electronics] A silicon diode has Vf=0.7 V at 25°C with temperature coefficient −2 mV/°C. Approximate Vf at 70°C is:

0.610 V

0.654 V

0.665 V

0.552 V

#60. [Digital Systems] In unsigned 4-bit arithmetic, adding 12 and 6 sets carry-out flag to:

depends on signed interpretation

undefined

1

0

#61. [Computer Systems and Software] A 32-bit, direct-mapped cache has 512 sets and 128-byte blocks. Tag bits per line are:

18

14

16

19

#62. [Computer Networks] Ignoring loss, TCP throughput with receive window 64 kB and RTT 20 ms is approximately:

20.327 Mb/s

25.600 Mb/s

28.369 Mb/s

31.064 Mb/s

#63. [Computer Systems and Software] Cache hit rate=0.94, hit time=3.1 ns, miss penalty=46.2 ns. AMAT is:

5.872 ns

5.372 ns

7.162 ns

6.873 ns

#64. [Circuit Analysis] A branch dissipates 135 W with RMS current 4.68 A. Equivalent resistance is:

5.214

6.164

5.517

7.156

#65. [Computer Networks] For IPv4 subnet /22, how many usable host addresses are available?

1031

1022

1024

1020

#66. [Power] A 2-pole induction motor on 60 Hz runs at 3565 rpm. Rotor current frequency is closest to:

0.583 Hz

0.697 Hz

0.672 Hz

0.483 Hz

#67. [Circuit Analysis] Node A is connected to 29 V through 7 Ω and to 8 V through 3 Ω. What is node voltage VA?

14.3

15.5

15.8

12.9

#68. [Probability and Statistics] A lot has independent defect probability 0.03 per board. For 12 boards, what is P(at least 3 defect)?

0.004

0.006

0.005

0.007

#69. [Computer Networks] A router has routes 10.2.0.0/16, 10.2.32.0/19, and 10.2.32.128/25. Packet to 10.2.32.200 follows which route?

10.2.32.128/25 (longest-prefix match)

10.2.32.0/19

Default route only

10.2.0.0/16

#70. [Probability and Statistics] A lot has independent defect probability 0.04 per board. For 13 boards, what is P(at least 1 defect)?

0.412

0.313

0.475

0.356

#71. [Engineering Economics] A public project has PV of benefits = $215,916 and PV of costs = $150,332. Benefit-cost ratio is:

1.436

1.275

1.631

1.595

#72. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=16, unit-step steady-state error is:

0.047

0.072

0.059

0.076

#73. [Communications] For M-ary signaling with M=8 and bit rate 50 kb/s, symbol rate is:

3 ksym/s

35 ksym/s

32 ksym/s

16 ksym/s

#74. [Electronics] An ideal 10-bit ADC with Vref=5.0 V measures Vin=1.509 V. Output code is closest to:

289

340

309

337

#75. [Ethics and Professional Practice] A colleague asks you to provide a professional reference overstating their experience on power systems projects to help them obtain a contract. The correct action is:

Provide the reference but add subtle caveats the reviewer will notice

Provide the reference since exaggeration is common in competitive bidding

Decline and only provide an honest, accurate representation of their qualifications

Agree to provide the reference if the colleague does the same for you

#76. [Digital Systems] In unsigned 4-bit arithmetic, adding 7 and 5 sets carry-out flag to:

0

undefined

depends on signed interpretation

1

#77. [Mathematics] An engineer linearizes a calibration model and obtains equations 2x + 2y = 14 and 4x + 3y = 25. What is x?

4.577

4.747

3.458

4.000

#78. [Engineering Economics] What present value is equivalent to a future replacement cost of $52,661 in 9 years at i=8%?

23905.4 USD

23343.9 USD

22913.0 USD

26343.6 USD

#79. [Circuit Analysis] A branch dissipates 302 W with RMS current 5.38 A. Equivalent resistance is:

10.434

11.481

11.880

8.940

#80. [Mathematics] An engineer linearizes a calibration model and obtains equations 7x + 2y = 50 and 3x + 3y = 34. What is x?

4.441

4.918

5.467

6.097

#81. [Engineering Sciences] A dielectric coolant (ρ=909.2 kg/m³, μ=2.05e-03 Pa·s) flows at 1.49 m/s through a pipe of diameter 0.051 m. Reynolds number is:

27352.2

27872.0

33702.5

39651.1

#82. [Electromagnetics] Transmission line has Z0=62 Ω and load ZL=113 Ω (real). Reflection coefficient Γ is:

0.186

0.225

0.196

0.291

#83. [Engineering Sciences] A vibration-sensitive electronics tray is modeled as an underdamped SDOF system with m=1.47 kg, damping ratio ζ=0.27, and natural frequency ωn=23.28 rad/s. What is the damped natural frequency ωd?

26.145 rad/s

25.534 rad/s

22.415 rad/s

20.533 rad/s

#84. [Ethics and Professional Practice] On a data-center power upgrade, a supplier offers premium sports tickets while you are evaluating their bid. The correct action is:

Accept the tickets as a professional courtesy and disclose to your manager

Decline the gift and keep procurement decisions objective and fully documented

Accept the tickets but recuse yourself from the final vendor decision

Accept the tickets since they do not exceed company gift limits

#85. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.48. Percent overshoot is:

22.435 %

12.894 %

17.926 %

20.622 %

#86. [Linear Systems] A transfer function has poles at s=-6.16 and s=-15.19. Dominant time constant is:

0.176 s

0.145 s

0.192 s

0.162 s

#87. [Computer Systems and Software] Worst-case comparisons for binary search on sorted array of size 512 are closest to:

10

9

8

11

#88. [Engineering Economics] Compute capital recovery (EUAC) for P=$245,430, S=$12,153, n=12 years, i=6%.

32873.5 USD/yr

28553.8 USD/yr

30331.8 USD/yr

23761.3 USD/yr

#89. [Ethics and Professional Practice] On a municipal water-treatment SCADA project, you still have access to proprietary firmware from a former employer. The correct action is:

Do not reuse protected material; obtain authorization or create an original implementation

Reuse the firmware and credit your former employer in the documentation

Reuse the firmware since you wrote it yourself during prior employment

Use only small portions of the code to avoid copyright infringement

#90. [Digital Systems] Pipeline stage has tCQ=1.42 ns, combinational delay=7.09 ns, setup=1.02 ns. Max clock frequency is:

121.3 MHz

123.5 MHz

79.6 MHz

104.9 MHz

#91. [Electronics] Ideal inverting op-amp with Rin=8 kΩ, Rf=86 kΩ, Vin=0.224 V. Output is:

-2.176 V

-2.408 V

-2.870 V

-1.914 V

#92. [Mathematics] Compute the integral ∫_1^3 x^3 dx.

20.0

21.9

17.4

23.2

#93. [Mathematics] For first-order decay dy/dt = -8y with y(0)=1, find y(0.88 s).

0.001

#94. [Probability and Statistics] Assuming normal process variation with mean 85 and std dev 19, what is the 95th percentile?

126.9

133.6

116.3

101.4

#95. [Power] A balanced 3-phase load consumes 211 kW at 327 V line-line and pf=0.75 lagging. Line current is:

586.8 A

415.2 A

535.6 A

496.7 A

#96. [Ethics and Professional Practice] During a transmission line design review, you realize you lack sufficient expertise in the specific soil conditions affecting tower foundations. The correct action is:

Rely on standard foundation designs from similar projects in different soil types

Use conservative safety factors to compensate for your knowledge gap

Complete the design and have another PE review it before submission

Disclose your limitation and recommend engaging a qualified geotechnical specialist

#97. [Circuit Analysis] In an RL step response with V=18 V, R=14 Ω, L=0.46 H, find i(t) at t=0.006 s.

0.256

0.163

0.215

0.247

#98. [Communications] For an AM wave, envelope Vmax=7.79 and Vmin=1.05. Modulation index m is:

0.762

0.620

0.698

0.919

#99. [Control Systems] A loop has crossover ωc=23.4 rad/s and phase margin 45.5°. Which interpretation is correct?

Negative phase margin indicates instability at the crossover frequency

The system is marginally stable and requires gain reduction

Positive phase margin indicates closed-loop stability with moderate robustness

Phase margin has no bearing on closed-loop stability

#100. [Engineering Sciences] For coupled electro-thermal design, which modeling approach most directly captures bidirectional coupling?

Single thermal simulation with fixed electrical parameters

Monte Carlo sampling of temperature-dependent parameters

Iterative multiphysics solution that updates electrical parameters with temperature each step

Independent electrical and thermal solutions combined at the end

#101. [Probability and Statistics] Sum of 8 independent variables, each with mean 18 and std dev 5. Standard deviation of the sum is:

12.67

16.08

11.51

14.14

#102. [Signal Processing] For FIR filter y[n]=x[n]+0.66x[n-1]+0.19x[n-2], with x[0]=6, x[1]=4, x[2]=6, find y[2].

7.76

9.78

11.76

7.89

#103. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.39. Percent overshoot is:

26.432 %

18.608 %

22.811 %

31.923 %

#104. [Electronics] Half-wave rectifier with peak input 14 V, diode drop 0.7 V, RL=455 Ω. Approximate average DC current is:

10.754 mA

9.304 mA

11.249 mA

8.558 mA

#105. [Digital Systems] In unsigned 4-bit arithmetic, adding 6 and 9 sets carry-out flag to:

1

depends on signed interpretation

0

undefined

#106. [Linear Systems] For system y” + 5y’ + 3y = u(t), which statement about stability is true?

Unstable because the natural frequency is too high

Marginally stable with oscillatory response

Stable because all coefficients are positive and roots have negative real parts

Cannot determine without initial conditions

#107. [Electromagnetics] For a long straight conductor carrying 94 A, magnetic flux density at radius 0.062 m is:

0.00e+00 T

3.03e-04 T

0.00e+00 T

#108. [Mathematics] An engineer linearizes a calibration model and obtains equations 6x + 4y = 37 and 4x + 6y = 50. What is x?

0.967

1.100

1.230

0.936

#109. [Engineering Sciences] Cooling air for a power converter has mass flow 0.051 kg/s and specific heat cp=1010 J/(kg·K). With ΔT = 36 K, heat removed is:

1854.4 W

2151.8 W

1514.4 W

2017.4 W

#110. [Control Systems] For characteristic equation s^2 + 3s + 1=0, which range of k ensures stability?

k > 3

k > 0

k < 0

All values of k

ARE YOU READY?

LET’S PRACTICE!

Results

#1. [Computer Networks] Ignoring loss, TCP throughput with receive window 256 kB and RTT 40 ms is approximately:

#2. [Power] Ideal transformer with turns ratio Np:Ns=5:1 feeds load 15 Ω on secondary. Reflected primary impedance is:

#3. [Linear Systems] For a 2nd-order system with damping ratio ζ=0.5 and ωn=11.25 rad/s, estimate 2% settling time.

#4. [Computer Systems and Software] Which data structure gives O(1) average-time lookup for symbol tables while allowing dynamic insertion?

#5. [Circuit Analysis] A branch dissipates 443 W with RMS current 5.59 A. Equivalent resistance is:

#6. [Circuit Analysis] A current source 11 A feeds two parallel resistors 12 Ω and 6 Ω. Node voltage across them is:

#7. [Linear Systems] For G(s)=1/(s+6), unit-step response final value is:

#8. [Properties of Electrical Materials] A 1.2 mm insulation layer withstands 20527 V. The electric field stress is:

#9. [Mathematics] A phasor is V = 6 + j2. What is |V|?

#10. [Power] A balanced 3-phase load consumes 402 kW at 291 V line-line and pf=0.79 lagging. Line current is:

#11. [Mathematics] In a fully connected sensor graph with 11 nodes, how many unique undirected links exist?

#12. [Power] Transformer no-load secondary voltage is 124 V and full-load is 119 V. Voltage regulation is:

#13. [Properties of Electrical Materials] A package heat spreader has k=127.7 W/m·K, area=0.00e+00 m², thickness=0.026 m, ΔT=34 K. Heat flow is:

#14. [Engineering Economics] A retrofit costs $122,356 now and saves $46,074/year for 8 years. At MARR = 8%, NPV is:

#15. [Digital Systems] In unsigned 4-bit arithmetic, adding 1 and 14 sets carry-out flag to:

#16. [Electromagnetics] Transmission line has Z0=63 Ω and load ZL=53 Ω (real). Reflection coefficient Γ is:

#17. [Circuit Analysis] A current source 5 A feeds two parallel resistors 7 Ω and 11 Ω. Node voltage across them is:

#18. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=13, unit-step steady-state error is:

#19. [Signal Processing] For an ideal 16-bit ADC, quantization-limited SQNR is closest to:

#20. [Signal Processing] A tone at 9339 Hz is sampled at fs=10000 Hz. Observed baseband alias frequency is:

#21. [Signal Processing] For y[n]=0.58y[n-1]+(-0.14)y[n-2]+x[n], which is correct?

#22. [Mathematics] In a fully connected sensor graph with 10 nodes, how many unique undirected links exist?

#23. [Circuit Analysis] Node A is connected to 18 V through 3 Ω and to 30 V through 3 Ω. What is node voltage VA?

#24. [Communications] A TDM PCM system multiplexes 18 channels, each sampled at 16000 Hz with 12 bits/sample. Total data rate is:

#25. [Circuit Analysis] An AC source of 148 Vrms drives impedance Z = 12 + j23 Ω. RMS current magnitude is:

#26. [Engineering Economics] For a test fixture: fixed cost $140,736, unit price $91, variable cost $44. Breakeven quantity is:

#27. [Electromagnetics] For a long straight conductor carrying 88 A, magnetic flux density at radius 0.051 m is:

#28. [Electronics] A BJT in active mode has β=121 and base current 136.4 µA. Collector current is closest to:

#29. [Circuit Analysis] A Thevenin source Vth=40 V with Rth=3 Ω feeds RL=22 Ω. Load current is:

#30. [Digital Systems] Pipeline stage has tCQ=1.04 ns, combinational delay=4.48 ns, setup=1.71 ns. Max clock frequency is:

#31. [Electronics] Ideal inverting op-amp with Rin=3 kΩ, Rf=30 kΩ, Vin=0.543 V. Output is:

#32. [Mathematics] Compute the integral ∫_1^3 x^3 dx.

#33. [Circuit Analysis] In an RL step response with V=40 V, R=32 Ω, L=0.383 H, find i(t) at t=0.019 s.

#34. [Electromagnetics] If electric field changes at dE/dt=4.64e+06 V/m·s in a dielectric with permittivity ε=0.00e+00 F/m, displacement current density is:

#35. [Linear Systems] For low-pass H(jω)=1/(1+jωτ) with τ=0.627 s, find |H(jω)| at ω=7 rad/s.

#36. [Properties of Electrical Materials] Estimate skin depth δ for a conductor with σ=2.12e+07 S/m, μr=1, at f=50 Hz.

#37. [Properties of Electrical Materials] A conductor has resistivity 0.00e+00 Ω·m at 20°C and temperature coefficient 0.0033/°C. Estimate resistivity at 78°C.

#38. [Signal Processing] A first-order analog low-pass has cutoff 5000 Hz. At cutoff frequency, output magnitude relative to passband is:

#39. [Digital Systems] Pipeline stage has tCQ=1.89 ns, combinational delay=4.05 ns, setup=0.96 ns. Max clock frequency is:

#40. [Ethics and Professional Practice] On a substation relay upgrade, you identify an ungrounded metallic enclosure that poses a shock hazard. The correct professional action is:

#41. [Electromagnetics] For a lossless medium with εr=2.56 and μr=1.5, intrinsic impedance η is:

#42. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(1.02 s).

#43. [Mathematics] Evaluate Re(e^(j2t)) at t = 0.28 s.

#44. [Circuit Analysis] A Thevenin source Vth=11 V with Rth=3 Ω feeds RL=25 Ω. Load current is:

#45. [Probability and Statistics] Assuming normal process variation with mean 103 and std dev 9, what is the 95th percentile?

#46. [Electronics] Using square-law saturation model Id=0.5k(VGS−VT)^2, find Id for k=0.004 A/V², VGS=3.56 V, VT=0.76 V.

#47. [Mathematics] For first-order decay dy/dt = -4y with y(0)=1, find y(0.8 s).

#48. [Communications] Using Shannon capacity C = B log2(1+SNR), with B=5.8 MHz and linear SNR=50, capacity is:

#49. [Engineering Sciences] A busbar support bracket experiences elastic strain 872 με. Assuming Young’s modulus E = 202.7 GPa, stress is:

#50. [Circuit Analysis] An AC source of 211 Vrms drives impedance Z = 14 + j9 Ω. RMS current magnitude is:

#51. [Control Systems] A loop has crossover ωc=2.3 rad/s and phase margin 58.8°. Which interpretation is correct?

#52. [Mathematics] A phasor is V = 4 + j2. What is |V|?

#53. [Mathematics] For f(t) = t^5 – t^2 + 3t, evaluate df/dt at t = 8.

#54. [Power] A component has reactance 0.17 pu on 50 MVA base (same kV base). On 25 MVA base, reactance is:

#55. [Digital Systems] Pipeline stage has tCQ=2.09 ns, combinational delay=6.4 ns, setup=1.73 ns. Max clock frequency is:

#56. [Communications] In M-ary digital modulation, what is the trade-off when increasing the modulation order M?

#57. [Power] At a 22 kV bus with Thevenin reactance 0.284 Ω (line-line basis), 3-phase bolted fault current is:

#58. [Power] Ideal transformer with turns ratio Np:Ns=3:1 feeds load 23 Ω on secondary. Reflected primary impedance is:

#59. [Electronics] A silicon diode has Vf=0.7 V at 25°C with temperature coefficient −2 mV/°C. Approximate Vf at 70°C is:

#60. [Digital Systems] In unsigned 4-bit arithmetic, adding 12 and 6 sets carry-out flag to:

#61. [Computer Systems and Software] A 32-bit, direct-mapped cache has 512 sets and 128-byte blocks. Tag bits per line are:

#62. [Computer Networks] Ignoring loss, TCP throughput with receive window 64 kB and RTT 20 ms is approximately:

#63. [Computer Systems and Software] Cache hit rate=0.94, hit time=3.1 ns, miss penalty=46.2 ns. AMAT is:

#64. [Circuit Analysis] A branch dissipates 135 W with RMS current 4.68 A. Equivalent resistance is:

#65. [Computer Networks] For IPv4 subnet /22, how many usable host addresses are available?

#66. [Power] A 2-pole induction motor on 60 Hz runs at 3565 rpm. Rotor current frequency is closest to:

#67. [Circuit Analysis] Node A is connected to 29 V through 7 Ω and to 8 V through 3 Ω. What is node voltage VA?

#68. [Probability and Statistics] A lot has independent defect probability 0.03 per board. For 12 boards, what is P(at least 3 defect)?

#69. [Computer Networks] A router has routes 10.2.0.0/16, 10.2.32.0/19, and 10.2.32.128/25. Packet to 10.2.32.200 follows which route?

#70. [Probability and Statistics] A lot has independent defect probability 0.04 per board. For 13 boards, what is P(at least 1 defect)?

#71. [Engineering Economics] A public project has PV of benefits = $215,916 and PV of costs = $150,332. Benefit-cost ratio is:

#72. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=16, unit-step steady-state error is:

#73. [Communications] For M-ary signaling with M=8 and bit rate 50 kb/s, symbol rate is:

#74. [Electronics] An ideal 10-bit ADC with Vref=5.0 V measures Vin=1.509 V. Output code is closest to:

#75. [Ethics and Professional Practice] A colleague asks you to provide a professional reference overstating their experience on power systems projects to help them obtain a contract. The correct action is:

#76. [Digital Systems] In unsigned 4-bit arithmetic, adding 7 and 5 sets carry-out flag to:

#77. [Mathematics] An engineer linearizes a calibration model and obtains equations 2x + 2y = 14 and 4x + 3y = 25. What is x?