FE ELECTRICAL – FIFTH SIMULATION

#1. [Power] Ideal transformer with turns ratio Np:Ns=2:1 feeds load 30 Ω on secondary. Reflected primary impedance is:

7.5 Ω

8.85 Ω

6.75 Ω

9.375 Ω

#2. [Linear Systems] For low-pass H(jω)=1/(1+jωτ) with τ=0.397 s, find |H(jω)| at ω=6 rad/s.

0.318

0.387

0.291

0.426

#3. [Mathematics] For first-order decay dy/dt = -2y with y(0)=1, find y(0.77 s).

0.214

0.268

0.161

0.193

#4. [Power] Transformer no-load secondary voltage is 126 V and full-load is 120 V. Voltage regulation is:

5.9 %

5 %

6.25 %

5.5 %

#5. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 17 and x + 4y = 10. What is x?

6.608

4.2

5.6

5.04

#6. [Linear Systems] For system y” + 6y’ + 2y = u(t), which statement about stability is true?

Unstable because input is a step function

Unstable unless b > a^2

Marginally stable because second-order systems always oscillate

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

#7. [Probability and Statistics] Assuming normal process variation with mean 84 and std dev 9, what is the 95th percentile?

98.805

74.104

81.02

108.7

#8. [Electronics] A BJT in active mode has β=117 and base current 40.3 µA. Collector current is closest to:

3.54 mA

4.72 mA

5.192 mA

3.87 mA

#9. [Ethics and Professional Practice] On a hospital emergency feeder project, you still have access to proprietary firmware from a former employer that could accelerate this project to avoid liquidated damages. According to professional practice expectations, what is the MOST appropriate action?

Accept the risk if no incident has yet occurred

Transfer responsibility to the contractor and continue work

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

Proceed temporarily and document the issue only at project closeout

#10. [Properties of Electrical Materials] A conductor has resistivity 1.76e-08 Ω·m at 20°C and temperature coefficient 0.0040/°C. Estimate resistivity at 104°C.

2.04e-08 Ω·m

1.71e-08 Ω·m

2.67e-08 Ω·m

2.35e-08 Ω·m

#11. [Engineering Sciences] A vibration-sensitive electronics tray is modeled as an underdamped SDOF system with m=2.24 kg, damping ratio ζ=0.28, and natural frequency ωn=22.83 rad/s. What is the damped natural frequency ωd?

21.945 rad/s

16.459 rad/s

27.431 rad/s

19.75 rad/s

#12. [Digital Systems] Pipeline stage has tCQ=2.17 ns, combinational delay=5.45 ns, setup=1.11 ns. Max clock frequency is:

126.0 MHz

114.6 MHz

103.1 MHz

93.931 MHz

#13. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(0.76 s).

0.012

0.013

0.01

0.009

#14. [Properties of Electrical Materials] Estimate skin depth δ for a conductor with σ=3.66e+07 S/m, μr=50, at f=1000 Hz.

4.65e-04 m

3.35e-04 m

3.05e-04 m

3.72e-04 m

#15. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(1.34 s).

3.25e-04

2.44e-04

3.58e-04

2.93e-04

#16. [Electronics] A BJT in active mode has β=139 and base current 87.7 µA. Collector current is closest to:

13.405 mA

12.186 mA

15.233 mA

14.38 mA

#17. [Mathematics] An engineer linearizes a calibration model and obtains equations 4x + 2y = 12 and x + 6y = 7. What is x?

2.497

2.741

3.045

3.807

#18. [Computer Systems and Software] In interrupt-driven embedded systems, which design choice best reduces worst-case interrupt latency?

Move all ISR work into polling loops

Use deeply nested interrupts without masking policy

Disable caches during interrupt handling

Keep critical sections short and prioritize ISRs with bounded execution

#19. [Circuit Analysis] Node A is connected to 15 V through 4 Ω and to 6 V through 3 Ω. What is node voltage Va (no load)?

9.857 V

12.321 V

8.871 V

11.631 V

#20. [Digital Systems] Pipeline stage has tCQ=0.95 ns, combinational delay=7.03 ns, setup=1.16 ns. Max clock frequency is:

129.0 MHz

109.4 MHz

120.3 MHz

89.676 MHz

#21. [Circuit Analysis] Node A is connected to 26 V through 6 Ω and to 6 V through 6 Ω. What is node voltage Va (no load)?

20 V

18.88 V

16 V

12 V

#22. [Engineering Economics] Compute capital recovery (EUAC) for P=$184,831, S=$34,349, n=6 years, i=8%.

28945.6 USD/yr

31769.5 USD/yr

41653.4 USD/yr

35299.5 USD/yr

#23. [Digital Systems] In unsigned 4-bit arithmetic, adding 8 and 3 sets carry-out flag to:

0

1

undefined

depends on signed interpretation

#24. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 14 and x + 5y = 7. What is x?

3.722

4.538

3.404

4.992

#25. [Digital Systems] Pipeline stage has tCQ=2.44 ns, combinational delay=7.33 ns, setup=2.14 ns. Max clock frequency is:

105.0 MHz

92.389 MHz

83.99 MHz

99.108 MHz

#26. [Properties of Electrical Materials] A package heat spreader has k=162.1 W/m·K, area=2.93e-04 m², thickness=0.038 m, and ΔT=23 K. Conduction heat rate is:

23.686 W

21.664 W

31.774 W

28.886 W

#27. [Digital Systems] In unsigned 4-bit arithmetic, adding 0 and 14 sets carry-out flag to:

0

1

depends on signed interpretation

undefined

#28. [Computer Systems and Software] Worst-case comparisons for binary search on sorted array of size 1024 are closest to:

11

10

7.5

8.2

#29. [Computer Systems and Software] Which testing strategy is best for validating boundary behavior of ADC register parsing logic?

Integration testing only after deployment

Random testing only, without deterministic edge cases

Boundary value analysis with explicit min/max and off-by-one cases

Code formatting checks as primary validation

#30. [Computer Networks] Ignoring loss, TCP throughput with receive window 64 kB and RTT 40 ms is approximately:

11.796 Mb/s

10.748 Mb/s

16.384 Mb/s

13.107 Mb/s

#31. [Control Systems] For characteristic equation s^2 + 4s + 1=0, which range of k ensures stability?

k > 0

k < 0

k = 0 only

k > 16 only

#32. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.44. Percent overshoot is closest to:

19.351 %

21.501 %

23.651 %

16.125 %

#33. [Power] At a 26 kV bus with Thevenin reactance 0.263 Ω (line-line basis), 3-phase bolted fault current is approximately:

51366.3 A

62781.1 A

57073.7 A

46800.4 A

#34. [Circuit Analysis] A branch dissipates 509 W with RMS current 6.01 A. Equivalent resistance is:

11.555 Ω

16.628 Ω

10.569 Ω

14.092 Ω

#35. [Engineering Sciences] A vibration-sensitive electronics tray is modeled as an underdamped SDOF system with m=3.90 kg, damping ratio ζ=0.19, and natural frequency ωn=27.17 rad/s. What is the damped natural frequency ωd?

26.695 rad/s

24.025 rad/s

29.364 rad/s

31.5 rad/s

#36. [Computer Networks] Ignoring loss, TCP throughput with receive window 128 kB and RTT 40 ms is approximately:

23.593 Mb/s

26.214 Mb/s

28.836 Mb/s

30.933 Mb/s

#37. [Engineering Sciences] Cooling air for a power converter has mass flow 0.145 kg/s and specific heat cp=905.3 J/kg·K. If temperature rise across the cabinet is 35.1 K, required heat removal rate is:

3450.8 W

5061.1 W

4601.0 W

5429.2 W

#38. [Power] A component has reactance 0.158 pu on 50 MVA base (same kV base). On 75 MVA base, pu reactance is:

0.194 pu

0.279 pu

0.261 pu

0.237 pu

#39. [Probability and Statistics] Assuming normal process variation with mean 101 and std dev 10, what is the 95th percentile?

117.5

146.8

138.6

96.309

#40. [Engineering Sciences] A busbar support bracket experiences elastic strain 999 με. Assuming Young’s modulus E=204.4 GPa, normal stress is:

167.4 MPa

204.2 MPa

240.9 MPa

224.6 MPa

#41. [Ethics and Professional Practice] On a campus EV-charger expansion, a client requests you to seal calculations prepared by a subcontractor you did not supervise to avoid liquidated damages. According to professional practice expectations, what is the MOST appropriate action?

Transfer responsibility to the contractor and continue work

Proceed temporarily and document the issue only at project closeout

Decline to seal until you have responsible charge and sufficient independent verification

Rely on schedule urgency as justification for delayed correction

#42. [Mathematics] A phasor is V = 5 + j7. What is |V|?

9.463

7.054

10.151

8.602

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

0

1

depends on signed interpretation

undefined

#44. [Electromagnetics] For a long straight conductor carrying 77 A, magnetic flux density at radius 0.094 m is:

2.06e-04 T

1.65e-04 T

1.35e-04 T

1.81e-04 T

#45. [Power] A balanced 3-phase load consumes 331 kW at 216 V line-line and pf=0.92 lagging. Line current is:

866.8 A

1059.4 A

963.1 A

1136.5 A

#46. [Electromagnetics] Transmission line has Z0=45 Ω and load ZL=92 Ω (real). Reflection coefficient Γ at load is:

0.257

0.429

0.281

0.343

#47. [Engineering Economics] A retrofit costs $244,331 now and saves $46,339/year for 10 years. At MARR = 8%, what is NPV?

66607.5 USD

54618.1 USD

78596.8 USD

73268.2 USD

#48. [Probability and Statistics] A lot has independent defect probability 0.04 per board. For 12 boards, what is P(at least 2 defect)?

0.089

0.081

0.096

0.066

#49. [Circuit Analysis] A branch dissipates 865 W with RMS current 4.82 A. Equivalent resistance is:

46.491 Ω

27.895 Ω

37.193 Ω

33.474 Ω

#50. [Communications] For an AM wave, envelope Vmax=9.08 and Vmin=0.77. Modulation index m is:

0.692

1.054

0.759

0.843

#51. [Mathematics] Compute the integral ∫_0^7 x^2 dx.

114.3

134.9

85.75

142.9

#52. [Probability and Statistics] A lot has independent defect probability 0.02 per board. For 8 boards, what is P(at least 2 defect)?

0.011

0.01

0.008

0.013

#53. [Signal Processing] For y[n]=0.27y[n-1]+(-0.37)y[n-2]+x[n], which is correct?

Always stable because coefficients are finite

Always unstable for second-order IIR filters

BIBO stable (dominant poles inside unit circle)

Cannot determine stability without x[n]

#54. [Circuit Analysis] In an RL step response with V=40 V, R=31 Ω, L=0.345 H, find i(t) at t=0.025 s.

1.275 A

0.87 A

1.449 A

1.16 A

#55. [Electromagnetics] For a lossless medium with εr=2.25 and μr=1, intrinsic impedance η is:

251.3 Ω

188.5 Ω

226.2 Ω

276.5 Ω

#56. [Mathematics] For first-order decay dy/dt = -2y with y(0)=1, find y(0.64 s).

0.227

0.277

0.249

0.305

#57. [Digital Systems] Pipeline stage has tCQ=2.41 ns, combinational delay=4.84 ns, setup=1.32 ns. Max clock frequency is:

87.476 MHz

128.3 MHz

116.6 MHz

137.6 MHz

#58. [Electronics] Ideal inverting op-amp with Rin=8 kΩ, Rf=95 kΩ, Vin=0.560 V. Output is:

-7.31 V

-5.981 V

-7.842 V

-6.646 V

#59. [Signal Processing] For y[n]=0.53y[n-1]+(-0.26)y[n-2]+x[n], which is correct?

BIBO stable (dominant poles inside unit circle)

Always unstable for second-order IIR filters

Cannot determine stability without x[n]

Always stable because coefficients are finite

#60. [Engineering Economics] A retrofit costs $230,024 now and saves $42,662/year for 8 years. At MARR = 12%, what is NPV?

-16285.1 USD

-18094.6 USD

-13570.9 USD

-22618.2 USD

#61. [Circuit Analysis] A current source 4 A feeds two parallel resistors 9 Ω and 6 Ω. Node voltage across the pair is:

12.96 V

15.84 V

14.4 V

16.992 V

#62. [Mathematics] A phasor is V = 8 + j5. What is |V|?

11.792

8.491

10.377

9.434

#63. [Computer Systems and Software] A 32-bit, direct-mapped cache has 64 sets and 32-byte blocks. Tag bits per line are:

21

23.1

17.22

24.78

#64. [Signal Processing] A first-order analog low-pass has cutoff 2000 Hz. At cutoff frequency, output magnitude relative to passband is:

-6 dB (half amplitude)

-3 dB (approximately 0.707 of passband amplitude)

0 dB (unity)

+3 dB (resonant peak)

#65. [Probability and Statistics] Assuming normal process variation with mean 86 and std dev 15, what is the 95th percentile?

130.6

99.608

110.7

90.753

#66. [Computer Networks] For IPv4 subnet /24, how many usable host addresses are available?

279.4

299.7

208.3

254

#67. [Circuit Analysis] An AC source of 188 Vrms drives impedance Z = 9 + j17 Ω. RMS current magnitude is:

9.774 A

10.751 A

8.014 A

11.533 A

#68. [Engineering Economics] What present value is equivalent to a future replacement cost of $74,641 in 7 years at 11%?

32356.3 USD

35951.5 USD

42422.7 USD

26963.6 USD

#69. [Circuit Analysis] A current source 9 A feeds two parallel resistors 4 Ω and 9 Ω. Node voltage across the pair is:

31.154 V

29.409 V

24.923 V

27.415 V

#70. [Circuit Analysis] Node A is connected to 16 V through 5 Ω and to 15 V through 7 Ω. What is node voltage Va (no load)?

17.142 V

14.025 V

11.688 V

15.583 V

#71. [Electronics] Ideal inverting op-amp with Rin=15 kΩ, Rf=83 kΩ, Vin=0.320 V. Output is:

-1.77 V

-2.212 V

-1.451 V

-2.088 V

#72. [Ethics and Professional Practice] On a hospital emergency feeder project, field staff are bypassing arc-flash PPE requirements to recover schedule to maintain outage schedule commitments. According to professional practice expectations, what is the MOST appropriate action?

Rely on schedule urgency as justification for delayed correction

Suspend the task and enforce required safety controls before restarting

Transfer responsibility to the contractor and continue work

Proceed temporarily and document the issue only at project closeout

#73. [Linear Systems] For G(s)=1/(s+3), unit-step response final value is:

0.225

0.205

0.25

0.275

#74. [Communications] Using Shannon capacity C = B log2(1+SNR), with B=4.0 MHz and linear SNR=20, capacity is:

19.326 Mb/s

14.407 Mb/s

20.732 Mb/s

17.569 Mb/s

#75. [Circuit Analysis] A Thevenin source Vth=31 V with Rth=7 Ω feeds RL=8 Ω. Load current is:

2.067 A

1.86 A

2.439 A

2.583 A

#76. [Communications] A TDM PCM system multiplexes 19 channels, each sampled at 16000 Hz with 10 bits/sample. Aggregate data rate is:

2.736 Mb/s

3.04 Mb/s

3.344 Mb/s

3.8 Mb/s

#77. [Mathematics] A phasor is V = 4 + j6. What is |V|?

9.014

5.913

7.211

6.49

#78. [Computer Systems and Software] Cache hit rate=0.98, hit time=2.75 ns, miss penalty=59.8 ns. AMAT is:

5.213 ns

4.921 ns

4.588 ns

4.171 ns

#79. [Control Systems] For unity-feedback type-0 system with open-loop DC gain K=9, unit-step steady-state error is:

0.1

0.082

0.075

0.09

#80. [Electronics] Half-wave rectifier with peak input 14 V, diode drop 0.7 V, RL=239 Ω. Approximate average load current:

14.525 mA

17.713 mA

22.142 mA

13.285 mA

#81. [Communications] For an AM wave, envelope Vmax=9.27 and Vmin=2.92. Modulation index m is:

0.428

0.469

0.521

0.652

#82. [Ethics and Professional Practice] On a campus EV-charger expansion, a supplier offers premium event tickets while your team is evaluating bids to maintain outage schedule commitments. According to professional practice expectations, what is the MOST appropriate action?

Proceed temporarily and document the issue only at project closeout

Implement a short-term workaround and postpone formal disclosure

Transfer responsibility to the contractor and continue work

Decline the gift and keep procurement decisions objective and fully documented

#83. [Control Systems] A loop has crossover ωc=29.2 rad/s and phase margin 46.5°. Which interpretation is best?

Positive phase margin indicates closed-loop stability with moderate robustness

System is unstable because crossover frequency is finite

Phase margin does not relate to time-domain overshoot

System is marginally stable only if gain margin is exactly 0 dB

#84. [Properties of Electrical Materials] A conductor has resistivity 1.84e-08 Ω·m at 20°C and temperature coefficient 0.0041/°C. Estimate resistivity at 90°C.

1.73e-08 Ω·m

2.37e-08 Ω·m

2.06e-08 Ω·m

2.70e-08 Ω·m

#85. [Power] Ideal transformer with turns ratio Np:Ns=2:1 feeds load 16 Ω on secondary. Reflected primary impedance is:

5 Ω

4.4 Ω

4 Ω

4.72 Ω

#86. [Mathematics] A phasor is V = 9 + j4. What is |V|?

11.622

12.311

7.387

9.849

#87. [Mathematics] For first-order decay dy/dt = -3y with y(0)=1, find y(1.05 s).

0.043

0.039

0.054

0.032

#88. [Signal Processing] A tone at 7100 Hz is sampled at fs=12000 Hz. Observed baseband alias frequency is:

4410 Hz

4900 Hz

3675 Hz

5390 Hz

#89. [Mathematics] For first-order decay dy/dt = -5y with y(0)=1, find y(1.11 s).

0.281

0.003

0.004

0.005

#90. [Control Systems] A loop has crossover ωc=12.5 rad/s and phase margin 51.7°. Which interpretation is best?

System is marginally stable only if gain margin is exactly 0 dB

System is unstable because crossover frequency is finite

Phase margin does not relate to time-domain overshoot

Positive phase margin indicates closed-loop stability with moderate robustness

#91. [Power] A balanced 3-phase load consumes 262 kW at 479 V line-line and pf=0.95 lagging. Line current is:

332.5 A

392.3 A

272.6 A

365.7 A

#92. [Linear Systems] For a 2nd-order system with damping ratio ζ=0.69 and ωn=7.53 rad/s, estimate 2% settling time.

0.627 s

0.765 s

0.688 s

0.841 s

#93. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.75. Percent overshoot is closest to:

2.447 %

3.731 %

2.984 %

2.238 %

#94. [Circuit Analysis] A Thevenin source Vth=34 V with Rth=7 Ω feeds RL=18 Ω. Load current is:

1.496 A

1.7 A

1.115 A

1.36 A

#95. [Electronics] An ideal 12-bit ADC with Vref=5.0 V measures Vin=4.166 V. Output code is closest to:

3412

4026.2

2559

2797.8

#96. [Electromagnetics] If electric field changes at dE/dt=5.10e+06 V/m·s in a dielectric with permittivity 3.54e-11 F/m, displacement current density Jd is:

2.13e-04 A/m²

1.81e-04 A/m²

1.99e-04 A/m²

1.35e-04 A/m²

#97. [Control Systems] A loop has crossover ωc=25.8 rad/s and phase margin 57.8°. Which interpretation is best?

Phase margin does not relate to time-domain overshoot

System is unstable because crossover frequency is finite

Positive phase margin indicates closed-loop stability with moderate robustness

System is marginally stable only if gain margin is exactly 0 dB

#98. [Signal Processing] For FIR filter y[n]=x[n]+0.5x[n-1]+0.25x[n-2], with x[0]=5, x[1]=3, x[2]=5, find y[2].

9.688

6.355

6.975

7.75

#99. [Circuit Analysis] An AC source of 213 Vrms drives impedance Z = 16 + j11 Ω. RMS current magnitude is:

10.97 A

13.713 A

12.067 A

9.873 A

#100. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 16 and x + 5y = 11. What is x?

4.289

5.231

6.172

5.754

#101. [Engineering Sciences] A dielectric coolant (ρ=981.5 kg/m³, μ=8.06e-04 Pa·s) flows at 1.43 m/s through a pipe of diameter 0.045 m. Reynolds number is closest to:

58919.0

70702.7

78558.6

98198.3

#102. [Power] A 4-pole induction motor on 60 Hz runs at 1787 rpm. Rotor current frequency is closest to:

0.542 Hz

0.477 Hz

0.325 Hz

0.433 Hz

#103. [Circuit Analysis] In an RL step response with V=36 V, R=11 Ω, L=0.101 H, find i(t) at t=0.015 s.

2.642 A

3.303 A

2.907 A

2.378 A

#104. [Electromagnetics] Transmission line has Z0=59 Ω and load ZL=29 Ω (real). Reflection coefficient Γ at load is:

-0.375

-0.341

-0.426

-0.28

#105. [Ethics and Professional Practice] On a data-center UPS modernization, you identify an ungrounded metallic enclosure in a temporary power panel to maintain outage schedule commitments. According to professional practice expectations, what is the MOST appropriate action?

Proceed temporarily and document the issue only at project closeout

Rely on schedule urgency as justification for delayed correction

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

Implement a short-term workaround and postpone formal disclosure

#106. [Mathematics] An engineer linearizes a calibration model and obtains equations 5x + 2y = 10 and x + 3y = 5. What is x?

2.308

1.385

2.031

1.846

#107. [Electronics] Using square-law saturation model Id=0.5k(VGS−VT)^2, find Id for k=0.0026 A/V², VGS=3.44 V, VT=1.43 V.

5.193 mA

5.713 mA

6.492 mA

3.895 mA

#108. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 8 and x + 6y = 4. What is x?

2.876

2.438

3.047

1.999

#109. [Engineering Economics] For a test fixture: fixed cost $112,813, unit price $86, variable cost $49. Break-even quantity is closest to:

2286.8 units

3597.8 units

3049 units

3353.9 units

#110. [Linear Systems] A transfer function has poles at s=-4.38 and s=-10.64. Dominant time constant is closest to:

0.286 s

0.206 s

0.27 s

0.229 s

ARE YOU READY?

LET’S PRACTICE!

Results

#1. [Power] Ideal transformer with turns ratio Np:Ns=2:1 feeds load 30 Ω on secondary. Reflected primary impedance is:

#2. [Linear Systems] For low-pass H(jω)=1/(1+jωτ) with τ=0.397 s, find |H(jω)| at ω=6 rad/s.

#3. [Mathematics] For first-order decay dy/dt = -2y with y(0)=1, find y(0.77 s).

#4. [Power] Transformer no-load secondary voltage is 126 V and full-load is 120 V. Voltage regulation is:

#5. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 17 and x + 4y = 10. What is x?

#6. [Linear Systems] For system y” + 6y’ + 2y = u(t), which statement about stability is true?

#7. [Probability and Statistics] Assuming normal process variation with mean 84 and std dev 9, what is the 95th percentile?

#8. [Electronics] A BJT in active mode has β=117 and base current 40.3 µA. Collector current is closest to:

#9. [Ethics and Professional Practice] On a hospital emergency feeder project, you still have access to proprietary firmware from a former employer that could accelerate this project to avoid liquidated damages. According to professional practice expectations, what is the MOST appropriate action?

#10. [Properties of Electrical Materials] A conductor has resistivity 1.76e-08 Ω·m at 20°C and temperature coefficient 0.0040/°C. Estimate resistivity at 104°C.

#11. [Engineering Sciences] A vibration-sensitive electronics tray is modeled as an underdamped SDOF system with m=2.24 kg, damping ratio ζ=0.28, and natural frequency ωn=22.83 rad/s. What is the damped natural frequency ωd?

#12. [Digital Systems] Pipeline stage has tCQ=2.17 ns, combinational delay=5.45 ns, setup=1.11 ns. Max clock frequency is:

#13. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(0.76 s).

#14. [Properties of Electrical Materials] Estimate skin depth δ for a conductor with σ=3.66e+07 S/m, μr=50, at f=1000 Hz.

#15. [Mathematics] For first-order decay dy/dt = -6y with y(0)=1, find y(1.34 s).

#16. [Electronics] A BJT in active mode has β=139 and base current 87.7 µA. Collector current is closest to:

#17. [Mathematics] An engineer linearizes a calibration model and obtains equations 4x + 2y = 12 and x + 6y = 7. What is x?

#18. [Computer Systems and Software] In interrupt-driven embedded systems, which design choice best reduces worst-case interrupt latency?

#19. [Circuit Analysis] Node A is connected to 15 V through 4 Ω and to 6 V through 3 Ω. What is node voltage Va (no load)?

#20. [Digital Systems] Pipeline stage has tCQ=0.95 ns, combinational delay=7.03 ns, setup=1.16 ns. Max clock frequency is:

#21. [Circuit Analysis] Node A is connected to 26 V through 6 Ω and to 6 V through 6 Ω. What is node voltage Va (no load)?

#22. [Engineering Economics] Compute capital recovery (EUAC) for P=$184,831, S=$34,349, n=6 years, i=8%.

#23. [Digital Systems] In unsigned 4-bit arithmetic, adding 8 and 3 sets carry-out flag to:

#24. [Mathematics] An engineer linearizes a calibration model and obtains equations 3x + 2y = 14 and x + 5y = 7. What is x?

#25. [Digital Systems] Pipeline stage has tCQ=2.44 ns, combinational delay=7.33 ns, setup=2.14 ns. Max clock frequency is:

#26. [Properties of Electrical Materials] A package heat spreader has k=162.1 W/m·K, area=2.93e-04 m², thickness=0.038 m, and ΔT=23 K. Conduction heat rate is:

#27. [Digital Systems] In unsigned 4-bit arithmetic, adding 0 and 14 sets carry-out flag to:

#28. [Computer Systems and Software] Worst-case comparisons for binary search on sorted array of size 1024 are closest to:

#29. [Computer Systems and Software] Which testing strategy is best for validating boundary behavior of ADC register parsing logic?

#30. [Computer Networks] Ignoring loss, TCP throughput with receive window 64 kB and RTT 40 ms is approximately:

#31. [Control Systems] For characteristic equation s^2 + 4s + 1=0, which range of k ensures stability?

#32. [Control Systems] A standard 2nd-order closed-loop system has damping ratio ζ=0.44. Percent overshoot is closest to:

#33. [Power] At a 26 kV bus with Thevenin reactance 0.263 Ω (line-line basis), 3-phase bolted fault current is approximately:

#34. [Circuit Analysis] A branch dissipates 509 W with RMS current 6.01 A. Equivalent resistance is:

#35. [Engineering Sciences] A vibration-sensitive electronics tray is modeled as an underdamped SDOF system with m=3.90 kg, damping ratio ζ=0.19, and natural frequency ωn=27.17 rad/s. What is the damped natural frequency ωd?

#36. [Computer Networks] Ignoring loss, TCP throughput with receive window 128 kB and RTT 40 ms is approximately:

#37. [Engineering Sciences] Cooling air for a power converter has mass flow 0.145 kg/s and specific heat cp=905.3 J/kg·K. If temperature rise across the cabinet is 35.1 K, required heat removal rate is:

#38. [Power] A component has reactance 0.158 pu on 50 MVA base (same kV base). On 75 MVA base, pu reactance is:

#39. [Probability and Statistics] Assuming normal process variation with mean 101 and std dev 10, what is the 95th percentile?

#40. [Engineering Sciences] A busbar support bracket experiences elastic strain 999 με. Assuming Young’s modulus E=204.4 GPa, normal stress is:

#41. [Ethics and Professional Practice] On a campus EV-charger expansion, a client requests you to seal calculations prepared by a subcontractor you did not supervise to avoid liquidated damages. According to professional practice expectations, what is the MOST appropriate action?

#42. [Mathematics] A phasor is V = 5 + j7. What is |V|?

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

#44. [Electromagnetics] For a long straight conductor carrying 77 A, magnetic flux density at radius 0.094 m is:

#45. [Power] A balanced 3-phase load consumes 331 kW at 216 V line-line and pf=0.92 lagging. Line current is:

#46. [Electromagnetics] Transmission line has Z0=45 Ω and load ZL=92 Ω (real). Reflection coefficient Γ at load is:

#47. [Engineering Economics] A retrofit costs $244,331 now and saves $46,339/year for 10 years. At MARR = 8%, what is NPV?

#48. [Probability and Statistics] A lot has independent defect probability 0.04 per board. For 12 boards, what is P(at least 2 defect)?

#49. [Circuit Analysis] A branch dissipates 865 W with RMS current 4.82 A. Equivalent resistance is:

#50. [Communications] For an AM wave, envelope Vmax=9.08 and Vmin=0.77. Modulation index m is:

#51. [Mathematics] Compute the integral ∫_0^7 x^2 dx.

#52. [Probability and Statistics] A lot has independent defect probability 0.02 per board. For 8 boards, what is P(at least 2 defect)?

#53. [Signal Processing] For y[n]=0.27y[n-1]+(-0.37)y[n-2]+x[n], which is correct?

#54. [Circuit Analysis] In an RL step response with V=40 V, R=31 Ω, L=0.345 H, find i(t) at t=0.025 s.

#55. [Electromagnetics] For a lossless medium with εr=2.25 and μr=1, intrinsic impedance η is:

#56. [Mathematics] For first-order decay dy/dt = -2y with y(0)=1, find y(0.64 s).

#57. [Digital Systems] Pipeline stage has tCQ=2.41 ns, combinational delay=4.84 ns, setup=1.32 ns. Max clock frequency is:

#58. [Electronics] Ideal inverting op-amp with Rin=8 kΩ, Rf=95 kΩ, Vin=0.560 V. Output is:

#59. [Signal Processing] For y[n]=0.53y[n-1]+(-0.26)y[n-2]+x[n], which is correct?

#60. [Engineering Economics] A retrofit costs $230,024 now and saves $42,662/year for 8 years. At MARR = 12%, what is NPV?

#61. [Circuit Analysis] A current source 4 A feeds two parallel resistors 9 Ω and 6 Ω. Node voltage across the pair is:

#62. [Mathematics] A phasor is V = 8 + j5. What is |V|?

#63. [Computer Systems and Software] A 32-bit, direct-mapped cache has 64 sets and 32-byte blocks. Tag bits per line are:

#64. [Signal Processing] A first-order analog low-pass has cutoff 2000 Hz. At cutoff frequency, output magnitude relative to passband is:

#65. [Probability and Statistics] Assuming normal process variation with mean 86 and std dev 15, what is the 95th percentile?

#66. [Computer Networks] For IPv4 subnet /24, how many usable host addresses are available?

#67. [Circuit Analysis] An AC source of 188 Vrms drives impedance Z = 9 + j17 Ω. RMS current magnitude is:

#68. [Engineering Economics] What present value is equivalent to a future replacement cost of $74,641 in 7 years at 11%?

#69. [Circuit Analysis] A current source 9 A feeds two parallel resistors 4 Ω and 9 Ω. Node voltage across the pair is:

#70. [Circuit Analysis] Node A is connected to 16 V through 5 Ω and to 15 V through 7 Ω. What is node voltage Va (no load)?

#71. [Electronics] Ideal inverting op-amp with Rin=15 kΩ, Rf=83 kΩ, Vin=0.320 V. Output is:

#72. [Ethics and Professional Practice] On a hospital emergency feeder project, field staff are bypassing arc-flash PPE requirements to recover schedule to maintain outage schedule commitments. According to professional practice expectations, what is the MOST appropriate action?

#73. [Linear Systems] For G(s)=1/(s+3), unit-step response final value is:

#74. [Communications] Using Shannon capacity C = B log2(1+SNR), with B=4.0 MHz and linear SNR=20, capacity is:

#75. [Circuit Analysis] A Thevenin source Vth=31 V with Rth=7 Ω feeds RL=8 Ω. Load current is:

#76. [Communications] A TDM PCM system multiplexes 19 channels, each sampled at 16000 Hz with 10 bits/sample. Aggregate data rate is:

#77. [Mathematics] A phasor is V = 4 + j6. What is |V|?