Training Electrical Engineering Placement Test Practice — Electrical Engineering
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Placement Test Practice — Electrical Engineering

25 min Electrical Engineering

Placement Test Practice — Electrical Engineering

These problems cover circuit analysis, AC phasors, transfer functions, poles and zeros, and Laplace transforms.

Practice Test — 25 Questions

1. Three resistors 10 Ω, 15 Ω, 30 Ω in parallel. Find $R_{\text{eq}}$.
2. A 24 V source drives a series combination of 8 Ω and 4 Ω. Find the power dissipated in the 8 Ω resistor.
3. Find the Thévenin voltage across terminals A-B if $V_s = 30$ V, $R_1 = 10\,\Omega$, $R_2 = 20\,\Omega$ (voltage divider).
4. An RL series circuit: $R = 50\,\Omega$, $L = 0.2$ H, $f = 60$ Hz. Find $|Z|$.
5. Find the resonant frequency of $L = 100$ mH, $C = 10\,\mu$F.
6. At resonance in a series RLC, what is the impedance if $R = 10\,\Omega$?
7. Convert $170\sin(377t + 30°)$ V to phasor form.
8. Find $V_{\text{rms}}$ for $v(t) = 100\sin(\omega t)$ V.
9. A load draws 5 A at PF = 0.8 from 240 V. Find the real power.
10. Find the poles of $H(s) = \dfrac{5}{s^2 + 4s + 13}$.
11. Is the system in #10 stable?
12. Find the zeros of $H(s) = \dfrac{s^2 - 4}{s^2 + 3s + 2}$.
13. Find $\mathcal{L}\{5e^{-3t}\sin(4t)\}$.
14. Find $\mathcal{L}^{-1}\left\{\dfrac{6}{s(s+3)}\right\}$.
15. Final value theorem: $\lim_{s \to 0} s \cdot \dfrac{20}{s(s+4)} = ?$
16. An RC circuit $R = 2$ kΩ, $C = 0.5\,\mu$F. Find the time constant.
17. The step response of the RC circuit in #16 reaches what percentage after one time constant?
18. A capacitor of 100 μF has 50 V across it. Find the stored energy.
19. An inductor of 0.5 H carries 3 A. Find the stored energy.
20. Superposition: if $I_1 = 2$ A due to source 1 alone, and $I_2 = -0.5$ A due to source 2 alone, find the total current.
21. Norton equivalent: if $V_{th} = 12$ V and $R_{th} = 4\,\Omega$, find $I_N$ and $R_N$.
22. $Z_C$ at $\omega = 500$ rad/s for $C = 20\,\mu$F. Find $|Z_C|$.
23. Max power transfer occurs when $R_L = R_{th}$. If $V_{th} = 10$ V, $R_{th} = 5\,\Omega$, find max power to $R_L$.
24. A second-order system has $\zeta = 0.707$, $\omega_n = 10$ rad/s. Find the poles.
25. Find the transfer function of a system with poles at $s = -2, -5$ and DC gain of 1.
Show Answer Key

1. $1/R = 1/10+1/15+1/30 = 6/30 = 1/5$; $R_{eq} = 5\,\Omega$

2. $I = 24/12 = 2$ A; $P = 2^2 \times 8 = 32$ W

3. $V_{th} = 30 \times 20/30 = 20$ V

4. $X_L = 2\pi(60)(0.2) = 75.4\,\Omega$; $|Z| = \sqrt{2500+5685} = 90.4\,\Omega$

5. $f_0 = 1/(2\pi\sqrt{0.1 \times 10^{-5}}) = 159.2$ Hz

6. $Z = R = 10\,\Omega$

7. $\mathbf{V} = (170/\sqrt{2})\angle 30° = 120.2\angle 30°$ V rms, or $170\angle 30°$ peak phasor

8. $V_{\text{rms}} = 100/\sqrt{2} = 70.7$ V

9. $P = 240 \times 5 \times 0.8 = 960$ W

10. $s = (-4 \pm \sqrt{16-52})/2 = -2 \pm 3j$

11. Real parts $= -2 < 0$ → stable

12. $s^2 - 4 = (s-2)(s+2) = 0$; zeros at $s = 2$ and $s = -2$

13. $\frac{5 \cdot 4}{(s+3)^2 + 16} = \frac{20}{s^2+6s+25}$

14. $2(1 - e^{-3t})$

15. $20/4 = 5$

16. $\tau = RC = 2000 \times 0.5 \times 10^{-6} = 10^{-3}$ s $= 1$ ms

17. $63.2\%$

18. $E = \frac{1}{2}CV^2 = 0.5 \times 10^{-4} \times 2500 = 0.125$ J

19. $E = \frac{1}{2}LI^2 = 0.5 \times 0.5 \times 9 = 2.25$ J

20. $I = 2 + (-0.5) = 1.5$ A

21. $I_N = V_{th}/R_{th} = 3$ A; $R_N = R_{th} = 4\,\Omega$

22. $|Z_C| = 1/(500 \times 20 \times 10^{-6}) = 100\,\Omega$

23. $P_{\max} = V_{th}^2/(4R_{th}) = 100/20 = 5$ W

24. $s = -\omega_n\zeta \pm \omega_n\sqrt{\zeta^2-1}$. Since $\zeta < 1$: $s = -7.07 \pm j7.07$

25. $H(s) = \frac{K}{(s+2)(s+5)}$; DC gain: $H(0) = K/10 = 1$ → $K=10$; $H(s) = \frac{10}{(s+2)(s+5)}$

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