110年 - 110台灣聯合大學系統_碩士班招生考試_電機類:電磁學#105808

1. (5%) A cylindrical capacitor consists of an inner conductor of radius a, and an outer conductor whose inner radius is b. The space between the conductors is filled with a dielectric of permittivity ε. The length of the capacitor is L. The capacitance of this this capacitor is
  (A) C=2πεL/ln(b/a) (B) C=2πεL/In(a/b)(C)C=2πεL/In(ab) (D) none of the mentioned

2. (5%) Four capacitance C₁=1(μF), C₂=2(μF), C₃=3(μF), C₄=4(μF), are connected as following figure. The total equivalent capacitance is
(A) 5.5 (μF) (B) 10 (μF) (C) 1.9 (μF) (D) none of the mentioned

3. (5%) The Poisson's equation determines the relation of electric potential V, electric field, and charge density p. The correct Poisson's equation in simple medium is (A)(B)(C)(D)

4. (5%) The parallel-plate capacitor is shown in following figure. The electric field is
(A)(B)(C)(D)

5. (5%) Two conductors in a simple lossy dielectric medium with ε&σ is shown in following figure. The RC product is (A) 1/εσ (B) σ/ε (C) εσ (D) ε/σ

6. (5%) The fundamental postulates for magnetostatics state/infer: (A)(B) (C)(D) None mentioned.

8. (5%) The derivation of the Biot-Savart Law requires Coulomb gauge. Coulomb gauge states: (A) (B)(C) (D) None mentioned.

10. (5%) If we define β as the phase constant (also called the propagation constant), the group velocity is  (A)(B)(C) (D) None of the above. 

11.(5%) Wedefine . Which one of the following expressions is the correct Poynting's theorem? (A) (B)솔(C)(D) None of the above.

12. (5%) The E-field of a uniform plane wave propagating in a dielectric medium is given by . Assume this dielectric medium is lossless and non-magnetic (σ =0, μ_r= 1). Which of the following statements is correct? (A) The dielectric constantε_r of this medium is 4. (B) This plane wave is linearly polarized. (C) The wavelength in the dielectric medium is 6 m. (D) None of the above.

13. (5%) The instantaneous expression for the electric field of a uniform plane wave in vacuum is given by .We denote the intrinsic impedance of the free space by no. The magnetic field is (A)(B)(C) (D) None of the above.

14. (5%) Assume there is a short end transmission line with infinite length as the figure shown below. The distributed parameters of the transmission line are R=0.057(Ω/m) ,L=0.25(μH/m) ,G=22.8(HS/m) ,c=0.1 (nF/m). Please evaluate the input impedance at 1 GHz.
(A) 0.057 2 (B) 2500 Ω (C) 50 Ω(D) None of the above.

15. (5%) A matching network composed of an ideal shunt capacitor C_m transfers a load impedance of Zx to input impedance of 50Ω, as the figure shown below. Please. indicate which one is the possible changing procedure of reflection coefficient on a Smith Chart (Z-Chart) from load to input port while matching? (A)   (B)(C) (D)None of the above.

16. (5%) Given a 75-Ω characteristic impedance transmission line with length larger than the wavelength related to the sinusoidal input signal. Please evaluate the magnitude of the reflection coefficient | Γ | on this transmission line terminated by an 50Ω load impedance. (A) 0.385, (B)2.25, (C)0.2, (D)None of the above.

17. (5%) A rectangular pulse V_g(t) of an amplitude 15 (V) and a duration 1(μs) is applied through a series resistance R_g of 25(Ω) to the input terminals of a 50(Ω) Jossless transmission line. Given the speed of EM wave in this line is 1.5 x 10m⁸/ s. The line is 400 (m) long and short-circuited at the far end, as the figure shown below. Determine the voltage at the midpoint of the line at the time of 2 μs.
(A) 10V, (B)-10V, (C)OV, (D)None of the above.

18. (5%) In an air-filled metallic rectangular waveguide, which of the following will be the most likely answer for the fundamental mode? (A) (B) (C) (D) TEM