6. 下列有關三相同步發電機並聯運轉的敘述何者錯誤？
(A)兩機必須相序才可並聯。
(B)調整兩機的轉速可以作有效功率的轉移。
(C)調整兩機的激磁電流可以作無效功率的轉移。
(D)兩機電壓稍異時，並聯會產生有效功率轉移的整步電流。

7. 功率因數為1 的三相同步電動機在電壓固定且無載時，若將激磁電流降低，則會發生下列何種狀況？ (A)功率因數變小且成為電感性。 (B)電樞電流下降。 (C)感應電勢上升。 (D)產生的電樞反應包含交磁與去磁現象。

8. 下列對於特殊電機的敘述何者正確？ (A)步進電動機的轉動角度與輸入脈波數成反比。 (B)交流伺服電動機為開迴路控制系統(Open-Loop Control System)。 (C)外轉子型的直流無刷電動機，其定子為永久磁鐵。 (D)增加電源頻率可以提升同步線性電動機的移動速度。

1. Given the vector function A = 3x²eˣx̂ + x³y³ŷ. Please evaluate ∮ around the rectangular area from P₁(0,0,0), to P₂(3,0,0), to P₃(3,4,0), to P₄(0,4,0), and back to P₁(0,0,0). (A) 0 (B) 864 (C) 1728 (D) None of the above

2. A point charge Q is placed at the original point inside a hollow sphere, as shown in the figure below. The material of the hollow sphere is perfect electrical conductor (PEC). The total outward flux of the electric field intensity over the closed surface S (∮) is: (A) 0 (B) Q/ε₀ (C) -Q/ε₀ (D) None of the above

3. A lossy dielectrics (conductivity = σ, absolute permittivity = ε) is placed between two parallel perfect metal plates, as shown in the figure below. The areas of the metal plates are A (A = W×L). The distance between the metal plates is d and is much smaller than the length or width of the metal plates (d ＜＜ W and d ＜＜ L). Applying a voltage V₀ between the perfect metal plates, please evaluate the ratio between the storage energy and dissipated power of this structure (Estorage/Pdiss). (A) (B) (C) (D) None of the above

4. Given two problems (Problem A, and Problem B) in the free space shown below. Assume the solution of the scalar electrical potential distribution of Problem A is Vₐ, and the solution of the scalar electrical potential distribution of Problem B is Vb. Please evaluate: [Vₐ(x,0,z) - V_b(x,0,z)] ∇[Vₐ(x,0,z) - Vb(x,0,z)] · ŷ dxdz (A)(B) (C) 0 (D) None of the above

5. A positive point charge Q is at the center of a spherical dielectric sphere with radius of R. The material of this dielectric sphere is simple medium with relative permittivity of εᵣ. Please evaluate the equivalent polarization surface charge density (or bound surface charge density) of the surface of the sphere. (A) 0 (B) (C) (D) None of the above

6. A charge is moving in a magnetic field. Which of the following statements is true? (A) The magnetic field does no work on the charge only if the magnetic field is static. (B) The magnetic field does no work on the charge only if the magnetic field is time-dependent. (C) The magnetic field never does work on the charge. (D) None of the above.

7. The mutual inductance between two coils is M. Which of the following statements is true? (A) When the currents of two coils are doubled, their mutual inductance is halved. (B) The mutual inductance is changed when the materials of the coils are changed. (C) Mutual inductance depends on the geometry of the coils, specifically their shape, size, and the relative positions of their windings. (D) None of the above.

8. A solenoid has n turns per unit length. The self-inductance of a solenoid is proportional to (A) n (B) n² (C) n³ (D) None of the above

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