milk>試卷(2022/01/18)

# 109 年 - 109 國立臺灣大學_碩士班招生考試_電機工程研究所乙組:電力工程(含電力系統、電機機械、電力電子)#105857

【非選題】
1.

1. Given the 60 Hz, balanced three-phase system shown below, find v (t), (11%) 【非選題】
2.

2. Consider the 60 Hz, 345 KV, completely transposed balanced three phase lines as shown below. The radius of each sub-conductor is 0.9 cm. Find the per phase inductance in H/m and per phase capacitance to neutral in F/m. (11%) 【非選題】
3.

3. Find the radius-and center of the power circle for S = P+ j Q with P as the abscissa (x-axis) and Q as the ordinate (y-axis). (1.1%) 【非選題】
4.4. A round rotor synchronous generator delivers p = 0.8 (real power) at 0.9 power factor lagging to a bus with voltage of 1.0. Assume that the synchronous reactance of the generator is 0.6 and the armature resistance can be neglected. Find the open-circuit voltage of the synchronous generator. (11%)

【非選題】
5.5. A 380V, 10HP, four- pole, 60 Hz, Y- connected three phase induction motor has a full-load slip of 3 percent. Find the synchronous speed of this motor and the rotor speed of this motor at the rated load. (11%)

【非選題】
6.6. A 50 KVA, 2200: 220 V, 60 Hz distribution transformer has a leakage impedance of 0.62 + j 1.02 ohm in the high voltage winding and 0.006 + j 0.01 ohm in the low voltage winding. At rated voltage and frequency, the admittance of the shunt branch accounting for the exciting current is 0.003 - j 0.02 mho when viewed from the low voltage side. Draw the equivalent circuit referred to the high voltage side. (11%)

【非選題】
7.
 True or False [20 pts]

【題組】 7a. A sine wave and triangle wave have the same (positive and negative) amplitude. The RMS value is the same for both waveforms. [2 pts]

【非選題】
8.【題組】7b. Average power is equivalent to real power, and RMS power is equivalent to reactive power. [2 pts]

【非選題】
9.【題組】7c. For a periodic waveform, the average valuc will always be the same or lower than the RMS value. [2 pts]

【非選題】
10.【題組】7d. For a periodic waveform, the maximum theoretical value for total harmonic distortion (THD) is 1. [2 pts]

【非選題】
11.【題組】

7e. In the square-wave shown below, the amplitude of the fundamental' component is larger than A. [2 pts] 【非選題】
12.【題組】7f. The total harmonic distortion (THD) of a pure square wave (50% duty) is the same regardless of frequency and amplitude. [2 pts]

【非選題】
13.【題組】7g. For a diode rectification circuit with a resistive and inductive (R-L) load, the instantaneous output voltage (over the load) may become negative. [2 pts]

【非選題】
14.【題組】7h.Th. For an ideal buck converter operating in disco ontinuous conduction m node (DCM), the input- to-output voltage relationship does not depend on the output capacitor value C. [2 pts]

【非選題】
15.【題組】7i. A half-bridge inverter creates 2 different voltages over the output, while the full-bridge inverter creates 4 different voltages over the output. [2 pts]

【非選題】
16.【題組】7j. For a flyback converter, ideally, the coupled inductor has zero magnetizing inductance. [2 pts]

【非選題】
17.

【題組】 8a. Name two converter topologies with galvanic isolation between input and output. [2 pt].

【非選題】
18.【題組】8b. Explain why galvanic isolation is sometimes required and give a specific example. [2 pts]

【非選題】
19.【題組】8c. A buck-boost converter is operating in discontinuous conduction mode (DCM). The inductor value is doubled, but switching frequeney, duty ratio, and average inductor current remain the same. Which mode does the new circuit operate in? Explain your answer. [2pts]

【非選題】
20.

 Rectifier circuit analysis: [8 pts]
For the circuit below, the output resistor is R = 1Ωand output voltage source is . The input is a sine wave with RMS value and period T = 1 s. Assume all diodes have a voltage drop of VD = 0.5 V and the circuit is operating in steady state. 【題組】9a. Find . the maximum value of the input voltage vi [1 pts]

【非選題】
21.【題組】9b. Find . the maximum value of the output voltage vo. [I pts]

【非選題】
22.【題組】9c. Caiculate the average output voltage value, ＜vo> . [2 pts]

【非選題】
23.【題組】9d. Calculate the average power through the resistor, PR. [2 pts]

【非選題】
24.【題組】9e. Next, a capacitor is added over the output (vo). Which of the previous values (parts a to d) will change? [2 pts]

### 懸賞詳解

#### 國一歷史下第一次

【題組四】下表為台灣於 1905-1940 年各產業生產品價值統計表，請根據表中資料回答下列問題： 【題組】33.從表中各產業產值的統計分析，日治初期總�...