CRAC Class C (2025) — Questions 911–920

U1157. For a capacitor whose capacitive reactance is measured as some number of ohms at a certain frequency, if the frequency is increased N-fold, its capacitive reactance will:

一个电容器，在某一频率下测得容抗为若干欧姆。如果频率提高N倍，其容抗将：

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容抗 (capacitive reactance) is Xc = 1/(2πfC). It is inversely proportional to frequency, so raising f by a factor N reduces Xc to 1/N of its original value. A is correct; B reverses the relation, and C/D wrongly insert 2π.

U1158. The component capable of storing energy in the form of a magnetic field is:

能够以磁场形式储存能量的元件是：

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An 电感 (inductor) stores energy in a magnetic field built up by current through its coil. A resistor dissipates energy; a capacitor stores electric-field energy; an electromagnet is a specialized coil but the generic energy-storage component named here is the inductor.

U1159. If a sinusoidal AC voltage is applied across a coil, the magnitude of the current flowing through the coil:

若在线圈两端施加一个正弦交流电压，则流过线圈的电流的大小：

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For an inductor I = V/(ωL) = V/(2πfL). The current magnitude is directly proportional to the applied voltage and inversely proportional to the inductance L, so A is correct.

U1160. For an inductive coil whose inductive reactance is measured as some ohms at a certain frequency, if the frequency is increased N-fold, its inductive reactance will:

一个电感线圈，在某一频率下测得感抗为若干欧姆。如果频率提高N倍，其感抗将：

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感抗 (inductive reactance) is XL = 2πfL, directly proportional to frequency. Raising f by N makes XL N times larger. A is correct; B is the capacitive behavior, and C/D wrongly insert 2π.

U1161. The term "phase difference" is typically used to describe the lead or lag relationship in time between two periodic signals of the same frequency. Which of the following descriptions of the phase difference of periodic signals is correct? (Choose all that apply.)

术语“相位差”通常用来描述频率相同的两个周期信号在时间上的超前或滞后关系。关于周期信号的相位差，以下描述正确的是：

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相位差 (phase difference): 0/360°/even multiples of 180° = in- phase (同相); odd multiples of 180° = anti-phase (反相) (A). A 90° difference is quadrature (正交) (B). Reactive elements (L/C) make voltage and current out of phase (C). Superposition of same-frequency waves gives constructive (in-phase) or destructive (anti-phase) interference (D). All four are correct.

U1162. Connecting two sinusoidal voltage sources of equal amplitude and with a phase difference of 360° in series yields:

将两个幅度相等，相位相差360°的正弦电压源串联，所得结果是：

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A 360° phase difference is equivalent to 0° — the two equal sources are in phase, so series addition doubles the amplitude while keeping the same phase. A is correct; B is the 180° (anti- phase) result, C/D are wrong.

U1163. Connecting two sinusoidal voltage sources of equal amplitude and with a phase difference of 180° in series yields:

将两个幅度相等，相位相差180°的正弦电压源串联，所得结果是：

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Two equal, 180°-apart (anti-phase) sources in series cancel completely, giving 0 V (A). This is the destructive-interference case; B is the in-phase result.

U1164. Connecting two sinusoidal voltage sources of equal amplitude and with a phase difference of 90° in series yields:

将两个幅度相等，相位相差90°的正弦电压源串联，所得结果是：

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Two equal sources 90° apart add by the Pythagorean theorem: resultant amplitude = √(V²+V²) = 1.41 V (√2). The result lies exactly halfway in phase, i.e. 45° from each. A is correct.

U1165. When a sinusoidal AC voltage is applied across a capacitor, the current through it is a sinusoidal AC current. The phase of this current:

在电容器两端施加正弦交流电压，则流过其中的电流是正弦交流电流。该电流的相位：

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In a capacitor the current leads the voltage by 90° (电流超前电压90°). This follows from I = C·dV/dt. A is correct; an inductor is the opposite (current lags).

U1166. If a sinusoidal AC current flows through a capacitor, the voltage across it is a sinusoidal AC voltage. The phase of this voltage:

若正弦交流电流流过电容器，则其两端的电压是正弦交流电压。该电压的相位：

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This is the same capacitor relationship viewed from the other side: since current leads voltage by 90°, the voltage lags the current by 90°. A is correct and consistent with U1165.