Chapter 9 : Alternating Current Basics (Gibilisco)

A degree of phase represents 1/360 cycle. In a complete cycle, there are 360 degrees. Therefore, when measuring phase, each degree represents 1/360th of a full cycle.

The period of an AC wave refers to the time it takes for one complete cycle of the wave to occur. In other words, it is the duration between two consecutive points in the wave that have the same position and direction. The frequency, on the other hand, represents the number of complete cycles that occur in one second. Since the period is the time for one cycle and the frequency is the number of cycles per second, they are inversely related. Therefore, the period can be calculated by dividing 1 by the frequency.

The length of time between a point in one cycle and the same point in the next cycle of an AC wave is known as the period. It represents the time taken for one complete cycle of the wave to occur. Frequency, on the other hand, refers to the number of cycles that occur in a given time period. Magnitude refers to the size or amplitude of the wave, while polarity refers to the direction of the wave.

Frequency is the only variable that can vary with AC but not with DC. AC stands for alternating current, which constantly changes direction, resulting in a fluctuating frequency. In contrast, DC, or direct current, flows in only one direction and has a fixed frequency. Power, voltage, and magnitude can all vary in both AC and DC systems.

AC (alternating current) is easier to transform one voltage to another compared to DC (direct current). This is because AC voltage can be easily stepped up or stepped down using transformers, which are not compatible with DC voltage. Transformers work on the principle of electromagnetic induction, which relies on the changing magnetic field produced by alternating current. Therefore, AC is preferred in utility applications as it allows for efficient voltage transformation, enabling the transmission and distribution of electricity at different voltage levels.

In a perfect sine wave, the pk-pk value refers to the peak-to-peak amplitude, which is the difference between the highest and lowest points of the wave. Since a sine wave oscillates above and below its zero line, the pk-pk value will be equal to twice the peak value, as it includes both the positive and negative peaks. Therefore, the correct answer is "Twice the peak value."

The type of natural energy source used does not affect the power output available from a particular AC generator. The power output of a generator is determined by factors such as the strength of the magnet, the number of turns in the coil, and the speed of rotation of the coil or magnet. The type of natural energy source used, such as wind, water, or steam, only determines how the generator is powered, but it does not directly affect the power output.

When two waves have the same frequency and amplitude but opposite phase, they are said to be in phase opposition. In this case, the peaks of one wave align with the troughs of the other wave, resulting in complete cancellation. As a result, the composite wave has an amplitude of zero, meaning it is effectively nonexistent.

The angular frequency of a signal is equal to the frequency multiplied by 2π. In this case, the frequency is given as 1770 Hz. Multiplying this by 2π gives us an angular frequency of 11,120 radians per second.

The correct answer is "Has three waves, all of the same magnitude." In a three-phase AC system, there are three separate waveforms, each representing a different phase. These waveforms are all of the same magnitude, meaning they have the same amplitude or peak value. This is a characteristic of three-phase AC power, where the three waves work together to provide a more efficient and balanced distribution of electrical power.

The sixth harmonic of an AC wave is obtained by multiplying the fundamental frequency by 6. Since the period of the wave is 0.001 seconds, the frequency can be calculated by taking the reciprocal of the period, which is 1/0.001 = 1000 Hz. Multiplying this by 6 gives us 6000 Hz, which is equivalent to 6 kHz. Therefore, the correct answer is 6kHz.

When two waves have the same frequency, the phase difference can be calculated by converting the fraction of a cycle into degrees. In this case, the phase difference is 1/20 cycle. To convert this to degrees, we use the fact that 1 cycle is equal to 360 degrees. Therefore, 1/20 cycle is equal to (1/20) * 360 = 18 degrees. So, the phase difference in degrees is 18.

In a 117V utility circuit, the peak voltage is 165V. The peak voltage refers to the maximum voltage reached during one cycle of an alternating current waveform. In this case, the peak voltage is calculated by multiplying the RMS voltage (117V) by the square root of 2 (√2 ≈ 1.414). Therefore, 117V * 1.414 ≈ 165V.

A pure ac signal, having just one frequency component, would appear as a single pip on a spectrum analyzer. This is because a single pip represents a specific frequency without any harmonics or additional components. It indicates a clear and distinct signal at a particular frequency, without any variations or distortions.

In the given situation, the pk-pk voltage refers to the peak-to-peak voltage, which is the difference between the maximum positive and maximum negative voltage values in an alternating current waveform. Out of the given options, the pk-pk voltage is 331 V, indicating that the waveform reaches a maximum positive voltage of 331 V and a maximum negative voltage of -331 V.

If a 175 V dc source were connected in series with the utility mains from a standard wall outlet, the result would be pulsating dc. This is because the utility mains provide alternating current (ac), which constantly changes direction. When the dc source is connected in series, it would create a combination of dc and ac. However, since the dc source is not constant and fluctuates, the resulting current would be pulsating dc.

A triangular frequency has equal rise and decay rates. This means that the frequency increases and decreases at the same rate, resulting in a symmetrical triangular shape. This is different from options that mention fast rise time and slow decay time, or slow rise time and fast decay time, which indicate an asymmetrical shape. Additionally, the option that says the frequency rises and falls abruptly does not describe a triangular frequency, as it suggests an instantaneous change rather than a gradual increase and decrease.

In a 117V utility circuit, the peak-to-peak voltage refers to the total variation between the highest and lowest voltage points. The peak voltage is the maximum voltage reached in one direction, while the peak-to-peak voltage is twice that value. Therefore, if the peak-to-peak voltage is 331V, it means that the highest voltage point is 165.5V above the average voltage (117V) and the lowest voltage point is 165.5V below the average voltage.

When two waves have the same frequency and the same phase, they are said to be in phase. In this case, the peaks and troughs of the waves align perfectly, resulting in constructive interference. The composite wave formed by the combination of these waves will have a magnitude equal to the sum of the magnitudes of the two original waves. This is because the peaks of one wave will add to the peaks of the other wave, and the troughs will add to the troughs, resulting in a larger amplitude. Therefore, the correct answer is that the composite wave has a magnitude equal to the sum of the two originals.

When a 45Vdc battery is connected in series with the 117V utility mains, the peak voltage will be the sum of the peak voltages of the battery and the utility mains. The peak voltage of the battery is +45V and -45V, while the peak voltage of the utility mains is +117V and -117V. Therefore, the total peak voltage will be +45V + +117V = +162V and -45V + -117V = -72V. Therefore, the correct answer is +162V and -72V.