Electricity Demystified, 2nd edition

Stan Gibilisco

Explanations for Quiz Answers in Chapter 7

1. In an AC voltage transformer, the primary-to-secondary turns ratio equals the primary-to-secondary RMS voltage ratio. In this example, the RMS primary voltage is exactly twice the RMS secondary voltage, so the primary winding must have exactly twice as many turns as the secondary winding. We're told that the primary has 500 turns, so we can conclude that the secondary has half that many, or 250 turns. The correct choice is C.

2. A full AC cycle contains 360º of phase. If we see a phase shift of 120º, it represents 1/3 of a cycle, because 120º is exactly 1/3 of 360º. The correct choice is C.

3. Before we calculate, let's convert the current to amperes RMS. We're told that it's 335 mA RMS, which equals 0.335 A RMS. To find the power P that the resistor dissipates, we must square the current (in amperes RMS) and then multiply by the resistance (in ohms). We know that the resistor has a value of 47 ohms, so

P = 0.335² x 47
= 5.3 W

The correct choice is A.

4. To find the power P that the resistor dissipates, we must square the voltage (in volts RMS) and then divide by the resistance (in ohms). We're told that the AC voltage across the resistor equals 10.0 V RMS, while the resistor has a value of 100 ohms. Therefore

P = 10.0² / 100
= 1.00 W

The correct choice is B.

5. Recall the formula for energy in terms of voltage, resistance, and time:

Q = (E_RMS)² t / R

where Q represents the total dissipated energy (in watt-hours), E_RMS represents the AC voltage (in volts RMS), t represents the elapsed time (in hours), and R represents the load resistance (in ohms). When we scrutinize this formula, we can see that if we want to double Q by changing only the voltage while all other factors remain the same, we must increase E_RMS by a factor equal to the square root of 2, or approximately 1.41. If we start out with 100 V RMS, we'll have to increase it to approximately 141 V RMS to double the total amount of dissipated energy. The correct choice is A.

6. When two waves have the same frequency and occur 1/2 cycle apart, then they're 180º out of phase. If the waves both have perfect sinusoidal shapes and neither of them has a DC component, then a 180º phase difference produces the same effect, in practice, as phase opposition does. The correct choice is C.

7. When you see lightning and then hear the thunder from the same stroke, count the number of seconds between the stroke and the first audible noise. Divide by 3 to get the distance to the stroke in kilometers. In this case, you're told that the delay equals 9 seconds, so the stroke must be 9/3 or 3 kilometers distant. The correct choice is B.

8. The turns ratio between the primary and the top half of the secondary (connecting to the X terminals) equals 100/20, or 5:1 (an exact value). If we apply 234 V RMS to the primary, then we'll observe 234 / 5, or 46.8 V RMS between the X terminals. The turns ratio between the primary and the entire secondary (connecting to the Y terminals) equals 100/40, or 2.5:1 (again, an exact value). If we apply 234 V RMS to the primary, then we'll get 234 / 2.5, or 93.6 V RMS between the Y terminals. The correct choice is D.

9. When we have two sine waves of the same frequency in phase coincidence, and if neither wave has any DC component, then the peak-to-peak voltage of the composite wave equals the sum of the peak-to-peak voltages of the component waves. In this case, the component waves exhibit 25 V pk-pk and 11 V pk-pk, so the composite wave must have 25 + 11, or 36 V pk-pk. The correct choice is D.

10. The composite wave in the scenario of Question 9 has no DC component, because neither of the component waves have DC components. In that case, the RMS voltage equals approximately 0.3536 times the peak-to-peak voltage. That's 36 x 0.3536, or 13 V RMS (rounded off to two significant digits). The correct choice is A.