Teach Yourself Electricity and Electronics, 5th edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 14 |

1. If we have a theoretically ideal circuit containing no resistance and a finite, nonzero capacitive reactance, then the current leads the voltage by 90º. Because the reactance is capacitive rather than inductive, we say, by convention, that the phase angle is negative, so it equals -90º in this case. The correct answer is (d). |

2. When we have a circuit in which the resistance and the absolute value of the
capacitive reactance are equal and nonzero, the current leads the voltage by 45º. That
means the phase angle equals -45º. We can figure this out from the formula for the phase
angle in an RC circuit:
R)where R represents the resistance (in the same
units as the capacitive reactance). We know that in this particular case, the ratio X / _{C
}R equals -1:1, so
The correct answer is (c). |

3. In a circuit containing pure resistance with no capacitive reactance, the current and the voltage coincide in phase (assuming that the circuit has no inductive reactance). Therefore, the phase angle equals 0º. The correct choice is (b). |

4. Let's remember the formula for capacitive reactance in terms of frequency and
capacitance. If the frequency of an AC source equals f (in hertz) and the
capacitance of a component equals C (in farads), then we can calculate the
capacitive reactance X (in ohms) using the approximate formula_{C}
fC)This formula also works for values of
= -125 ohms The correct choice is (a). |

5. We can use the formula from the solution to Question 4 to solve this problem, but
we'll have to do a little algebra to get the answer. We're told that C = 0.0100 µF
and X = -75.0 ohms. If we plug these values directly into the formula_{C}
fC)and then solve for -75.0 = -1 / (6.2832 x When we negate both sides of this equation, we get 75.0 = 1 / (6.2832 x Multiplying through by 75.0 Dividing through by 75.0, we get the answer as |

6. As the ratio X / _{C }R increases negatively without limit, the phase angle, which equals the Arctangent of the ratio X / _{C }R, approaches -90º.
The correct choice is (a). |

7. If we increase the spacing between the plates of a capacitor while leaving all
other factors unchanged, the capacitance decreases. From the formula for capacitive
reactance X in terms of the frequency _{C}f and the capacitance C,
assuming a constant value of f and a diminishing value of C, we can see that
X increases negatively. The correct answer is therefore (a)._{C} |

8. Let's use the formula for capacitive reactance, inputting the value of f in
megahertz and the value of C in microfarads:
fC)We have to convert both the capacitance and the frequency to the
proper units in order for this formula to work here. We know that
= -10,000 ohms When we convert this result to kilohms and then round it off to three
significant figures (the extent of the input accuracy), we get |

9. If we double the frequency, we double the denominator in the formula. Therefore, the capacitive reactance drops to 1/2 its previous value (negatively, of course). The correct answer is (b). |

10. We can use the formula for capacitive reactance here. However, as in the solution
to Question 5, we must work through some algebra. We're told that X =
-433 ohms and _{C}f = 433 kHz. If we convert to megahertz, we get f = 0.433 MHz,
so our answer will come out in microfarads. (We can convert to picofarads, the units that
appear in all the answer choices, after we've finished our calculations.) Let's plug X
= -433 and _{C}f = 0.433 into the formula
fC)and then solve for -433 = -1 / (6.2832 x 0.433 x When we negate both sides, we get 433 = 1 / (6.2832 x 0.433 x Multiplying through by 433 Dividing through by 433, we obtain |

11. To solve this problem, we must use the formula for phase angle in terms of
capacitive reactance X and resistance _{C}R. Once again, that
formula is
R)where R = 100 ohms. Therefore
The correct choice is (b). |

12. If we double the capacitive reactance (negatively) while leaving all other factors
constant in the above-described scenario, we cause the ratio X / _{C }R
to increase (negatively) to -150/100, or -1.5. The Arctangent of -1.5 equals approximately
-56º, which is larger negatively than the previous angle. The correct choice is therefore
(a). |

13. We must solve this problem in two steps. First, let's find the capacitive
reactance, inputting the value of f in megahertz and the value of C in
microfarads:
fC)When we convert the frequency of 770 kHz to megahertz, we get
= -4.3977 ohms which rounds off to -4.40 ohms. We know that the resistance has a value of
R)= Arctan (-4.40/4.40) = Arctan -1 = -45º The correct choice is (c). |

14. If we double the resistance while leaving all other factors constant in the
scenario of Question 13, we cut the ratio X / _{C }R in half
(negatively). That causes the Arctangent to decrease negatively (get closer to 0º). The
correct choice is (d). |

15. If we short out the resistor in the situation of Question 13, we're left with only the capacitance. Therefore, the current will lead the voltage by 90º for all practical purposes. The phase angle will equal essentially -90º. The correct answer is (a). |

16. If we double the frequency and change nothing else in the situation of Question
13, we cut the capacitive reactance in half (negatively), so we cut the ratio X / _{C }R
in half (negatively). That causes the Arctangent to decrease negatively (get closer to
0º). The correct answer is (d). |

17. We're told that C = 680 pF and X = -680 ohms. The
capacitance is equivalent to 0.000680 µF. If we plug these values directly into the
formula_{C}
fC)we can solve for -680 = -1 / (6.2832 x When we negate both sides of this equation, we get 680 = 1 / (6.2832 x Multiplying through by 680 Dividing through by 680, we get the answer as |

18. We're told that X = -870 ohms and _{C}f = 4.78 MHz. We can
plug these values directly into the formula
fC)and then solve for -870 = -1 / (6.2832 x 4.78 x When we negate both sides, we get 870 = 1 / (6.2832 x 4.78 x Multiplying through by 870 Dividing through by 870, we obtain |

19. We can see from Fig. 14-13 that the capacitive reactance equals approximately -82
ohms and the resistance equals approximately 29 ohms. Therefore, the ratio X / _{C }R
equals approximately -82/29, or -2.83. The correct answer is (a). |

20. We can find the phase angle by taking the Arctangent of X / _{C }R.
In this case, that ratio equals approximately -2.83. Using a calculator to find the
Arctangent of -2.83, we get approximately -71º. The correct choice is (d). |