Physics Demystified, 2nd edition |

Stan Gibilisco |

Explanations for Quiz Answers in Chapter 10 |

1. The complex-impedance vector for a pure
inductance always points straight up in the resistance-reactance
(RX) half-plane along the inductive-reactance
(X) axis, as long as the inductance and frequency are both
nonzero. The complex-impedance vector for a pure capacitance always points
straight down along the capacitive-reactance (_{L}X) axis, as
long as the frequency and capacitance are both nonzero. Therefore, the
vectors for a pure inductance and a pure capacitance always point in
opposite directions in the _{C}RX half-plane. The correct choice is B. |

2. In order to determine the complex-number impedance of an inductor, we must know the frequency, and we must also know the amount of internal resistance (if any) that the component has. We haven't been given either of those two parameters, so we can't calculate an answer here. The correct choice is D, "We need more information to determine it." |

3. The schematic diagram of Fig. 10-13 shows two
pairs of series-connected capacitors wired in parallel with each
other. All four of the capacitors have the same value; let's call it
C. The capacitance of the upper pair of
series-connected components equals C/2; the capacitance of
the lower pair also equals C/2. When we connect these two series
combinations in parallel with each other, we get 2 x (C/2) =
C. The capacitance of this so-called two-by-two
series-parallel matrix is the same as the capacitance of any one of
the four components taken alone. The correct choice is B. |

4. Let's recall the formula for capacitive reactance in terms of
capacitance and frequency. If the capacitance equals
f C)^{-1}= -1 / (6.2832 f C)When we examine this formula, we can see that if we double
the value of X is negative. So, when we say that the value becomes
1/2 as great, we mean that it becomes 1/2 as great _{C}negatively.) |

5. A complex-number impedance figure of 50 +
j0 indicates no reactance whatsoever. The component in question
must therefore exhibit a pure resistance of 50 ohms at the specified frequency (in
this case 75 MHz). The correct choice is C. |

6. For any fixed value of inductance, the
inductive reactance varies directly in proportion to the AC frequency.
The reactance value X always equals a positive
number of ohms (as compared with negative ohmic values for capacitive
reactances). If we pass extremely low-frequency AC through an
inductor made from perfectly conducting wire (so that it has no resistance
at all), we'll observe an extremely small, positive reactance. The correct
choice is C._{L} |

7. For any fixed capacitance, the capacitive reactance varies inversely
in proportion to the negative of the AC frequency. The reactance
X always equals a negative number of ohms. If we pass
extremely low-frequency AC through a capacitor made from perfectly conducting
plates separated by dry air (an excellent dielectric medium), we'll observe
an extremely large, negative reactance. The correct choice is A.
_{C} |

8. Once again, let's recall that for any fixed inductance, the reactance varies in direct proportion to the frequency of applied AC. If we reduce the frequency of an AC signal passing through a component having a constant inductance, the reactance goes down, telling us that the component exhibits diminishing opposition to the AC. The correct choice is A. |

9. If we insert a high-permeability ferromagnetic
core inside an inductor that contains mostly air to begin with, we'll
increase the inductance a lot. At a fixed AC frequency, the inductive
reactance X of a coil varies in direct proportion to its
inductance. Therefore, the addition of the ferromagnetic core will cause
_{L}X to increase dramatically. The correct choice is A._{L} |

10. This question asks us to start
with a fixed capacitor in a vacuum, and then insert
a sample of material with a dielectric constant of 1.5 between the
plates. This action will increase the capacitance. At a fixed AC
frequency, we'll observe a reactance
figure that decreases in the negative sense.
When a number decreases negatively, its value remains
negative but gets closer to zero. The correct choice is therefore
B. |