Download Exercises – Chapter 12

Exercises – Chapter 12
1. If a very small piece of material contains only 10,000 electrons and those electrons have as little energy as possible,
how many different levels do they occupy in that material?
E.1
5000 levels.
2. If electrons had four different internal states that could be distinguished from one another, how many electrons
could occupy the same level without violating the Pauli exclusion principle?
E.2
Four electrons could then occupy the same level.
E.2
The Pauli exclusion principle only prevents indistinguishable Fermi particles from occupying the same
level. With four different distinguishable electrons, a level can hold four electrons.
3. If electrons were not Fermi particles, any number of them could occupy a particular level. How would these
electrons tend to arrange themselves among the levels in an object?
E.3
All in lowest energy level.
4. If electrons were not Fermi particles (Exercise 3), would there still be a distinction between metals and insulators?
Explain your answer.
E.4
No. All of the electrons could settle into the lowest levels in an any material and there would be no Pauli
exclusion principle effects to prevent them from shifting between levels in response to electric fields.
5. Thermal energy can shift some of the electrons in a hot semiconductor from valence levels to conduction levels.
What effect do these shifts have on the semiconductor’s ability to conduct electricity?
E.5
They will increase the semiconductor’s electrical conductivity.
6. Why do semiconductor devices often self-destruct when they are overheated?
E.6
At elevated temperatures, thermal energy is sufficient to shift electrons between valence and conduction
levels. The semiconductors become electrically conducting and undesirable, destructive currents can flow
through them.
7. Is the p-type half of a p-n junction electrically neutral, positive, or negative?
E.7
The p-type half has a negative net charge.
8. In which direction does the electric field point in the middle of a p-n junction?
E.8
The electric field points from the n-type half toward the p-type half.
9. Two capacitors are identical except that one has a thinner insulating layer than the other. If the two capacitors are
storing the same amount of separated electric charge, which one will have the larger voltage difference between its
plates?
E.9
The one with the thicker insulating layer.
10. Dynamic memory stores bits as the presence or absence of separated charge on tiny capacitors. It takes energy to
produce separated charge, and a computer that minimizes this energy will use less electric power. Why does making the
insulating layers of the memory capacitors very thin reduce the energy it takes to store each bit in them?
E.10 The closer the two plates of the capacitor are to one another, the smaller the voltage difference between the
plates when they contain a certain amount of separated charge and the less energy that separated charge
has.
11. Suppose a battery is transferring positive charges from one plate of a capacitor to the other. Why does the work that
the battery does in transferring a charge increase slightly with every transfer?
E.11 The voltage difference between the plates increases with each transfer, so the energy required to complete
the subsequent transfer is greater.
E.11 As the amount of separated charge increases, so does the voltage difference between the capacitor's two
plates. With an ever-increasing voltage rise required for each charge it transfers, the battery must do an
increasing amount of work with each transfer.
12. A charged capacitor resembles a battery in that both can supply electric power. However, as the capacitor delivers
its power, the voltage of the current it provides decreases. Why?
E.12 The voltage difference between the capacitor’s plates is proportional to the amount of separated charge it
contains. As the capacitor uses up its separated charge, that voltage difference decreases.
13. We combine the three decimal digits 6, 3, and 1 to form 631 in order to represent the number 631. What does the 6
in 631 mean? What are there 6 of?
E.13 There are 6 hundreds.
14. We combine the three binary bits 1, 0, and 1 to form 101 in order to represent the number 5. What does the
leftmost 1 in 101 mean? What is there 1 of?
E.14 The left-most bit in the binary expression 101 refers to the presence of one "4" in the number being
represented.
E.14 The expression 101 indicates that the number contains one "4" and one "1", for a total of 5. The binary
expression 101 thus represents the number 5.
15. What numbers do the two binary bytes 11011011 and 01010101 represent?
E.15 219 and 85.
16. How is the number 165 represented in binary?
E.16 The number 165 is represented by the binary expression 10100101.
17. Why are there no 2’s in the binary representation of a number? (In other words, why isn’t 1101121 a valid binary
representation?)
E.17 Instead of reporting 2 twos, the binary representation should report it as 1 four, the next higher power of
two.
18. For convenience, hexadecimal (powers of 16) is often used in place of binary. The traditional symbols used to
represent hexadecimal digits are 0–9 and A–F. In hexadecimal, 10 represents the number 16. Show that one
hexadecimal digit can substitute perfectly for four binary digits.
E.18 The numbers 0 through 15 can be represented by 4 binary digits (0000 through 1111) Those same
numbers can also be represented by 1 hexadecimal digit (0 through F). It’s thus possible to represent each
hexadecimal digit by 4 binary digits or vice versa.
19. The gate of a MOSFET is separated from the channel by a fantastically thin insulating layer. This layer is easily
punctured by static electricity, yet the manufacturers continue to use thin layers. Why would thickening the insulating
layer spoil the MOSFET’s ability to respond to charge on its gate?
E.19 The gate’s charge must be very near the channel so that it can attract opposite charge and draw that charge
into the channel.
20. In an n-channel MOSFET, the source and drain are connected by a thin strip of p-type semiconductor. Why is this
device labeled as having an n-channel rather than a p-channel?
E.20 The strip of chemically p-type semiconductor becomes effectively n-type when extra electrons are drawn
into it by nearby positive charge on its gate.
21. A MOSFET doesn’t change instantly from a perfect insulator to a perfect conductor as you vary the charge on its
gate. With intermediate amounts of charge on its gate, the MOSFET acts as a resistor with a moderate electrical
resistance. This flexibility allows the MOSFET to control the amount of current flowing in a circuit. Explain why a
MOSFET becomes warm as it controls that current.
E.21 When current experiences a voltage drop as it flows through a MOSFET, some of its energy is converted
into thermal energy.
22. The tiny MOSFETs that are used to move charge onto and off the capacitors in dynamic memory are so small that
they’re never very good conductors. Why do their modest electrical resistances lengthen the time it takes to store or
retrieve charge from the memory capacitors?
E.22 With the MOSFETs barely conducting current, it takes a significant amount of time for the charge on the
capacitors to pass through those MOSFETs.
23. Why does the effect described in Exercise 22 limit the speed with which a computer can store or retrieve bits from
its dynamic memory?
E.23 It takes time for a MOSFET to change the charge on a wire in order to store or retrieve a bit.
24. If you connect the output of one inverter to the input of a second inverter, how will the output of the second
inverter be related to the input of the first inverter?
E.24 The output of the second inverter will be the same as the input to the first inverter.
E.24 The two inverters will invert the input twice, producing an output that is the same as the input.
25. Suppose you connected a microphone directly to a large unamplified speaker. Why wouldn’t the speaker reproduce
your voice loudly when you talked into the microphone?
E.25 The microphone can’t provide enough power.
26. Why can’t an audio amplifier operate without batteries or a power supply?
E.26 To produce a larger, more powerful copy of an input signal, the amplifier needs a source of energy.
Otherwise it would be creating energy out of nothing.
27. You like to listen to old phonograph records but your new stereo amplifier has no input for a phonograph. You
connect the phonograph to the stereo’s CD player input but find that the volume is extremely low. Why?
E.27 The phonograph produces a much smaller voltage rise than a CD player would provide. The amplifier
expects a larger voltage.
28. To correct the volume problem in Exercise 27, you buy a small preamplifier and connect it between the
phonograph and the CD player input of the stereo. The volume problem is gone. What is the preamplifier doing to fix
the problem?
E.28 The preamplifier is boosting the voltage and current of the input signal, creating a new input signal that is
large enough for the amplifier to handle.