Chapter 18 Answers

All answers have been checked against the answer key, and should be presumed to be correct. You should ask for help in the recitations if you are unable to obtain these results.

6.   (a) 4.95 A,   (b) 6.11 A

8.   (a) 13 W,   (b) 8.1 x 10³C

10   2.5 mV

16.   a 29 degree C increase

20.   (a) 3.75 x 10^-4 W,   (b) 1.5 x 10^-3 W,   (c) 6.0 x 10^-3 W

44.   V₀ = 636 V,   I₀ = 5.66 A

2. The electric cell uses a chemical reaction to increase the number of electrons on the negative electrode. In the battery of figure 18-4, electrons accumulate on the zinc electrode because the zinc leaves two electrons behind when it is dissolved in the acid. These electrons then flow to the negative terminal of the battery, where they enter the wire and flow around to the positive terminal, to be collected by the carbon.

3. The heart pumps blood through the arteries, and a battery pumps electrons through wires. The blood vessels play the role of the wires. The heart plays the role of the battery.

4. You need two switches of the type shown in Figure 18-29. If both switches are in position 1, or both are in position 2, then current will flow to the light. Otherwise, the light will be off. This arrangement allows you to turn the light on or off from either switch, no matter whether it is already on.

5. Yes, but the aluminum wire has to have a larger cross section area. The diameter of the aluminum wire must be 25.6% larger than a copper wire of the same resistance and length, based on the resistivities given in the table.

6. (a) The least resistance is when the wires are separated by the length a. (b) The greatest resistance is when the wires are separated by the length 3a. This is because the resistance is proportional to the length between the wires, and inversely proportional to the cross-sectional area, which is the product of the remaining two lengths.

7. Ground is a reference potential with respect to all the other potentials in a system. In a car, the "Ground" is taken to be the terminal which is connected to the chassis of the car. By convention, this is the negative terminal of the battery. The chassis potential serves as a reference potential for all electrical circuits in the car.

8. There is no contradiction, because the expressions hold different variables constant. If R is increased with V held fixed, then the expression P = V²/R implies that the power decreases, because the current flowing, I = V/R, decreases. If R is increased with I held fixed, then the expression P = I²R implies that the power increases, because the voltage V = IR increases in this case.

9. A lightbulb burns out when too much power is dissipated in the filament, causing its temperature to increase until it melts. Over time, the power dissipated in the filament tends to damage it, and it melts first at the thinnest point, where the resistance is highest.

10. When a light bulb is first turned on, it is cold. Therefore, its resistance is lower than after it heats up. When the resistance is lower, the power dissipated in the bulb, P = V²/R, is greater. Therefore, it is most likely to burn out when first turned on.

11. The power is the voltage times the current, so the 100-W bulb draws more current than the 75-W bulb. Since P = V²/R, the 75-W bulb has higher resistance than the 100-W bulb.

12. The power output of the generator is fixed, and related to the voltage and current sent over the transmission line by P = IV. The power lost in a transmission line of resistance R is P_lost = I²R. Therefore, the ratio of power lost to the total power output is P_lost/P = IR/V = PR/V². Since P and R are fixed, the fraction of power lost in the transmission line is less if the voltage is very high.

13. Replacing a 15-A fuse that repeatedly blows with a 25-A fuse may keep the fuse from blowing, but allowing a higher current to flow through the circuit may be dangerous, since the original fuse was designed to blow before a dangerous current was reached which could overheat the wiring and cause a fire. Using too large a fuse could cause a fire when the circuit is overloaded.

14. The power in AC current fluctuates between a maximum value and zero as the voltage alternates, since the power is proportional to the square of the voltage. A 10 Hz power supply would cause the light to flash 10 times per second when the maximum power is reached.

15. In figure (a), placing the two batteries in series doubles the amount of voltage they produce, Allowing a higher-voltage light to be used. Doubling the voltage will draw half the current or the same power output, since P = VI. In figure (b), placing the two batteries in parallel provides the same voltage as a single cell, but draws only half as much current from each cell. This will cause the cells to last twice as long. In either case, the batteries will last longer for the same power output than a single cell would.

16. Every time the electrons are pushed through the bulb, some energy is transformed to light. The AC generator which drives the current is continually putting energy into the electrons to be converted to light energy with each cycle.

17. When a toaster is first turned on, the current is very high, because the wire is cool. As it heats up, the resistance increases, and the current decreases until a steady temperature is reached.

18. No - resistors do not "use up" current. Current is conserved when it passes through any object. The current loses energy in a resistor, because some of the electricial energy is converted to heat. However, all the electrons that go in must come out.