Physics chapter 19

1. Explain why birds can sit on power lines safely, whereas leaning a metal ladder up against a power line to fetch a stuck kite is extremely dangerous.

1. The birds are safe because they are not grounded. Both of their legs are essentially at the same voltage (the only difference being due to the small resistance of the wire between their feet), and so there is no current flow through their bodies since the potential difference across their legs is very small. If you lean a metal ladder against the power line, you are making essentially a short circuit from the high potential wire to the low potential ground. A large current will flow at least momentarily, and that large current will be very dangerous to anybody touching the ladder.

11. For what use are batteries connected in series? For what use are they connected in parallel? Does it matter if the batteries are nearly identical or not in either case?

11. Batteries are connected in series to increase the voltage available to a device. For instance, if there are two 1.5-V batteries in series in a flashlight, the potential across the bulb will be 3.0 V. The batteries need not be nearly identical. Batteries are connected in parallel to increase the total amount of current available to a device. The batteries need to be nearly identical. If they are not, the larger voltage batteries will recharge the smaller voltage batteries.

12. Can the terminal voltage of a battery ever exceed its emf? Explain.

12. The terminal voltage of a battery can exceed its emf if the battery is being charged - if current is passing through the battery "backwards" from positive pole to negative pole. Then the terminal voltage is the emf of the battery plus the voltage drop across the internal resistance.

13. Explain in detail how you could measure the internal resistance of a battery.

13. Connect the battery to a known resistance R, and measure the terminal voltage V(sub)ab. The current in the circuit is given by Ohm's law to be I= V(sub)ab/ R. It is also true that V(sub)ab= E-Ir and so the internal resistance can be calculated by r=E-V(sub)ab/I=R[(E-V(sub)ab)/V(sub)ab].

14. Compare and discuss the formulas for resistors and for capacitors when connected in series and in parallel.

14. The formulas are "opposite" each other in a certain sense. When connected in series, resistors add linearly but capacitors add reciprocally, according to the following rules. The series resistance is always larger than any one component resistance, and the series capacitance is always smaller than any one component capasitance. When connected in parallel, resistors add reciprocally but capacitors add linearly, according to the following rules. The parallel resistance is always smaller than any one component resistance, and the parallel capacitance is always larger than any one component capacitance. One way to consider the source of this difference is that the voltage across a resistor is proportional to the resistance, by V=IR, but the voltage across a capacitor is inversely proportional to the capacitance, by V=Q/C.

15. Suppose that three identical capacitors are connected to a battery. Will they store more energy if connected in series or in parallel?

15. The energy stored in capacitor network can be calculated by PE=(.5)CV(squared). Since the voltage for the capacitor network is the same in this proble for both configurations, the configuration with the highest equivalent capacitance will store the most energy. The parallel combination has the highest equivalent capacitance, and so stores the most energy. Another way to consider this is that the total stored energy is the sum of the quantity PE=(.5)CV(squared) for each capacitor. Each capacitor has the same capacitance, but in the parallel circuit, each capacitor has a larger voltage than in the series circuit. Thus the parallel circuit stores more energy.

2. Discuss the advantages and disadvantages of Christmas tree lights connected is parallel versus those connected in series.

2. If the lights are connected in parallel, if one bulb burns out, the rest of the string stays lit. That makes it easy to tell which light has gone out. A parallel string is more complicated to assemble than a series string, since two wires must be attached from bulb to bulb. If the lights are connected in series, if one bulb burns out, all of the bulbs will go out. That makes it difficult to tell which light has gone out. A series string is simpler to assemble than one in parallel, since only one wire must be attached from bulb to bulb. A "blinker bulb" can make the entire string flash on and off the current.

3. If all you have is a 120-V line, would it be possible to light several 6-V lamps without burning them out? How?

3. If 20 of the 6-V lamps were connected in series and then connected to the 120-V line, there would be a voltage drop of 6 V for each of the lamps, and they would not burn out due to too much voltage. Being in series, if one of the bulbs went out for any reason, they would all turn off.

4. Two lightbulbs of resistance R(sub)1 and R(sub)2 (R2 > R1) are connected in series. Which is brighter? What if they are connected in parallel? Explain.

4. If the lightbulbs are in series, each will have the same current. The power dissipated by the bulb as heat and light is given by P=I(squared)R. Thus the bulb with the higher resistance will be brighter. if the bulbs are in parallel, each will have the same voltage. The power dissipated by the bulb as heat and light is given by P=V(squared)/R. Thus the bulb with the lower resistance will be brighter.

5. Household outlets are often double outlets. Are these connected in series or parallel? How do you know?

5. The outlets are connected in parallel to each other, because you can use one outlet without using the other. If they were in series, both outlets would have to be used at the same time to have a completed circuit. Also, both outlets supply the same voltage to whatever device is plugged in to the outlet, which indicates that they are wired in parallel to the voltage source.

6. With two identical lightbulbs and two identical batteries, how would you arrange the bulbs and batteries in a circuit to get the maximum possible total power out? (Assume the batteries have negligible internal resistance.)

6. The power output from a resistor is given by P=V(squared)/R. To maximize this value, the voltage needs to be as large as possible and the resistance as small as possible. That can be accomplished by putting the two batteries in series, and then connecting the two resistors in parallel to each other, across the full 2-battery voltage.

7. If two identical resistors are connected in series to a battery, does the battery have to supply more power or less power than when only one of the resistors is connected? Explain.

7. The power supplied by the battery is the product of the battery voltage times the total current flowing from the battery. With the two resistors in series, the current is half that with a single resistor. Thus the battery has to supply half the power for the two series resistors than for the single resistor.

8. You have a single 60-W bulb on in your room. How does the overall resistance of your room's electric circuit change when you turn on an additional 100-W bulb?

8. There is more current flowing in the room's wiring when both bulbs are on, yet the voltage remains the same. Thus the resistance of the room's circuit must have decreased. Also, since the bulbs are in parallel, adding two resistors in parallel always results in a net resistance that is smaller than either of the individual resistances.

9. When applying Kirchoff's loop rule does the sign (or direction) of a battery's emf depend on the direction of current through the battery? What about the terminal voltage?

9. No, the sign of the battery's emf does not depend on the direction of the current through the battery. The sign of the battery's emf depends on the direction you go through th battery applying the loop rule. If you go from positive pole to negative pole, the emf is subtracted. But the terminal voltage does depend on the direction of the current through the battery. If current is flowing through the battery in the normal orientation (leaving the positive terminal, flowing through the circuit, and arriving at the negative terminal) then there is a voltage drop across the internal resistance, and the terminal voltage is less than the emf. If the current flows in the opposite sense (as in charging the battery), then there is a voltage rise across the terminal reistance, and the terminal voltage is higher than the emf.