Electric Currents 18-9
Electric Currents / 18Responses to Questions
1. In the circuit (not in the battery), electrons flow from high potential energy (at the negative terminal) to low potential energy (at the positive terminal). Inside the battery, the chemical reaction does work on the electrons to take them from low potential energy to high potential energy (to the negative terminal). A chemical description could say that the chemical reaction taking place at the negative electrode leaves electrons behind on the terminal, and the positive ions created at the negative electrode pull electrons off the positive electrode.
2. Battery energy is what is being “used up.” As charges leave the battery terminal, they have a relatively high potential energy. Then as the charges move through the flashlight bulb, they lose potential energy. The battery uses a chemical reaction to replace the potential energy of the charges, by lowering the battery’s chemical potential energy. When a battery is “used up,” it is unable to give potential energy to charges.
3. Ampere-hours measures charge. The ampere is a charge per unit time, and the hour is a time, so the product is charge. One ampere-hour of charge is 3600 coulombs of charge.
4. Resistance is given by the relationship If the ratio of resistivity to area is the same for the copper wire and the aluminum wire, then the resistances will be the same. Thus if or then the resistances will be the same.
Also, resistance changes with temperature. By having the two wires at different temperatures, it might be possible to have their resistance be the same.
5. The terminal of the battery (usually the negative one) is connected to the metal chassis, frame, and engine block of the car. This means that all voltages used for electrical devices in the car are measured with respect to the car’s frame. Also, since the frame is a large mass of metal, it can supply charges for current without significantly changing its electric potential.
6. To say that indicates a decrease in power as resistance increases implies that the voltage is constant. To say that indicates an increase in power as resistance increases implies that the current is constant. Only one of those can be true for any given situation in which the resistance is changing. If the resistance changes and the voltage is constant, then the current must also change. Likewise, if the resistance changes and the current is constant, then the voltage must also change.
7. When a lightbulb burns out, its filament burns to the point of breakage. Once the filament (part of the conducting path for the electricity flowing through the bulb) is broken, current can no longer flow through the bulb. It no longer gives off any light.
8. We assume that the voltage is the same in both cases. If the resistance increases, then the power delivered to the heater will decrease according to If the power decreases, then the heating process will slow down.
9. Resistance is given by the relationship Thus, to minimize the resistance, you should have a small length and a large cross-sectional area. Likewise, to maximize the resistance, you should have a large length and a small cross-sectional area.
(a) For the least resistance, connect the wires to the faces that have dimensions of 2a by 3a, which maximizes the area and minimizes the length (a).
(b) For the greatest resistance, connect the wires to the faces that have dimensions of a by 2a, which minimizes the area and maximizes the length (3a).
10. When a lightbulb is first turned on, it will be cool and the filament will have a lower resistance than when it is hot. This lower resistance means that there will be more current through the bulb while it is cool. This momentary high current will make the filament quite hot. If the temperature is too high, then the filament will vaporize, and the current will no longer be able to flow in the bulb. After the light has been on for some time, the filament is at a constant high temperature, with a higher resistance and a lower current. Since the temperature is constant, there is less thermal stress on the filament than when the light is first turned on.
11. Assuming that both lightbulbs have the same voltage, since the higher-power bulb will draw the most current. Likewise, assuming that both lightbulbs have the same voltage, since the higher-power bulb will have the lower resistance. So the 100-W bulb will draw the most current, and the 75-W bulb will have the higher resistance.
12. Transmission lines have resistance and therefore will change some electrical energy to thermal energy (heat) as the electrical energy is transmitted. We assume that the resistance of the transmission lines is constant. Then the “lost” power is given by where I is the current carried by the transmission lines. The transmitted power is given by where V is the voltage across the transmission lines. For a given value of the higher the voltage is, the lower the current has to be. As the current is decreased, is also decreased, so there is a lower amount of power lost.
13. The 15-A fuse is blowing because the circuit is carrying more than 15 A of current. The circuit is probably designed to only carry 15 A, so there might be a “short” or some other malfunction causing the current to exceed 15 A. Replacing the 15-A fuse with a 25-A fuse will allow more current to flow and thus make the wires carrying the current get hotter. A fire or damage to certain kinds of electrical equipment might result. The blown fuse is a warning that something is wrong with the circuit.
14. At only 10 Hz, the metal filament in the wire will go on and off 20 times per second. (It has a maximum magnitude of current at the maximum current in each direction.) The metal filament has time to cool down and get dim during the low current parts of the cycle, and your eye can detect this. At 50 or 60 Hz, the filament never cools enough to dim significantly. Also, the human eye and brain cannot distinguish the on-off cycle of lights when they are operated at the normal 60-Hz frequency. At much lower frequencies, such as 5 Hz, the eye and brain are able to process the on-off cycle of the lights, and they will appear to flicker.
15. There are several factors which can be considered. As the voltage reverses with each cycle of AC, the potential energy of the electrons is raised again. Thus with each “pass” through the light, the electrons lose their potential energy and then get it back again. Secondly, the heating of the filament (which causes the light) does not depend on the direction of the current, but only on the fact that a current exists, so the light occurs as the electrons move in both directions. Also, at 60 Hz, the current peaks 120 times per second. The small amount of time while the magnitude of the current is small is not long enough for the hot metal filament to cool down, so it stays lit the entire cycle. Finally, the human eye sees anything more rapid than about 20 Hz as continuous, even if it is not. So even if the light was to go dim during part of the cycle, our eyes would not detect it.
16. When the toaster is first turned on, the Nichrome wire is at room temperature. The wire starts to heat up almost immediately. Since the resistance increases with temperature, the resistance will be increasing as the wire heats. Assuming the voltage supplied is constant, the current will be decreasing as the resistance increases.
17. Current is NOT used up in a resistor. The current that flows into the resistor is the same as the current that flows out of the resistor. If that were not the case, then there would be either an increase or decrease in the charge of the resistor, but the resistor actually stays neutral, indicating equal charge flow both in and out. What does get “used up” is potential energy. The charges that leave a resistor have lower potential energy than the charges that enter a resistor. The amount of energy decrease per unit time is given by
18. If you turn on an electric appliance when you are outside with bare feet, and the appliance shorts out through you, the current has a direct path to ground through your feet, and you will receive a severe shock. If you are inside wearing socks and shoes with thick soles, and the appliance shorts out, the current will not have an easy path to ground through you and will most likely find an alternate path. You might receive a mild shock, but not a severe one.
19. In the two wires described, the drift velocities of the electrons will be about the same, but the current density, and therefore the current, in the wire with twice as many free electrons per atom will be twice as large as in the other wire.
20. (a) If the length of the wire doubles, then its resistance also doubles, so the current in the wire will be reduced by a factor of 2. Drift velocity is proportional to current, so the drift velocity will be halved.
(b) If the wire’s radius is doubled, then the drift velocity remains the same. (Although, since there are more charge carriers, the current will quadruple.)
(c) If the potential difference doubles while the resistance remains constant, then the drift velocity and current will also double.
Responses to MisConceptual Questions
1. (c) It may be thought that the orientation of the battery is important for the bulb to work properly. But the lightbulb and it will glow equally bright regardless of the direction in which current flows through it.
2. (c) A common misconception is that the lightbulb “uses up” the current, causing more current to flow in one portion of a loop than in another. For a single loop, the current is the same at every point in the loop. Therefore, the amount of current that flows through the lightbulb is the same as the amount that flows through the battery.
3. (a) Ohm’s law is an empirical law showing that for some materials the current through the material is proportional to the voltage across the material. For other materials, such as diodes, fluorescent lightbulbs, and superconductors, Ohm’s law is not valid. Since it is not valid for all objects, it cannot be a fundamental law of physics.
4. (e) A common misconception is that the electrons are “used up” by the lightbulb. A good analogy would be water flowing across a water wheel in a flour mill. The water flows onto the wheel at the top (high potential) and causes the wheel to rotate as the water descends along the wheel. The amount of water that leaves the bottom of the wheel is the same as the amount that entered at the top, but it does so at a lower point (low potential). The change in potential energy goes into work in the wheel. In a lightbulb, electrons at higher potential energy enter the lightbulb and give off that energy as they pass through the bulb. As with the water on the wheel, the number of electrons exiting and entering the bulb is the same.
5. (e) A misconception commonly found when dealing with electric circuits is that electrons are “used up” by the lightbulb. The current is a measure of the rate that electrons pass a given point. If the current were different at two points in the circuit, then electrons would be building up (or being depleted) between those two points. The buildup of electrons would cause the circuit to be time dependent and not a steady state system. The flow of electrons (current) must be the same at all points in a loop.
6. (b) Ohm’s law requires that the ratio of voltage to current be constant. Since it is not constant in this case, the material does not obey Ohm’s law.
7. (d) A common misconception is that the charge or current is “used up” in a resistor. The resistor removes energy from the system, such that the electrons exiting the resistor have less potential energy than the electrons entering, but the number of electrons (charge carriers) entering and exiting the resistor is the same. The rate of electrons entering and exiting is equal to the constant current in the circuit.
8. (c) Since the unit of kilowatt-hour contains the word “watt,” it is often incorrectly thought to be a unit of power. However, the kilowatt-hour is the product of the unit of power (kilowatt) and a unit of time (hour), resulting in a unit of energy.
9. (b) Each device added to the circuit is added in parallel. The voltage across the circuit does not change as the devices are added. Each new device, however, creates a path for additional current to flow, causing the current in the circuit breaker to increase. When the current becomes too high, the circuit breaker will open.
10. (b) For current to flow through an object it must complete a circuit. When a bird lands on a wire, the bird creates a loop in parallel with the segment of wire between its feet. The voltage drop across the bird is equal to the voltage drop across the wire between the bird’s feet. Since the wire has a small resistance, there will be very little voltage drop across the wire between the bird’s feet and very little voltage drop across the bird. The bird is a good conductor (similar to a human), but since there is little voltage drop, it will experience little current flow. When a ladder is placed between the ground and the wire, it creates a path for the current to flow from the high-voltage wire to ground (zero voltage). This large potential difference will enable a large current to flow through the ladder.
11. (b) A common misconception is that the electrons must travel from the switch to the lightbulb for the lightbulb to turn on. This is incorrect because there are electrons throughout the circuit, not just at the switch. When the switch is turned on, the electric potential across the circuit creates an electric field in the wire that causes all of the conduction electrons in the wire to move.