Chapter 18: Q12Q (page 755)
What is the difference between emf and electric potential difference?
Emf is the total energy provided to each mobile charge by the battery and potential energy is the energy lost by the charges while moving through a particular section of the circuit.
Over 30 million students worldwide already upgrade their learning with Vaia!
All the tools & learning materials you need for study success - in one app.
Get started for free
In the circuit shown in Figure 18.91, all of the wire is made of Nichrome, but one segment has a much smaller cross-sectional area. On a copy of this diagram, using the same scale for magnitude that you used in the previous question for Figure 18.90, show the steady-state electric field at the locations indicated, including in the thinner segment. Before attempting to answer these questions, draw a copy of this diagram. All of the locations indicated by letters are inside the wire.
(a)On your diagram, show the electric field at the locations indicated, paying attention to relative magnitude. Use the same scale for magnitude as you did in the previous question.
(b)Carefully draw pluses and minuses on your diagram to show the approximate surface charge distribution that produces the electric field you drew. Make your drawing show clearly the differences between regions of high surface charge density and regions of low surface-charge density. Use your diagram to determine which of the following statements about this circuit are true.
(1) There is a large gradient of surface charge on the wire between locations Cand E. (2) The electron current is the same at every location in this circuit.
(3) Fewer electrons per second pass location Ethan location C.
(4) The magnitude of the electric field at location Gis smaller in this circuit than it
was in the previous circuit (Figure 18.90).
(5) The magnitude of the electric field is the same at every location in this circuit.
(6) The magnitude of the electric field at location D is larger than the magnitude of the electric field at location G.
(7) There is no surface charge at all on the wire near location G.
(8) The electron current in this circuit is less than the electron current in the previous circuit (Figure 18.90).
At a typical drift speed of , an electron traveling at that speed would take about to travel through one of your connecting wires. Why, then, does the bulb light immediately when the connecting wire is attached to the battery?
Question: Some students intended to run a light bulb off two batteries in series in the usual way, but they accidentally hooked up one of the batteries backwards, as shown in Figure 18.89 (the bulb is shown as a thin filament).
(a)Use+’s and -’s to show the approximate steady-state charge distribution along the wires and bulb.
(b)Draw vectors for the electric field at the indicated locations inside the connecting wires and bulb.
(c)Compare the brightness of the bulb in this circuit with the brightness the bulb would have had if one of the batteries hadn’t been put in backwards.
(d)Try the experiment to check your analysis. Does the bulb glow about as you predicted?
The emf of a particular flashlight battery is 1.7 V. If the battery is 4.5 cm long and radius of cylindrical battery is 1 cm, estimate roughly the amount of charge on the positive end plate of the battery.
In the circuit shown in Figure 18.87, bulbs 1 and 2 are identical in mechanical construction (the filaments have the same length and the same cross-sectional area), but the filaments are made of different metals. The electron mobility in the metal used in bulb 2 is three times as large as the electron mobility in the metal used in bulb 1, but both metals have the same number of mobile electrons per cubic meter. The two bulbs are connected in series to two batteries with thick copper wires (like your connecting wires).
(a)In bulb 1, the electron current is and the electric field is . In terms of these quantities, determine the corresponding quantities and for bulb 2, and explain your reasoning.
(b)When bulb 2 is replaced by a wire, the electron current through bulb 1 is and the electric field in bulb 1 is . How big is in terms of ? Explain your answer, including explicit mention of any approximations you must make. Do not use ohms or series-resistance equations in your explanation, unless you can show in detail how these concepts follow from the microscopic analysis introduced in this chapter.
(c)Explain why the electric field inside the thick copper wires is very small. Also explain why this very small electric field is the same in all of the copper wires, if they all have the same cross-sectional area.
(d)Figure 18.88 is a graph of the magnitude of the electric field at each location around the circuit when bulb 2 is replaced by a wire. Copy this graph and add to it, on the same scale, a graph of the magnitude of the electric field at each location around the circuit when both bulbs are in the circuit. The very small field in the copper wires has been shown much larger than it really is in order to give you room to show how that small field differs in the two circuits.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
