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Chapter 18: Q15Q (page 755)

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+鈥檚 and -鈥檚 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鈥檛 been put in backwards.

(d)Try the experiment to check your analysis. Does the bulb glow about as you predicted?

Short Answer

Expert verified

(a) The distribution of charges in the circuit are as follows:

Step by step solution

01

Given data

Two batteries are connected opposing each other in series with a filament.

02

Flow of charges

The negative terminal of the battery forces negative charges to flow from the negative terminal to the positive through the circuit. The positive terminal of the battery forces positive charges to flow from the positive terminal to the negative through the circuit.

03

(a) Determination of the charge distribution in the circuit

The negative terminals of both the batteries are directed towards the circuit and the positive terminal are directed towards each other. Thus there will be a larger concentration of negative charges in the circuit and that of positive charges in between the batteries. The distribution can be depicted as follows:

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Most popular questions from this chapter

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).

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 i1and the electric field is E1. In terms of these quantities, determine the corresponding quantities i2and E2for bulb 2, and explain your reasoning.

(b)When bulb 2 is replaced by a wire, the electron current through bulb 1 is i0and the electric field in bulb 1 is E0. How big is i1 in terms of i0? 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.

Compare the direction of the average electric field inside a battery to the direction of the electric field in the wires and resistors of a circuit.

In the circuit shown in Figure 18.110, the two thick wires and the thin wire are made of Nichrome.

(a) Show the steady-state electric field at indicated locations, including in the thin wire. (b) Carefully draw pluses and minuses on your own diagram to show the approximate surface-charge distribution in the steady state. Make your drawing show the differences between regions of high surface-charge density and regions of low surface-charge density. (c) The emf of the battery is1.5V. In Nichrome, there are n=9脳1028 mobile electrons per m3, and the mobility of mobile electrons is 渭=7脳10-5(m/s)(V/m). Each thick wire has a length of L1 =20cm=0.2m and a cross-sectional area of A1 =9脳10-8 m2. The thin wire has a length of L2=5cm=0.05m and a cross-sectional area of A2=1.5脳10-8m2. (The total length of the three wires is 45cm)Calculate the number of electrons entering the thin wire every second in the steady state. Do not make any approximations, and do not use Ohm鈥檚 law or series-resistance equations. State briefly where each of your equations comes from.

A Nichrome wire 48 cm long and 0.25 mm in diameter is connected to a 1.6 V flashlight battery. What is the electric field inside the wire? Why you don鈥檛 have to know how the wire is bent? How would your answer change if the wire diameter change were 0.20 mm? (Not that the electric field in the wire is quiet small compared to the electric field near a charged tape.)
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