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Chapter 19: Q55P (page 799)
Suppose that you charge a 1 F capacitor in a circuit containing two batteries, so the final potential difference across the plates is.How much charge is on each plate? How many excess electrons are on the negative plate?
(i) 3 C (ii)
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You connect a battery to a capacitor consisting of two circular plates of radius separated by an air gap of , what is the charge on the positive plate?
In copper at room temperature, the mobility of mobile electrons is about ,and there are aboutmobile electrons perCalculate the conductivityand include the correct units. In actual practice, it is usually easier to measure the conductivityand deduce the mobilityfrom this measurement.
A long Iron slab of width w and height h emerges from a furnace, as shown in Figure 19.79. Because the end of the slab near the furnace is hot and the other end Is cold, the electron mobility increases significantly with the distance x. The electron mobility iswhere u0is the mobility of the iron at the hot end of the slab. There are n iron atoms per cubic meter, and each atom contributes one electron to the sea of the mobile electron (we can neglect the small thermal expansion of the iron). A steady state conventional current runs through the slab from the hot end towards cold end, and an ammeter (not shown) measures the current to have a magnitude I in amperes. A voltmeter is connected to two locations a distance d apart, as shown. (a) Show the electric field inside the slab at two locations marked with. Pay attention to the relative magnitudes of the two vectors that you draw. (b) Explain why the magnitude of the electric field is different at these two locations. (c) At a distance x from the left voltmeter connection, what is the magnitude of the electric field in terms x and the given quantities w, h, d, u0, k, l, and n ( and fundamental constants)? (d) What is the sign of potential difference displayed on the voltmeter? Explain briefly. (e) In terms of the given quantitiesw, h, d, u0, k, l, and n and ( and fundamental constants), what is the magnitude of the voltmeter reading? Check your work. (f) What is the resistance of this length of the iron slab?
Question: How does the final (equilibrium) charge on the capacitor plates depend on the particular resistor (for example, the kind of bulb or the length of Nichrome wire) in the circuit during charging? Explain briefly.
Question: in circuit 1 (Figure 19.72), an uncharged capacitor is connected in series with two batteries and one light bulb. Circuit 2 (Figure 19.72) contains two light bulbs identical to the bulb in the circuit; in all other respects, it is identical to circuit 1. In circuit 1, the light bulb stays lit for 25 s. The following questions refer to these circuits. You should draw diagrams representing the fields and charges in each circuit at the times mentioned, in order to answer the questions.
(a)One microsecond after connecting both circuits, which of the following are true? Chose all that apply: (1) the net electric field at location B in circuit 1 is larger than the net electric field at location B in circuit 2. (2) At location A in 1, electrons flow to the left. (3) At location A in circuit 1, the electric fields due to charges on the surface of the wires and batteries points to the right. (4) in circuit 1 the potential difference across the capacitor plates is equal to the emf of the batteries. (5) The current in circuit 1 is larger than the current in circuit 2.
(b)Two seconds after connecting both circuits, which of the following are true? Choose all that apply: (1) there is more charge on the plates of capacitor 1 than there is on the plates of capacitor 2. (2) there is negative charge on the right plate of the capacitor in circuit 1. (3) At location B in circuit 2 the net electric field points to the right. (4) At location B in circuit 2 the fringe field of the capacitor points to the right. (5) At location A in circuit 1 the fringe field of the capacitor points to the left.
(c)Which of the graphs in Figure 19.73 represents the amount of charge on the positive plate of the capacitor in circuit 1 as a function of time?
(d)Which of the graphs in Figure 19.73 represents the current in circuit 1 as a function of time?
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