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Chapter 19: Q1Q (page 794)
How is the initial current through a bulb affected by putting a capacitor in series in the circuit? Explain briefly.
In the presence of a capacitor, the direct current, flowing in the circuit, starts reducing and becomes zero after a certain time interval.
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The two circuits shown in Figure 19.59 have different capacitors but the same batteries and thin-filament bulbs. The capacitors in circuit and circuit areidentical exceptthat the capacitor in circuit was constructed with its plates closer together. Both capacitors have air between their plates. The capacitors are initially uncharged. In each circuit the batteries are connected for a short time compared to the time required to reach equilibrium, and then they are disconnected. In which circuit (1or 2) does the capacitor now have more charge? Explain your reasoning in detail.
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 is where 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?
In the circuit shown in Figure 19.77 the emf of the battery is . Resistor has a resistance of , resistor has a resistance of , and resistor has a resistance of . A steady current flows through the circuit.
(a)What is the equivalent resistance of and ? (b) What is the equivalent resistance of all three resistors? (c) What is the conventional current through
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.
Suppose that instead of placing an insulating layer between the plates of the capacitor shown in Figure 19.57, you inserted a metal slab of the same thickness, just barely not touching the plates. In the same circuit, would this capacitor keep the current more nearly constant or less so than capacitor 2 in Question Q4? Explain why this is essentially equivalent to making a capacitor with a shorter distance between the plates.
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