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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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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.
(a) If the current through a battery is doubled, by what factor is the battery power increased? (b) If the current through a resistor is doubled, by what factor is the power dissipation increased? (c) Explain why these factors are the same or different (depending on what you find).
Using thick connecting wires that are very good conductors, a Nichrome wire (鈥渨ire 1鈥�) of length L1 and cross-sectional area A1 is connected in series with a battery and an ammeter (this is circuit 1). The reading on the ammeter is I1. Now the Nichrome wire is removed and replaced with a different wire (鈥渨ire 2鈥�), which is 2.5 times as long and has 5.5 times the cross-sectional area of the original wire (this is circuit 2). In the following question, a subscript 1 refers to circuit 1, and a subscript 2 refers to circuit 2. It will be helpful to write out your solutions to the following questions algebraically before doing numerical calculations. (Hint: Think about what is the same in these two circuits.)(a) What is the value of I2/ I1, the ratio of the conventional currents in the two circuits? (b) What is the value of R2/ R1, the ratio of the resistances of the wires? (c) What is the value of E2/ E1, the ratio of the electric fields inside the wires in the steady states?
Suppose that you charges a capacitor with two batteries. How much charge would be on each plate in the final state? How many excess electrons would be on the negative plate?
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.
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