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Chapter 19: Q47P (page 799)
When a thin-filament light bulb is connected to two batteries in series, the current isWhat is the resistance of the glowing thin-filament bulb?
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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 circuit consists of a battery, whose emf is K, and five Nichrome wires, three thick and two thin as shown in Figure 19.78. The thicknesses of the wires have been exaggerated in order to give you room to draw inside the wires. The internal resistance of the battery is negligible compared to the resistance of the wires. The voltmeter is not attached until part (e) of the problem. (a) Draw and label appropriately the electric field at the locations marked × inside the wires, paying attention to appropriate relative magnitudes of the vectors that you draw. (b) Show the approximate distribution of charges for this circuit. Make the important aspects of the charge distribution very clear in your drawing, supplementing your diagram if necessary with very brief written descriptions on the diagram. Make sure that parts (a) and (b) of this problem are consistent with each other. (c) Assume that you know the mobile-electron density n and the electron mobility u at room temperature for Nichrome. The lengths and diameters of the wires are given on the diagram. Calculate accurately the number of electrons that leave the negative end of the battery every second. Assume that no part of the circuit gets very hot. Express your result in terms of the given quantities . Explain your work and identify the principles you are using. (d) In the case that , what is the approximate number of electrons that leave the negative end of every second? (e) A voltmeter is attached to the circuit with its + lead connected to location B (halfway along the leftmost thick wire) and its - lead connected to location C (halfway along the leftmost thin wire). In the case that , what is the approximate voltage shown on the voltmeter, including sign? Express your result in terms of the given quantities .
For the circuit shown in figure 19.86, which consists of batteries with known emf and ohmic resistors with known resistance, write the correct number of energy-conservation and current node rule equations that would be adequate to solve for the unknown currents, but do not solve the equations. Label nodes and currents on the diagram, and identify each equation (energy or current, and for which loop or node).
Consider two capacitors whose only difference is that the plates of capacitor number 2 are closer together than those of capacitor number 1 (Figure 19.56). Neither, capacitors has an insulating layer between the plates. They are placed in two different circuits having similar batteries and bulbs in series with the capacitor.
Show that in the first fraction of a second, the current stays nearly constant (decreases less rapidly) in the circuit with capacitor number 2. Explain your reasoning in detail.
Hint: Show charges on metal plates, and consider the electric fields they produce in the nearby wires. Remember that the fringe field near a plate outside a circular capacitor is approximately-
More extensive analysis shows that this trend holds true for the entire charging process: the capacitor with the narrower gap ends up with more charge on the plates.
How is the charging time for a capacitor correlated with the initial current? That is, if the initial current is bigger, is the charging time, longer, shorter, or the same?
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