800 ideal capacitors are connected in parallel to an ideal voltage source, forming an ideal circuit. The first capacitor has a capacitance of 3.52 μF. If the capacitors are arranged such that every capacitor, starting from the second one, has a capacitance that is 1/3 that of the neighbor- ing capacitor on its left (C2 = C1/6, C3 = C2/6, C4 = C3/6, · · ·), the equivalent capacitance of the parallel connection is most nearly

800 ideal capacitors are connected in parallel to an ideal voltage source, forming an ideal circuit. The first capacitor has a capacitance of 3.52 μF. If the capacitors are arranged such that every capacitor, starting from the second one, has a capacitance that is 1/3 that of the neighbor- ing capacitor on its left (C2 = C1/6, C3 = C2/6, C4 = C3/6, · · ·), the equivalent capacitance of the parallel connection is most nearly

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter20: Electric Potential And Capacitance

Section: Chapter Questions

Problem 18OQ

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A pair of capacitors with capacitances CA = 3.70 F and CB = 6.40 F are connected in a network. What is the equivalent capacitance of the pair of capacitors if they are connected a. in parallel and b. in series?
Assume a length of axon membrane of about 0.10 m is excited by an action potential (length excited = nerve speed pulse duration = 50.0 m/s 2.0 103 s = 0.10 m). In the resting state, the outer surface of the axon wall is charged positively with K+ ions and the inner wall has an equal and opposite charge of negative organic ions, as shown in Figure P18.43. Model the axon as a parallel-plate capacitor and take C = 0A/d and Q = C V to investigate the charge as follows. Use typical values for a cylindrical axon of cell wall thickness d = 1.0 108 m, axon radius r = 1.0 101 m, and cell-wall dielectric constant = 3.0. (a) Calculate the positive charge on the outside of a 0.10-m piece of axon when it is not conducting an electric pulse. How many K+ ions are on the outside of the axon assuming an initial potential difference of 7.0 102 V? Is this a large charge per unit area? Hint: Calculate the charge per unit area in terms of electronic charge e per squared (2). An atom has a cross section of about 1 2 (1 = 1010 m). (b) How much positive charge must flow through the cell membrane to reach the excited state of + 3.0 102 V from the resting state of 7.0 102 V? How many sodium ions (Na+) is this? (c) If it takes 2.0 ms for the Na+ ions to enter the axon, what is the average current in the axon wall in this process? (d) How much energy does it take to raise the potential of the inner axon wall to + 3.0 102 V, starting from the resting potential of 7.0 102 V? Figure P18.43 Problem 43 and 44.
Two capacitors provide an equivalent capacitance of 16.00 μμF when connected in parallel and 4.00 μμF when connected in series. 1)What is the smaller capacitance of the capacitors? If both capacitors have the same capacitance, enter this value. (Express your answer to three significant figures.) 2)What is the larger capacitance of the capacitors? If both capacitors have the same capacitance, enter this value. (Express your answer to three significant figures.)
A potential difference of 151 V is applied to a series connection of two capacitors of capacitances C = 3.13 µF and C2= 8.00 µF. What are (a) chargeq, and (b) potential difference V, on capacitor 1 and (c) q2 and (d) V, on capacitor 2? The charged capacitors are then disconnected from each other and from the battery. Then the capacitors are reconnected with plates of the same signs wired together (the battery is not used). What now are (e) q1, (f) V1, (g) 92, and (h) V,? Suppose, instead, the capacitors charged in part (a) are reconnected with plates of opposite signs wired together. What now are (i) q1. G) V1, (k) q2, and (I) V2? (a) Number Units (b) Number i Units (c) Number i Units (d) Number i Units Units (e) Number i Units (f) Number
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You measure the capacitance C1 of a capacitor by doing the following: First connect capacitors C1 and C2 in series to a power supply that provides a voltage V that can be varied. The capacitance of С2 is known to be 5.00 μF. Then vary the applied voltage V, and for each value of V measure the voltage V2 across C2 . After plotting your data as V2 versus V, you find that the data fall close to a straight line that has slope 0.650. What is the capacitance C1?
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Four capacitors are connected as shown in Fig. 1. C1 = 4.50 μF, C2 = 7.50 μF, C3 = 2.50 μF and C4 = 4.50 μF. V = 20.0 V. (a) What is the equivalent capacitance for this circuit? Enter your answer in μF. (b) What is the voltage across capacitor 2? (c) What is the voltage across capacitor 3?
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A combination of series and parallel connections of capacitors is shown in the figure. The sizes of these capacitors are given by the follow data:C1 = 4.9 μFC2 = 3.9 μFC3 = 9.7 μFC4 = 2.9 μFC5 = 0.95 μFC6 = 13 μF Express the total capacitance of this combination in terms of the capacitances C1 through C6.
The total capacitance of three capacitors connected in series is equal to 6.25 μF . Two of the three capacitors have the following capacitance values, 25 μF and 50 μF while the other one is to be determined. If the three capacitors are connected in parallel , calculate the total capacitance of the parallel combination. Express the answer in Farad (F) using scientific notation.
A combination of series and parallel connections of capacitors is shown in the figure. The sizes of these capacitors are given by the follow data:C1 = 5.3 μFC2 = 3.5 μFC3 = 8.5 μFC4 = 1.2 μFC5 = 0.95 μFC6 = 13.5 μF Find the total capacitance of the combination of capacitors in microfarads.