COLLEGE PHYSICS
2nd Edition
ISBN: 9781464196393
Author: Freedman
Publisher: MAC HIGHER
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Chapter 18, Problem 78QAP
To determine
The number of
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48. Biology Cell membranes contain channels that allow K+
ions to leak out, Consider a channel that has a diameter of 1.0
nm and a length of 10 nm. If the channel has a resistance of
18 GN, what is the resistivity of the solution in the channel?
Example 18-6
87 The circuit of Fig. 27-75 shows a
capacitor, two ideal batteries, two
resistors, and a switch S. Initially S has
been open for a long time. If it is then
closed for a long time, what is the
change in the charge on the capacitor?
Assume C = 10 µF, E, = 1.0 V, 82 = 3.0 Figure 27-75 Problem 87.
V, R = 0.20 0, and R2 = 0.40 N.
R2
Question
Use the relationship between resistance, resistivity, length, and cross-sectional area to estimate values for the resistances of a membrane segment R mem and an axoplasm segment R axon.
Given values:
the diameter of the axon ~ 10 µm
the membrane thickness~ 10 nm
the resistivity of the axoplasm~1Ω-m
the average resistivity of the membrane - 10^8 Ω-m
the segment length-1 mm
Chapter 18 Solutions
COLLEGE PHYSICS
Ch. 18 - Prob. 1QAPCh. 18 - Prob. 2QAPCh. 18 - Prob. 3QAPCh. 18 - Prob. 4QAPCh. 18 - Prob. 5QAPCh. 18 - Prob. 6QAPCh. 18 - Prob. 7QAPCh. 18 - Prob. 8QAPCh. 18 - Prob. 9QAPCh. 18 - Prob. 10QAP
Ch. 18 - Prob. 11QAPCh. 18 - Prob. 12QAPCh. 18 - Prob. 13QAPCh. 18 - Prob. 14QAPCh. 18 - Prob. 15QAPCh. 18 - Prob. 16QAPCh. 18 - Prob. 17QAPCh. 18 - Prob. 18QAPCh. 18 - Prob. 19QAPCh. 18 - Prob. 20QAPCh. 18 - Prob. 21QAPCh. 18 - Prob. 22QAPCh. 18 - Prob. 23QAPCh. 18 - Prob. 24QAPCh. 18 - Prob. 25QAPCh. 18 - Prob. 26QAPCh. 18 - Prob. 27QAPCh. 18 - Prob. 28QAPCh. 18 - Prob. 29QAPCh. 18 - Prob. 30QAPCh. 18 - Prob. 31QAPCh. 18 - Prob. 32QAPCh. 18 - Prob. 33QAPCh. 18 - Prob. 34QAPCh. 18 - Prob. 35QAPCh. 18 - Prob. 36QAPCh. 18 - Prob. 37QAPCh. 18 - Prob. 38QAPCh. 18 - Prob. 39QAPCh. 18 - Prob. 40QAPCh. 18 - Prob. 41QAPCh. 18 - Prob. 42QAPCh. 18 - Prob. 43QAPCh. 18 - Prob. 44QAPCh. 18 - Prob. 45QAPCh. 18 - Prob. 46QAPCh. 18 - Prob. 47QAPCh. 18 - Prob. 48QAPCh. 18 - Prob. 49QAPCh. 18 - Prob. 50QAPCh. 18 - Prob. 51QAPCh. 18 - Prob. 52QAPCh. 18 - Prob. 53QAPCh. 18 - Prob. 54QAPCh. 18 - Prob. 55QAPCh. 18 - Prob. 56QAPCh. 18 - Prob. 57QAPCh. 18 - Prob. 58QAPCh. 18 - Prob. 59QAPCh. 18 - Prob. 60QAPCh. 18 - Prob. 61QAPCh. 18 - Prob. 62QAPCh. 18 - Prob. 63QAPCh. 18 - Prob. 64QAPCh. 18 - Prob. 65QAPCh. 18 - Prob. 66QAPCh. 18 - Prob. 67QAPCh. 18 - Prob. 68QAPCh. 18 - Prob. 69QAPCh. 18 - Prob. 70QAPCh. 18 - Prob. 71QAPCh. 18 - Prob. 72QAPCh. 18 - Prob. 73QAPCh. 18 - Prob. 74QAPCh. 18 - Prob. 75QAPCh. 18 - Prob. 76QAPCh. 18 - Prob. 77QAPCh. 18 - Prob. 78QAPCh. 18 - Prob. 79QAPCh. 18 - Prob. 80QAPCh. 18 - Prob. 81QAPCh. 18 - Prob. 82QAPCh. 18 - Prob. 83QAPCh. 18 - Prob. 84QAPCh. 18 - Prob. 85QAPCh. 18 - Prob. 86QAPCh. 18 - Prob. 87QAPCh. 18 - Prob. 88QAPCh. 18 - Prob. 89QAPCh. 18 - Prob. 90QAPCh. 18 - Prob. 91QAPCh. 18 - Prob. 92QAP
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- 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.arrow_forward4) You typically don't think of air being an insulator, but it is, though not perfect. Dry air does have a high resistivity of 3 x 1013 Qm. Two square plates, 10 cm on a side, are separated by 1.2 mm separated by dry air. Charging these plates, a capacitor is created, and potential difference of 250 V is created. What fraction of the charge will flow across the air gap in 1 minute? Note that the potential difference of 250 V is held fixed and constant.arrow_forwardA 58 F capacitor and a 471 resistor are connected to a battery of voltage 7 V as shown in the circuit. After closing the switch, when the capacitor voltage is half of battery voltage how much energy is stored in the capacitor? Express your answer in Joules (J) E 41- 7 C Rarrow_forward
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