College Physics: A Strategic Approach (3rd Edition)
3rd Edition
ISBN: 9780321879721
Author: Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher: PEARSON
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Textbook Question
Chapter 23, Problem 28CQ
Consider the model of nerve
a. How would this affect the resistance and the capacitance of one segment of the axon?
b. How would this affect the time constant for the charging of one segment?
c. How would this affect the signal propagation speed for the axon?
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Students have asked these similar questions
Consider the model of nerve conduction in myelinated axons presented in the chapter. Suppose the distance between the nodes of Ranvier was halved for a particular axon.a. How would this affect the resistance and the capacitance of one segment of the axon?b. How would this affect the time constant for the charging of one segment?c. How would this affect the signal propagation speed for the axon?
Opening of voltage-gated channels is driven by an intramembrane electric field acting on charged
voltage-sensor domains. These domains move across the membrane and generate gating
(displacement) currents. When these currents are integrated over time, they produce the gating
charge generated by a population of channels. What would be the gating charge passing through the
external circuit when the flat array of charges moves across the distance a inside the membrane?
The hydrophobic thickness of the membrane is d, the dielectric constant ɛ, the density of charges is
O and the area of the membrane is A (provide an analytic solution).
start
end
A
A
a
d
d
2. A simplified model of an axon based on a simple RC circuit is shown below. Consider
an incremental length of 5 x 10-10 m non-myelinated segment of an axon whose
properties are listed in the table below. A potential of 80 mV is maintained at point a.
a. How many discrete segments make up a distance of 0.01 mm?
b. What is the voltage at a point 0.01 mm away from a?
a
| R.
Rm
RT
R
Values
Property
Axon Radius
5 x 10m
Chapter 23 Solutions
College Physics: A Strategic Approach (3rd Edition)
Ch. 23 - The tip of a flashlight bulb is touching the top...Ch. 23 - A flashlight bulb is connected to a battery and is...Ch. 23 - Current Iin flows into three resistors connected...Ch. 23 - The circuit in Figure Q23.4 has two resistors,...Ch. 23 - The circuit in Figure Q23.5 has a battery and two...Ch. 23 - In the circuit shown in Figure Q23.6, bulbs A and...Ch. 23 - Figure Q23.7 shows two circuits. The two batteries...Ch. 23 - Figure Q23.8 shows two circuits. The two batteries...Ch. 23 - a. In Figure Q23.9, what fraction of current I...Ch. 23 - Two of the three resistors in Figure Q23.10 are...
Ch. 23 - Two of the three resistors in Figure Q23.11 are...Ch. 23 - Rank in order, from largest to smallest, the...Ch. 23 - The three bulbs in Figure Q23.13 are identical....Ch. 23 - The four bulbs in Figure Q23.14 are identical....Ch. 23 - Figure Q23.15 shows five identical bulbs connected...Ch. 23 - a. The three bulbs in Figure Q23.16 are identical....Ch. 23 - Initially, bulbs A and B in Figure Q23.17 are both...Ch. 23 - a. Consider the points a and b in Figure Q23.18....Ch. 23 - When the switch in Figure Q23.19 is closed, a....Ch. 23 - A voltmeter is (incorrectly) inserted into a...Ch. 23 - An ammeter is (incorrectly) inserted into a...Ch. 23 - Rank in order, from largest to smallest, the...Ch. 23 - Figure Q23.23 shows a circuit consisting of a...Ch. 23 - Figure Q23.24 shows the volt age as a function of...Ch. 23 - A charged capacitor could be connected to two...Ch. 23 - A flashing light is controlled by the charging and...Ch. 23 - A device to make an electrical measurement of skin...Ch. 23 - Consider the model of nerve conduction in...Ch. 23 - Adding a myelin sheath to an axon results in...Ch. 23 - What is the current in the circuit of Figure...Ch. 23 - Which resistor in Figure Q23.30 dissipates the...Ch. 23 - Normally, household lightbulbs are connected in...Ch. 23 - A metal wire of resistance R is cut into two...Ch. 23 - What is the value of resistor R in Figure Q23.34?...Ch. 23 - Two capacitors are connected in series. They are...Ch. 23 - If a cells membrane thickness doubles but the cell...Ch. 23 - If a cells diameter is reduced by 50% without...Ch. 23 - Draw a circuit diagram tor the circuit of Figure...Ch. 23 - Draw a circuit diagram for the circuit of Figure...Ch. 23 - Draw a circuit diagram for the circuit of Figure...Ch. 23 - In Figure P23.4, what is the current in the wire...Ch. 23 - The lightbulb in the circuit diagram of Figure...Ch. 23 - a. What are the magnitude and direction of the...Ch. 23 - a. What are the magnitude and direction of the...Ch. 23 - a. What is the potential difference across each...Ch. 23 - The current in a circuit with only one battery is...Ch. 23 - What is the equivalent resistance of each group of...Ch. 23 - What is the equivalent resistance of each group of...Ch. 23 - Prob. 12PCh. 23 - Prob. 13PCh. 23 - You have a collection of 1.0 k resistors. How can...Ch. 23 - You have a collection of six 1.0 k resistors. What...Ch. 23 - You have six 1.0 k resistors. How can you connect...Ch. 23 - What is the equivalent resistance between points a...Ch. 23 - What is the equivalent resistance between points a...Ch. 23 - The currents in two resistors in a circuit are...Ch. 23 - Two batteries supply current to the circuit in...Ch. 23 - Part of a circuit is shown in Figure P23.21. a....Ch. 23 - What is the value of resistor R in Figure P23.22?...Ch. 23 - What are the resistances R and the emf of the...Ch. 23 - The ammeter in Figure P23.24 reads 3.0 A. Find I1,...Ch. 23 - Find the current through and the potential...Ch. 23 - Find the current through and the potential...Ch. 23 - For the circuit shown in Figure P23.27, find the...Ch. 23 - Consider the potential differences between pairs...Ch. 23 - For the circuit shown in Figure P23.29, find the...Ch. 23 - A photoresistor, whose resistance decreases with...Ch. 23 - The two unknown resistors in Figure P23.31 have...Ch. 23 - A 6.0 F capacitor, a 10 F capacitor, and a 16 F...Ch. 23 - A 6.0 F capacitor, a 10 F capacitor, and a 16 F...Ch. 23 - You need a capacitance of 50 F, but you dont...Ch. 23 - You need a capacitance of 50 F, but you dont...Ch. 23 - What is the equivalent capacitance of the three...Ch. 23 - What is the equivalent capacitance of the three...Ch. 23 - For the circuit of Figure P23.38, a. What is the...Ch. 23 - For the circuit of Figure P23.39. a. What is the...Ch. 23 - What is the time constant for the discharge of the...Ch. 23 - What is the time constant for the discharge of the...Ch. 23 - After how many time constants has the voltage...Ch. 23 - A 10F capacitor initially charged to 20C is...Ch. 23 - A capacitor charging circuit consists of a...Ch. 23 - The switch in Figure P23.45 has been in position a...Ch. 23 - A 9.0-nm-thick cell membrane undergoes an action...Ch. 23 - A cell membrane has a resistance and a capacitance...Ch. 23 - Changing the thickness of the myelin sheath...Ch. 23 - A particular myelinated axon has nodes spaced 0.80...Ch. 23 - To measure signal propagation in a nerve in the...Ch. 23 - A myelinated axon conducts nerve impulses at a...Ch. 23 - How much power is dissipated by each resistor in...Ch. 23 - Two 75 W (120 V) lightbulbs are wired in series,...Ch. 23 - The corroded contacts in a lightbulb socket have...Ch. 23 - A real battery is not just an emf. We can If model...Ch. 23 - For the real battery shown in Figure P23.55,...Ch. 23 - Batteries are recharged by connecting them to a...Ch. 23 - When two resistors are connected in parallel...Ch. 23 - The 10 resistor in Figure P23.59 is dissipating 40...Ch. 23 - At this instant the current in the circuit of...Ch. 23 - What is the equivalent resistance between points a...Ch. 23 - What is the current through the battery in Figure...Ch. 23 - What is the ratio P parallel/P series of the total...Ch. 23 - You have a device that needs a voltage reference...Ch. 23 - There is a current of 0.25 A in the circuit of...Ch. 23 - A circuit youre building needs an ammeter that...Ch. 23 - A circuit youre building needs a voltmeter that...Ch. 23 - For the circuit shown in Figure P23.68, find the...Ch. 23 - You have three 12 F capacitors. Draw diagrams...Ch. 23 - Initially, the switch in Figure P23.70 is in...Ch. 23 - The capacitor in an RC circuit with a time...Ch. 23 - The capacitor in Figure P23.72 is initially...Ch. 23 - What value resistor will discharge a 1.0 F...Ch. 23 - The charging circuit for the flash system of a...Ch. 23 - A capacitor is discharged through a 100 resistor....Ch. 23 - A 50 /F capacitor that had been charged to 30 V is...Ch. 23 - The switch in Figure P23.77 has been closed for a...Ch. 23 - Intermittent windshield wipers use a variable...Ch. 23 - In Example 23.14 we estimated the capacitance of...Ch. 23 - The giant axon of a squid is 0.5 mm in diameter,...Ch. 23 - A cell has a 7.0-nm-thick membrane with a total...Ch. 23 - The Defibrillator A defibrillator is designed to...Ch. 23 - The Defibrillator A defibrillator is designed to...Ch. 23 - The Defibrillator A defibrillator is designed to...Ch. 23 - A defibrillator is designed to pass a large...Ch. 23 - The voltage produced by a single nerve or muscle...Ch. 23 - The voltage produced by a single nerve or muscle...Ch. 23 - The voltage produced by a single nerve or muscle...Ch. 23 - The voltage produced by a single nerve or muscle...
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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_forwardThe circuit in Figure P21.59 has been connected for a long time. (a) What is the potential difference across the capacitor? (b) If the battery is disconnected from the circuit, over what time interval does the capacitor discharge to one-tenth its initial voltage?arrow_forward(a) A defibrillator sends a 6.00-A current through the chest of a patient by applying a 10,000-V potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use this equation for power: P=I2 RP = .)arrow_forward
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