COLLEGE PHYSICS,AP EDITION >NASTA ED.<
4th Edition
ISBN: 9780134779218
Author: Knight
Publisher: PEARSON
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Chapter 23, Problem 84GP
The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1μF of capacitance per square centimeter of membrane area. When the axon is charged to the–70 mV resting potential, what is the energy stored in this capacitance?
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The giant axon of a squid is 0.5 mm in diameter, 10 cm long, and not myelinated. Unmyelinated cell membranes behave as capacitors with 1 μF of capacitance per square centimeter of membrane area. When the axon is charged to the -70 mV resting potential, what is the energy stored in this capacitance?
In Example 23.14 we estimated the capacitance of the cell membrane to be 89 pF, and in Example 23.15 we found that approximately 10,000 Na+ ions flow through an ion channel when it opens. Based on this information and what you learned about the action potential, estimate the total number of sodium channels in the membrane of a nerve cell.
The cell membranes of axons, which which are nerve cells in the human body, act as very small capacitors. A membrane is capable of storing 8.443e-9C of charge across a potential difference of 0.061V before discharging a nerve impulse. What is the capacitance of one of these axon membranes (in uF)?
Chapter 23 Solutions
COLLEGE PHYSICS,AP EDITION >NASTA ED.<
Ch. 23 - Prob. 1CQCh. 23 - Prob. 2CQCh. 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 - Prob. 6CQCh. 23 - Prob. 7CQCh. 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 - Prob. 12CQCh. 23 - Prob. 13CQCh. 23 - Prob. 14CQCh. 23 - Prob. 15CQCh. 23 - Prob. 16CQCh. 23 - Prob. 17CQCh. 23 - Prob. 18CQCh. 23 - Prob. 19CQCh. 23 - Prob. 20CQCh. 23 - Prob. 21CQCh. 23 - Prob. 22CQCh. 23 - Prob. 23CQCh. 23 - Prob. 24CQCh. 23 - Prob. 25CQCh. 23 - Prob. 26CQCh. 23 - Prob. 27CQCh. 23 - Prob. 28CQCh. 23 - Prob. 29CQCh. 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 - Prob. 34MCQCh. 23 - Prob. 35MCQCh. 23 - Prob. 36MCQCh. 23 - A metal wire of resistance R is cut into two...Ch. 23 - Prob. 38MCQCh. 23 - Prob. 39MCQCh. 23 - If a cells membrane thickness doubles but the cell...Ch. 23 - If a cells diameter is reduced by 50% without...Ch. 23 - Prob. 42MCQCh. 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 - Prob. 5PCh. 23 - Prob. 6PCh. 23 - a. What are the magnitude and direction of the...Ch. 23 - Prob. 8PCh. 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 - Prob. 17PCh. 23 - Prob. 18PCh. 23 - Prob. 19PCh. 23 - Prob. 20PCh. 23 - Prob. 21PCh. 23 - Prob. 22PCh. 23 - Prob. 23PCh. 23 - Prob. 24PCh. 23 - Prob. 25PCh. 23 - Prob. 26PCh. 23 - Prob. 27PCh. 23 - Prob. 28PCh. 23 - Prob. 29PCh. 23 - Prob. 30PCh. 23 - Prob. 31PCh. 23 - Prob. 32PCh. 23 - Prob. 33PCh. 23 - Prob. 34PCh. 23 - Prob. 35PCh. 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 - Prob. 40PCh. 23 - Prob. 41PCh. 23 - Prob. 42PCh. 23 - Prob. 43PCh. 23 - Prob. 44PCh. 23 - Prob. 45PCh. 23 - Prob. 46PCh. 23 - A 10F capacitor initially charged to 20C is...Ch. 23 - A capacitor charging circuit consists of a...Ch. 23 - Prob. 49PCh. 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 - Prob. 56GPCh. 23 - Two 75 W (120 V) lightbulbs are wired in series,...Ch. 23 - Prob. 58GPCh. 23 - A real battery is not just an emf. We can If model...Ch. 23 - Prob. 60GPCh. 23 - Batteries are recharged by connecting them to a...Ch. 23 - Prob. 63GPCh. 23 - Prob. 64GPCh. 23 - Prob. 65GPCh. 23 - Prob. 66GPCh. 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 - Prob. 69GPCh. 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 - Prob. 75GPCh. 23 - Prob. 76GPCh. 23 - Prob. 77GPCh. 23 - Prob. 78GPCh. 23 - Prob. 79GPCh. 23 - Prob. 80GPCh. 23 - Intermittent windshield wipers use a variable...Ch. 23 - Prob. 82GPCh. 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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- 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?arrow_forwardAssume 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_forwardA 1-megabit computer memory chip contains many 60.0 1015-F capacitors. Each capacitor has a plate area of 21.0 1012 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration.) The diameter of an atom is on the order of 1010 m = 1 . Express the plate separation in angstroms.arrow_forward
- In Figure P27.7, capacitor 1 (C1 = 20.0 F) initially has a potential difference of 50.0 V and capacitor 2 (C2 = 5.00 F) has none. The switches are then closed simultaneously. a. Find the final charge on each capacitor after a long time has passed. b. Calculate the percentage of the initial stored energy that was lost when the switches were closed. FIGURE P27.7arrow_forwardA 1-megabit computer memory chip contains many 60.0 1015-F capacitors. Each capacitor has a plate area of 21.0 1012 m2. Determine the plate separation of such a capacitor. (Assume a parallel-plate configuration.) The diameter of an atom is on the order of 1010 m = 1 . Express the plate separation in angstroms.arrow_forwardSuppose a biological membrane with a specific capacitance of 1 μF/cm^2 has a resting surface charge density of 0.1 μC/cm^2. Also suppose there are 50 sodium channels per μm^2 and thatwhen each opens for 1 ms, 1000 Na+ ions flow through the channel, resulting in a reduction of the potential difference (the membrane voltage). Compare this membrane’s resting potentialvoltage to the membrane voltage 1 ms after 10% of these channels open, assuming no other changes occur during this time.arrow_forward
- In a typical mammalian cell, the net transport by the sodiumpotassium exchange pump that maintains the 70 mV membrane potential is 500 singly charged ions per second. How much work does the pump do each second?arrow_forwardAn axon is the relatively long tail-like part of a neuron. The outer surface ofthe axon membrane (dielectric constant = 5, thickness = 1 x10 -8 m) ischarged positively, and the inner portion is charged negatively. Thus, themembrane is a kind of capacitor. Assuming that an axon can be treatedlike a parallel plate capacitor with a plate area of 5 x 10 -6 m 2 , what is itscapacitance?arrow_forwardWhat is the energy stored in such a cell membrane if the potential difference across it is 7.05×10−2 VV ? Express your answer using two significant figures.arrow_forward
- a potential difference of V = 85.1 V is applied across a capacitor arrangement with capacitances C1 = 10.3 μF, C2 = 5.37 μF, and C3 = 3.75 μF. If capacitor 3 undergoes electrical breakdown so that it becomes equivalent to conducting wire, what is the increase in (a) the charge on capacitor 1 and (b) the potential difference across capacitor 1?arrow_forwardA 20uF capacitor is charged to 120 V and then disconnected from the power supply. If a second uncharged capacitor with capacitance of 50uF is connected across the first capacitor, what would be the resulting voltage across their parallel combination?arrow_forward
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