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# bio Attenuator Chains and Axons. The infinite network of ISBN: 9780321675460 31

## Solution for problem 93CP Chapter 26

University Physics | 13th Edition

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Problem 93CP

bio Attenuator Chains and Axons. ?The infinite network of resistors shown in Fig. P26.83 is known as an ?attenuator chain, ?since this chain of resistors causes the potential difference between the upper and lower wires to decrease, or attenuate, along the length of the chain. (a) Show that if the potential difference between the points ?a ?and ?b ?in Fig. 26.83 is ?Vab ?, then the potential difference between points ?c ?and ?d ?is ?V?cd? ?= ?V?ab?/(?1 + ?), where ? = 2?R?1(?R?T + ?R?2)/?R?T?R?2 and R?T, the total resistance of the network, is given in Challenge 26.83. (See the hint given in that problem.) (b) If the potential difference between terminals ?a and ?b ?at the left end of the infinite network is ?V?0, show that the potential difference between the upper and lower wires ?n ?segments from the left end is ?V?n = ?V?0/(1 + ?)n. I? ?1 =? ?2, how many segments are needed to decrease the potential difference ?V?n? ?to less than 1.0% of ?V?0? (c) An infinite attenuator chain provides a model of the propagation of a voltage pulse along a nerve fiber, or axon. Each segment of the network in Fig. P26.83 represents a short segment of the axon of length ??x?. The resistors ?R?1 represent the resistance of the fluid inside and outside the membrane wall of the axon. The resistance of the membrane to current flowing through the wall is represented by ?R?2. For an axon segment of length ? x? ?= 1.0 mm, ?R? = 6.4 * 103 ? and ?R2? = 8.0 × 108 ? (the membrane wall is a good insulator). Calculate the total resistance ?R?T and b for an infinitely long axon. (This is a good approximation, since the length of an axon is much greater than its width; the largest axons in the human nervous system are longer than 1 m but only about 10-7 m in radius.) (d) By what fraction does the potential difference between the inside and outside of the axon decrease over a distance of 2.0 mm ? (e) The attenuation of the potential difference calculated in part (d) shows that the axon cannot simply be a passive, current-carrying electrical cable; the potential difference must periodically be reinforced along the axon’s length. This reinforcement mechanism is slow, so a signal propagates along the axon at only about 30 m/s. In situations where faster response is required, axons are covered with a segmented sheath of fatty myelin. The segments are about 2 mm long, separated by gaps called the ?nodes of Ranvier?. The myelin increases the resistance of a 1.0-mm-long segment of the membrane to ?R?2 = 3.3 × 1012 ?. For such a myelinated axon, by what fraction does the potential difference between the inside and outside of the axon decrease over the distance from one node of Ranvier to the next? This smaller attenuation means the propagation speed is increased.

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WEEK OF 4/4 – 4/8 NOTES IONIZATION ENERGY Ionization Energy – closely related to effective nuclear charge, energy when one mol of electron is removed by a gas, forming a cation - INCREASES across a period - DECREASES down a group o Because of shielding on the outer e-, more shielding means easier to pluck an electron off IE1 < IE2

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##### ISBN: 9780321675460

Since the solution to 93CP from 26 chapter was answered, more than 262 students have viewed the full step-by-step answer. The answer to “bio Attenuator Chains and Axons. ?The infinite network of resistors shown in Fig. P26.83 is known as an ?attenuator chain, ?since this chain of resistors causes the potential difference between the upper and lower wires to decrease, or attenuate, along the length of the chain. (a) Show that if the potential difference between the points ?a ?and ?b ?in Fig. 26.83 is ?Vab ?, then the potential difference between points ?c ?and ?d ?is ?V?cd? ?= ?V?ab?/(?1 + ?), where ? = 2?R?1(?R?T + ?R?2)/?R?T?R?2 and R?T, the total resistance of the network, is given in Challenge 26.83. (See the hint given in that problem.) (b) If the potential difference between terminals ?a and ?b ?at the left end of the infinite network is ?V?0, show that the potential difference between the upper and lower wires ?n ?segments from the left end is ?V?n = ?V?0/(1 + ?)n. I? ?1 =? ?2, how many segments are needed to decrease the potential difference ?V?n? ?to less than 1.0% of ?V?0? (c) An infinite attenuator chain provides a model of the propagation of a voltage pulse along a nerve fiber, or axon. Each segment of the network in Fig. P26.83 represents a short segment of the axon of length ??x?. The resistors ?R?1 represent the resistance of the fluid inside and outside the membrane wall of the axon. The resistance of the membrane to current flowing through the wall is represented by ?R?2. For an axon segment of length ? x? ?= 1.0 mm, ?R? = 6.4 * 103 ? and ?R2? = 8.0 × 108 ? (the membrane wall is a good insulator). Calculate the total resistance ?R?T and b for an infinitely long axon. (This is a good approximation, since the length of an axon is much greater than its width; the largest axons in the human nervous system are longer than 1 m but only about 10-7 m in radius.) (d) By what fraction does the potential difference between the inside and outside of the axon decrease over a distance of 2.0 mm ? (e) The attenuation of the potential difference calculated in part (d) shows that the axon cannot simply be a passive, current-carrying electrical cable; the potential difference must periodically be reinforced along the axon’s length. This reinforcement mechanism is slow, so a signal propagates along the axon at only about 30 m/s. In situations where faster response is required, axons are covered with a segmented sheath of fatty myelin. The segments are about 2 mm long, separated by gaps called the ?nodes of Ranvier?. The myelin increases the resistance of a 1.0-mm-long segment of the membrane to ?R?2 = 3.3 × 1012 ?. For such a myelinated axon, by what fraction does the potential difference between the inside and outside of the axon decrease over the distance from one node of Ranvier to the next? This smaller attenuation means the propagation speed is increased.” is broken down into a number of easy to follow steps, and 488 words. This textbook survival guide was created for the textbook: University Physics, edition: 13. This full solution covers the following key subjects: axon, potential, difference, length, resistance. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460. The full step-by-step solution to problem: 93CP from chapter: 26 was answered by , our top Physics solution expert on 05/06/17, 06:07PM.

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