Lecture 6 - Lord Kelvin and the transatlantic cable....

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Lord Kelvin and the transatlantic cable. How does the signal (dots and dashes) attenuate with distance along the cable? The so-called “cable equations.” (1824-1907)
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The attenuation of the signal with distance to ~1/3 its value is one space constant ( λ ).
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Membrane capacitance and resistance Most biological membranes have a unit capacitance (C M ) of ~1 μ F/cm 2 . The membrane resistance of biological membranes varies dramatically depending on which channels are open. Membrane resistance can change over a few milliseconds as channels open or close.
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If an axon were a perfect conductor, current going in one end would come out the other end without attenuation .
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However, axons are imperfect conductors and current leaks out across the membrane as well a flowing down the axon. The amount of current that flows down the axon is related to the ratio between the membrane resistance (r m ) and the internal or axoplasmic resistance (r i ) . That is, r m /r i . r i r m
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If r i > r m , all of the current would run out across the membrane and the axon would be “shorted out.” If r m > r i , current will run down the axon but some will leak out along the way. If r m >>>> r i most of the current will run along the axon and little will leak out. r i r m
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How do the dimensions of an axon influence r i and r m ? R
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Lecture 6 - Lord Kelvin and the transatlantic cable....

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