Modeling an Axon with an Electrical Circuit

This experiment implements the model developed in the text.

We will need a square wave generator, seven resistors (as close as possible to 200K, four 12K and two 58K ohms), a .001 mF capacitor, an oscilloscope and probe, a breadboard, wire and a multimeter.

Name:

Lab Partners:

When entering numeric data, use exponentials: ie., 1.6 * 10-19 = 1.6E-19.

Procedure

  1. Measure the resistor and capacitor values with the multimeter:

    Expected Value Measured Value
    12K W (top left)R12K, 1 = W
    12K W (top right)R12K, 2 = W
    12K W (bottom left)R12K, 3 = W
    12K W (bottom right)R12K, 4 = W
    58K W (left)R58K, 1 = W
    58K W (right)R58K, 2 = W
    200K WR200K = W
    .001 mFC = mF

    Construct the following circuit:

  2. Use channel 2 for the oscilloscope input. Adjust the output frequency of the generator to about 1 kHz, the output amplitude to about 100 mV and the horizontal sweep rate of the oscilloscope until a single waveform appears on the screen. The waveform should be gently sloping; if it is linear, reduce the frequency on the generator. Record the resulting time per division (one division = approximately 1 cm on the screen):
    Time / div = ms / div
    Adjust the amplitude of the generator and/or the gain of the oscilloscope until the waveform fills the screen. Record the voltage per division:
    Volts / div = mV / div
    In storage mode, depress the Save CH2 button to freeze the image. Record the number of divisions between the lowest and highest voltage and compute the voltage difference:
    Dy div =

    DV = Dy div * Volts / div

    = mV
    Compute the number of divisions corresponding to a voltage 15 mV above the lowest voltage:
    y15 mV = ( 15 / DV ) * Dy div

    = divisions
    Record the number of divisions horizontally from the lowest voltage to y15 mV and compute the time it takes for the wave to rise from its lowest voltage to 15 mV above its lowest:
    Dx div =

    Dt = Dx div * Time / div

    = ms
    and to its highest voltage:
    Dxmax div =

    Dtmax = Dxmax div * Time / div

    = ms

  3. Draw the waveform you observed above, as well as the waveform of the generator input.

Analysis

  1. Why do we use square waves?

  2. Calculate the equivalent resistance and the time constant:
    Requivalent = 1 / ( 1 / ( R12K, 1 + R12K, 3 + R58K, 1 ) + 1 / R200K + 1 / ( R12K, 2 + R12K, 4 + R58K, 2 ) )
    = W
    t = Requivalent * C
    = ms

    Compare the time constant to the time computed for the 15 ms rise above:

©2004, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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