Modeling the Cardiovascular System with an Electrical Circuit

The electrical circuit / fluid system analogy allows us to construct a circuit which mimmicks the behavior of the cardiovascular system. Simplifying that system for the sake of the experiment, we break the system up into three parallel subsystems between the aorta and vena cava:

The resistance of the vena cava is half that of the aorta.

For this experiment, we will need a power supply, a milliammeter, a voltmeter, an ohmmeter, 5 resistors (as close as possible to 500, 1000, 41K, 43K and 123K W ("ohms"); you may use multiple resistors in series for each of these resistors as convenient), a breadboard and wire.

Name:

Lab Partners:

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

Procedure

The color codes on the resistors begin at the end where the colored band is on the edge of the resistor. The first two encode the significant digits of a number between 10 and 99, and the last is the power of ten by which that number is multiplied:

((C1 * 10) + C2) x 10C3.

The colors are:

black = 0 yellow = 4 violet = 7
brown = 1 green = 5 gray = 8
red = 2 blue = 6 white = 9
orange = 3

So a code of "yellow, violet, red" would signify a 4700 W resistor (also called "4.7 K").

  1. Measure the resistance of each of the resistors (or combinations) with the ohmmeter:

    Expected Resistance Measured Resistance
    500 WR500 = W
    1000 WR1000 = W
    41K WR41K = W
    43K WR43K = W
    123K WR123K = W

  2. Construct the following circuit:

    where I is the milliammeter and V is the voltmeter. It is usually convenient to put the resistors on the breadboard first, and then add the wires. Be careful when bending wires and leads.

  3. Turn the power supply on and set it at 8 volts. Verify the output with the voltmeter:

    Vpower supply: V
    Record the voltage drop in Volts across the resistors:
    V500: V

    V1000: V

    V41K: V

    V43K: V

    V123K: V

    Turn the power supply off. All drops should be recorded as positive.

  4. Move the milliammeter to be in series with each of the resistors in turn (which necessitates breaking and reconnecting the circuit), and measure the current in Amperes:
    I500: A

    I1000: A

    I41K: A

    I43K: A

    I123K: A

    Turn the power supply off whenever changing the circuit. Use the 200 mA range for the resistors in parallel.

Analysis

  1. Verify Ohm's Law and Kirchoff's Laws for the circuit. You will have to check Ohm's Law for each of the resistors:
    I500 R500 = V = V500 ?

    I1000 R1000 = V = V1000 ?

    I41K R41K = V = V41K ?

    I43K R43K = V = V43K ?

    I123K R123K = V = V123K ?

    and Kirchoff's "junction" law:
    I41K + I43K + I123K = A

    = I1000 ?= I500 ?

    It will suffice to check the "loop" law for one loop:

    V500 + V1000 + V41K = V

    = Vpower supply ?

    and verify that the voltage drops across the parallel resistors were equal:

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

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