Download Measuring Body Fat the Problem

Measuring Body Fat
The resistivity of the body is a good measure of its overall composition. A measure of the resistance of
the upper arm is a good way to estimate the percent fat in a person’s body. Let’s model a person’s
upper arm as a cylinder of diameter 8.0 cm and length 20 cm. We can model the composition of the arm
by assuming that the muscle, far, and nonconductive portions (the bone) form simple regions. This
simple model actually works quite well. For a typical adult, the bone has a cross-sectional area of 1.0
cm2; to a good approximation, the balance of the arm is fatty tissue or muscle.
A.
Assume that the arm has 30% fat and 70% muscle. What is the resistance of the arm?
B.
Now, assume that the arm has only 10% muscle. What is the resistance now?
The measurement of the resistance of the arm is made by applying a voltage and measuring a current.
Too much current can be uncomfortable and, as we will see, can be dangerous. Suppose we wish to limit
the current to 1.0 mA. For each of the above cases, what is the maximum voltage that could be
employed?