The woman in the photo at the start of the chapter is gripping a device that passes a small current through her body. How does this permit a determination of body fat?
The exact details of how the device works are beyond the scope, but the basic principle is quite straight-forward: The device applies a small potential difference and measures the resulting current. Comparing multiple measurements allows the device to determine the resistance of one part of the body, the upper arm. The resistance of the upper arm depends sensitively on the percentage of body fat in the upper arm, and the percentage of body fat in the upper arm is a good predictor of the percentage of fat in the body overall. Let’s make a simple model of the upper arm to show how the resistance of the upper arm varies with the percentage of body fat.
The model of a person’s upper arm shown ignores the nonconductive elements (such as the skin and the mineralized portion of the bone) and groups the
a. An experimental subject’s upper arm, with the dimensions shown in the figure, is 40% fat and 60% muscle. A potential difference of 0.60 V is applied between the elbow and the shoulder. What current is measured?
b. A 0.60 V potential difference applied to the upper arm of a second subject with an arm of similar dimensions gives a current of 0.87 mA. What are the percentages of muscle and fat in this person’s upper arm?
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