The resistivity of the body is a good measure of its overall composition. A meas

Question

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. FAT : 25ohm, MUSCLE: 13 ohm, BONE: non conductive

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?

Explanation / Answer

area=A=5.0265*10^(-3)
l=0.2 m
resistance due to fat=Rf=25*0.2/(0.3*A)=3315.72 ohms
resistance due to muscle=13*0.2/(0.7*A)=738.94 ohms
so total resistance=(they are in parallel)=604.35 ohms
(b)
10% muscle

resistance due to fat=Rf=25*0.2/(0.9*A)=1105.25ohms
resistance due to muscle=13*0.2/(0.1*A)=5172.58 ohms
so total resistance=(they are in parallel)=910.66ohms area=A=5.0265*10^(-3)
l=0.2 m
resistance due to fat=Rf=25*0.2/(0.3*A)=3315.72 ohms
resistance due to muscle=13*0.2/(0.7*A)=738.94 ohms
so total resistance=(they are in parallel)=604.35 ohms
(b)
10% muscle

resistance due to fat=Rf=25*0.2/(0.9*A)=1105.25ohms
resistance due to muscle=13*0.2/(0.1*A)=5172.58 ohms
so total resistance=(they are in parallel)=910.66ohms area=A=5.0265*10^(-3)
l=0.2 m
resistance due to fat=Rf=25*0.2/(0.3*A)=3315.72 ohms
resistance due to muscle=13*0.2/(0.7*A)=738.94 ohms
so total resistance=(they are in parallel)=604.35 ohms
(b)
10% muscle

resistance due to fat=Rf=25*0.2/(0.9*A)=1105.25ohms
resistance due to muscle=13*0.2/(0.1*A)=5172.58 ohms
so total resistance=(they are in parallel)=910.66ohms

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