Bioelectrical impedance analysis is a commercially available method used to esti

Question

Bioelectrical impedance analysis is a commercially available method used to estimate body fat percentage. The device applies a small potential between two parts of the patient's body and measures the current that flows through. With an estimate of the resistance individually of the muscle and fat between the two points, the composition of the tissue can be estimated. Assume that the muscle and fat tissue can be modeled as resistors in parallel.

Part A

If the resistance of fat is 3 times that of muscle, what is the resistance of fat if a 1 mA current is measured when potential difference of 0.5 V is applied to the patient's arm?

Part B

If the resistance through the fat is 6 times that through the muscle, how much of the total current goes though the fat in terms of the current through the muscle?

Part C

If a potential difference of 1 V is applied across the patient's arm, what is the potential drop across the patient's fat?

Part D

If the measured resistance of the patient's arm is 750 and the resistance of fat is 3 times that of muscle, what is the resistance of the muscle?

Explanation / Answer

A)

r = resistance of muscle

R = resistance of fat

given that : R = 3r

Rtotal = total resistance = R r /(R + r) = 3r2 /4r= 0.75 r

V = potential difference = 1 Volts

i = current = 1 mA = 0.001 A

Using ohm's law

V = i Rtotal

0.5 = (0.001) (0.75r)

r = 666.67

R = 3r = 3 x 666.67 = 2000

hence 2000 ohm

b)

1/6 times the current through muscle.

since muscle and fat are in parallel , they have same voltage across each , hence

imuscle Rmuscle = ifat Rfat

imuscle Rmuscle = ifat (6)Rmuscle

ifat = (1/6) imuscle

c)

since fat and muscle are in parallel

hence Vfat = 1 Volts

d)

Rarm = arm resistance = 750

Rfat = fat resistance

Rmuscle = muscle resistance

given that

Rfat = 3 Rmuscle

since fat and muscle are in parallel their combination is given as

Rarm = Rfat Rmuscle /(Rfat + Rmuscle )

750 = (3 Rmuscle )Rmuscle /((3 Rmuscle)+ Rmuscle )

750 = 3 Rmuscle /4

Rmuscle = 1000

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