In one form of plethysmograph (a device for measuringvolume), a rubber capillary tube with an inside diameter of1.00 mm is filled with mercury at 20°C. The resistance of themercury is measured with the aid of electrodes sealed into theends of the tube. If 100.00 cm of the tube is wound in a spiralaround a patient’s upper arm, the blood flow during a heartbeatcauses the arm to expand, stretching the tube to a lengthof 100.04 cm. From this observation, and assuming cylindricalsymmetry, you can find the change in volume of the arm,which gives an indication of blood flow. (a) Calculate the resistanceof the mercury. (b) Calculate the fractional change inresistance during the heartbeat. Take ρHg = 9.4 x 10-7 Ω ⋅ m.Hint : Because the cylindrical volume is constant, V = Ai Li = AfLfand Af = Ai(Li /Lf ).

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Asked Dec 19, 2019
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In one form of plethysmograph (a device for measuring
volume), a rubber capillary tube with an inside diameter of
1.00 mm is filled with mercury at 20°C. The resistance of the
mercury is measured with the aid of electrodes sealed into the
ends of the tube. If 100.00 cm of the tube is wound in a spiral
around a patient’s upper arm, the blood flow during a heartbeat
causes the arm to expand, stretching the tube to a length
of 100.04 cm. From this observation, and assuming cylindrical
symmetry, you can find the change in volume of the arm,
which gives an indication of blood flow. (a) Calculate the resistance
of the mercury. (b) Calculate the fractional change in
resistance during the heartbeat. Take ρHg = 9.4 x 10-7 Ω ⋅ m.
Hint : Because the cylindrical volume is constant, V = Ai Li = AfLf
and Af = Ai(Li /Lf ).

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Expert Answer

Step 1

Given,

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Initial length of mercury L, =100 cm =1 m Final length of mercury L, =100.04 cm =1.0004 m Resistivity p.=9.4×10¬' N-m Initial diameter D, = 1 mm =1×10° m =0.785×10-6 m Area of crossection of tube A, = -

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Step 2

Part (a): Resistance of the mercury:

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pL, R A, 9.4 x10- ×1 0.785 ×10- =1.197 Q

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Step 3

Part (b): The fractional change in resistance:

The volume of mercury rema...

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A,L, = A;L; A,L, A, L; and PL; R, A; pL, R; A,L, L, pL, R, A,L,

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