Q30: Plethysmographs are devices used for measuring changes in the volume of internal organs or limbs. In one form of this device, a rubber capillary tube with an inside diameter of mm is filled with mercury at C. The resistance of the mercury is measured with the aid of electrodes sealed into the ends of the tube. If m of the tube is wound in a helix around a patient’s upper arm, the blood flow during a heart- beat causes the arm to expand, stretching the length of the tube by m. From this observation and assuming cylindrical symmetry, you can find the change in volume of the arm, which gives an indica- tion of blood flow. Taking the resistivity of mercury to be V ? m, calculate
(a) the resistance of the mercury and
(b) the fractional change in resistance during the heartbeat. Hint: The fraction by which the cross-sectional area of the mercury column decreases is the fraction by which the length increases because the volume of mercury is constant.