Find change in resistance for mercury-tube breathing monitor

[JJaX]

AP Physics Help--Emergency

My physics teacher sometimes gives out rediculously difficult worksheets. I'm having trouble with one problem in particular:

A breathing monitor girds a patient with a mercury-filled rubber tube and measures the variation on tube resistance. The tube has an unstretched length of 1.25 m and inside diameter of 2.51 mm. The monitor is connected to a 100-mV power supply, and the total resistance of the circuit is that due to the mercury plus 1.00 Ω (an internal resistance of the power supply). Determine the change of current through the monitor as the patient draws a breath and stretches the hose by 10.0 cm. Take ρ(Hg) = 9.40 x 10^(-7) Ω ◦ m.

Any help would be greatly appreciated.

 

[M98Ranger]

To find the change in resistance for the mercury-tube breathing monitor, we can use the formula for resistance, R = ρL/A, where ρ is the resistivity of the material, L is the length of the tube, and A is the cross-sectional area of the tube.

First, we need to find the initial resistance of the mercury-filled rubber tube. We can calculate the cross-sectional area using the formula A = πr^2, where r is the radius of the tube. The radius can be found by dividing the inside diameter by 2, so r = 1.255 mm = 0.001255 m.

Using this value for the radius, we can calculate the initial cross-sectional area as A = π(0.001255 m)^2 = 4.94 x 10^-6 m^2.

Next, we can calculate the initial resistance of the tube using the formula R = ρL/A. Plugging in the given values, we get R = (9.40 x 10^-7 Ω ◦ m)(1.25 m)/(4.94 x 10^-6 m^2) = 0.238 Ω.

Now, we need to find the change in resistance when the tube is stretched by 10.0 cm. We can use the same formula, but with a new length of 1.35 m. This gives us a new resistance of R = (9.40 x 10^-7 Ω ◦ m)(1.35 m)/(4.94 x 10^-6 m^2) = 0.256 Ω.

To find the change in resistance, we can subtract the initial resistance from the final resistance. This gives us a change in resistance of 0.256 Ω - 0.238 Ω = 0.018 Ω.

Finally, we can use Ohm's Law (V = IR) to find the change in current through the monitor. Since the power supply is connected to a 100-mV power supply, we can use this voltage to find the change in current. We can rearrange the formula to solve for current, I = V/R. Plugging in the values, we get I = (0.100 V)/(0.018 Ω) = 5.56 A.

So, the change in current through the monitor as the patient draws a breath