How to Calculate the Resistance Between the Ends of a Rubber Band

If you place two fingers inside a rubber band and pull them apart, you will notice that the rubber band makes this movement more difficult than it would otherwise be. This is because the rubber band's shape allows it to resist your pulling. The strength of this force, known as resistance, will depend upon several physical aspects of the rubber band. Using a common physics equation, you can calculate this value in terms of ohms, a unit also used for electrical resistance calculations.

Things You'll Need

  • Scientific calculator
  • Millimeter ruler
  • Scissors
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Instructions

    • 1

      Measure the length and diameter of the rubber band. Cut the rubber band and extend it along the side of a ruler, pulling it slightly so that it is straight and fully retracted but not enough so that it stretches. Measure its diameter to the nearest millimeter by placing the face of the end you cut onto your ruler.

    • 2

      Convert your length units to meters. For example, suppose you measure your rubber band to be 15 cm in length and have a diameter of 3 mm. Keeping in mind that there are 100 cm per meter and 1,000 mm per meter, convert the values as follows: 15/100 = .15 m; 3/1000 = .003 m.

    • 3

      Plug your values into the equation R =ρ(L/A), where "ρ" is the resistivity of rubber (1.0 x 10^13), "L" is the length of the rubber band in meters and "A" is its cross-sectional area, represented by the equation A=πr^2, where "π" is 3.14 and "r" is the radius, or one-half of the diameter you measured (in meters). Calculate the area first, which for the example rubber band is: π(.003/2)^2 = π(.0015)^2 = π(.00000225) = .000007065. Plug this value into the main equation as such: R = ρ(L/A) = (1.0 x 10^13)(.15/.000007065) = (1.0 x 10^13)(21,231.4225) = 2.12 x 10^16 ohms.

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