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A student measures the resistance, diameter, and length of a wire to determine its electrical resistivity. The measured values are: Resistance, R = (10.0 0.1) , Diameter, d = (2.00 0.02) mm Length, l = (50.0 0.5) cm The maximum percentage error in the calculated value of resistivity is:

Options

  1. A3
  2. B2
  3. C4
  4. D5

Correct answer

C. 4

Step-by-step solution

The formula for the electrical resistivity of a wire is given by: = R A l = R ( d^2 / 4) l The maximum fractional error in resistivity is the sum of the fractional errors of the individual quantities (with the power of d bringing a factor of 2): = R R + 2 d d + l l Calculating the individual percentage errors: Percentage error in R = ( 0.1 10.0 ) 100 = 1 % Percentage error in d = ( 0.02 2.00 ) 100 = 1 % Percentage error in l = ( 0.5 50.0 ) 100 = 1 % Substituting these into the error equation: Maximum percentage err

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