In an experiment to determine the specific resistance ( ) of a wire, the formula used is = R d^2 4l , where R is the resistance, d is the diameter, and l is the length of the wire. If the maximum permissible percentage error in the determination of is 8 % , and the measured percentage errors in R and l are 2 % and 1 % respectively, what is the maximum permissible percentage error in the measurement of the diameter (

Step-by-step solution

The formula for specific resistance is = R d^2 4l . The maximum percentage error in is given by the sum of the percentage errors of the individual quantities, taking into account their powers. Errors always add up to give the maximum possible error, regardless of whether the quantity is in the numerator or denominator: 100 = R R 100 + 2 ( d d 100 ) + l l 100 Given that the maximum percentage error in is 8 % , in R is 2 % , and in l is 1 % , we can substitute these values into the equation: 8 % = 2 % + 2 ( percentag