The resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

6%

zero

1%

3%

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Solution

straight R space equals space straight V over straight i rightwards double arrow space open vertical bar fraction numerator increment straight R over denominator straight R end fraction close vertical bar space equals space open vertical bar fraction numerator increment straight V over denominator straight V end fraction close vertical bar space plus open vertical bar fraction numerator increment straight i over denominator straight i end fraction close vertical bar fraction numerator increment straight V over denominator straight V end fraction space straight x 100 space equals space 3 rightwards double arrow fraction numerator increment straight V over denominator straight V end fraction space equals space 0.03 Similarly comma space fraction numerator increment space straight i over denominator straight i end fraction space equals space 0.03 Hence comma space fraction numerator increment straight R over denominator straight R end fraction space equals space 0.06 percent sign error space equals space fraction numerator increment straight R over denominator straight R end fraction space straight x 100 equals space 6 percent sign

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