Question # The resistance ( mathrm{R} ) of a wire is given by the relation

# The resistance ( mathrm{R} ) of a wire is given by the relation

( mathrm{R}=frac{rho ell}{pi r^{2}} . ) Percentage error in the measurement of ( rho, ell ) and ( r ) is ( 1 %, 2 % ) and ( 3 % ) respectively. Then the percentage error in the measurement of ( mathrm{R} ) is

(1) ( 6 % )

(2) ( 9 % )

(3) ( 8 % )

(4) ( 10 % )

Solution

( begin{aligned} P &=frac{rho 1}{pi r^{2}} frac{Delta R}{R} &=frac{Delta R}{rho} pm frac{D L}{l}+2 frac{Delta r}{r} &=1+2 pm 2(3) &=90 quad(2) Ans{}_{} end{aligned} )