Question

an wire is stretched to make it 0.1% longer then find percentage change in its resistance

Answer 1

The resistance will be increased by 0.2%. Explanation is given below:

Equation of the resistance is:

R = ρ*L/A (ρ is resistivity, L is length and A is area of the conductor)

Let initial area be A1, length be L1 and Resistance be R1.

Therefore equation of initial resistance R1 is:

R1 = ρ*L1/A1

After stretching, the length increases by 0.1% ie. 1.001 times. As volume is same, area is expected to be reduced by inverse of this i.e. 1/1.001 times. Therefore  R2 (new value of resistance) will be:

R2 =  ρ*(1.01L1)/(A1/1.001) = ρ*(1.001*1.001)*L1)/(A1) = ρ*1.002*L1/A1

Ratio of new resistance to original resistance is:

R2/R1 =(ρ*1.002*L1/A1)/(ρ*L1/A1)

= 1.002

= 100.2%. Hence percentage change is 0.2% increase.