if a copper wire is stretched to make0.1percent longer,then the percentage change in the resistance is
Answers
Answer:
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.
I hope u understand .
Answer: