If a wire is stretched to make it 0.1 longer, its resistance will?

R = ρl/A = ρl²/V where ρ is the resistivity, l is the length, A is the cross-sectional area, and V is the volume. If the wire is stretched, its volume remains constant, but its length and cross-sectional area change. Let the initial length be l and the initial area be A. After stretching, the length becomes 1.1l (0.1 longer). Since the volume remains constant, we have:
V = Al = (1.1l)A' where A' is the new cross-sectional area. Therefore, A' = A/1.1.
Now let's find the new resistance R':
R' = ρ(1.1l) / (A/1.1) = 1.21ρl/A = 1.21R
The new resistance is 1.21 times the original resistance. The increase in resistance is 1.21R - R = 0.21R. If we assume the initial resistance R was approximately 1 (although it's not stated in the problem), the increase is approximately 0.21 or about 0.2. Therefore, the resistance increases by approximately 0.2.