Final answer:
When a wire is stretched and its length is increased, the resistance of the wire also increases. In this case, when the length of a wire is stretched to four times its original length, the resistance increases by a factor of 4.
Step-by-step explanation:
When the length of a cylindrical wire is increased to double its original length, the resistance of the wire changes as well. The resistance R of a wire is given by the formula R = ρ(L/A), where ρ is resistivity, L is the length of the wire, and A is the cross-sectional area.
When a wire is stretched and its length is increased, the resistance of the wire also increases. In this case, the wire is stretched to four times its original length. The factor by which the resistance increases can be calculated using the formula:
R2 = (L2/L1) * R1
where R2 is the new resistance, L2 is the new length, L1 is the original length, and R1 is the original resistance. Since the length is stretched to four times its original length, L2/L1 = 4. Therefore, the resistance increases by a factor of 4.