A wire of length 1.0 m has a resistance of It is uniformly stretched to a length of 2.0 m . What is its new resistance?
To find the new resistance of the wire when it is stretched, we need to consider the relationship between resistance and length for a wire. The resistance of a wire is directly proportional to its length.
We can use the formula:
Resistance (R) = resistivity (ρ) × length (L) / cross-sectional area (A)
In this case, the length of the wire is doubled; therefore, the new length of the wire is 2.0 m. The initial length of the wire is 1.0 m.
Since we are only stretching the wire without changing its cross-sectional area, the resistivity and cross-sectional area remain constant.
We can set up a proportion to find the new resistance:
1.0 m / initial resistance = 2.0 m / new resistance
Cross-multiplying the above equation, we get:
1.0 m × new resistance = 2.0 m × initial resistance
new resistance = (2.0 m × initial resistance) / 1.0 m
Simplifying further, we have:
new resistance = 2.0 × initial resistance
Therefore, when the wire is stretched to a length of 2.0 m, its new resistance is twice the initial resistance.