What will be the resistance R(stretched) of the wire if it is stretched to twice its original length? Assume that the density and resistivity of the material do not change when the wire is stretched.
Resistance of a wire in Ω
R = ρL/A
ρ is resistivity of the material in Ω-m
L is length in meters
A is cross-sectional area in m²
A = πr², r is radius of wire in m
If you stretch it to double the length, the volume stays constant.
cylinder V = πr²h
so if h is doubled, for V to stay constant, the area ( πr² ) gets cut in half.
from the equation above, doubling the length will multiply the R by 2
Also from that equation, cutting the area in half will multiply the R by 2
so net result is the resistance is 4x the original value.
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