The product L*A remains constant after stretching. If L doubles, A decreases by 1/2
Resistance is proportional to L/A.
R2/R1 = L2/L1 *A1/A2 = 4
R1 is the original resistance and R2 is the final resistance.
Express your answer in terms of the wire's original resistance R.
Resistance is proportional to L/A.
R2/R1 = L2/L1 *A1/A2 = 4
R1 is the original resistance and R2 is the final resistance.
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R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
Since the resistivity and cross-sectional area of the wire do not change when it is stretched, we only need to focus on the change in length.
Let's denote the original length as L_0 and the stretched length as L_stretched. According to the problem, L_stretched = 2 * L_0.
Now we can find the resistance R_stretched when the wire is stretched:
R_stretched = (ρ * L_stretched) / A
= (ρ * (2 * L_0)) / A
= (2 * ρ * L_0) / A
Therefore, the resistance R_stretched of the wire when it is stretched to twice its original length is equal to 2 * R, where R is the original resistance.