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$A wire of resistance R = 10 Ω is stretched to double its original length. What will be the new resistance of the wire?$

A. $10 Ω$
B. $20 Ω$
C. $40 Ω$
D. $80 Ω$

Show correct answer & step-by-step solution

Correct answer: C — $40 Ω$

Solution

Since volume V = A \cdot L is constant, stretching the wire to L^{'} = 2 L results in A^{'} = A /2 . Using R = ρ L / A, the new resistance R^{'} = ρ (2 L) / (A /2) = 4 R = 40 Ω .

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