A length L₀ of wire has a resistance of 32.0 $\Omega$.The wire is uniformly stretched to four times its original length,i.e.,4 L₀.If a length L₀ is now cut from the stretched wire,what is its resistance? A) 512 $\Omega$ B) 128 $\Omega$ C) 32.0 $\Omega$ D) 8.00 $\Omega$ E) 2.00 $\Omega$

Question

Quizplus · Accepted Answer

When the wire is stretched to four times its original length, its resistance increases by the square of the factor by which the length increases (since resistance is proportional to length and inversely proportional to the cross-sectional area, which decreases). Therefore, the new resistance of the entire wire is $32 \times 4^2 = 512 \, \Omega$. Since the wire is now 4 times longer, a length $L_0$ of the stretched wire will have a resistance of $\frac{512}{4} = 128 \, \Omega$.

A Length L0 of Wire Has a Resistance of 32 Ω\OmegaΩ

A Length L₀ of Wire Has a Resistance of 32 $\Omega$