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BabaBlast [244]
3 years ago
12

A ductile metal wire has resistance R. What will be the resistance of this wire in terms of R if it is stretched to three times

its original length, assuming that the density and resistivity of the material do not change when the wire is stretched. (Hint: The amount of metal does not change, so stretching out the wire will affect its cross-sectional area.)
Physics
1 answer:
Ira Lisetskai [31]3 years ago
6 0

Answer:

9R

Explanation:

We know that the resistance is R=\rho *\frac{L}{A}.

If we stretch the wire to a new length L2 = 3L, the cross-sectional area will also change. If the cross-sectional area doesn't change throughout the wire, we can say that:

Volume = L*A = 3L * A2    being A2 the new area after stretching the wire.

Since the volume remains the same we conclude that A2 = A/3

With this information, we calculate the new resistance:

R2=\rho *\frac{L2}{A2}=\rho *\frac{3*L}{A/3}=\rho * 9 * \frac{L}{A}

Since R=\rho *\frac{L}{A}, and by simple inspection of the previous equation, we get:

<em>R2 = 9*R</em>

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