Chapter 27: Q. 71 (page 765)

71. A long, round wire has resistance $R$ . What will the wire's resistance be if you stretch it to twice its initial length?

Short Answer

Expert verified

The wire's resistance, if stretch to twice its initial length, is $4 R$ .

Step by step solution

Given information

A long, round wire has resistance $R$ . Resistance of the wire is $R = ρ \frac{L}{A},$ where p indicates the resistivity, L is the length and A is the cross sectional area.

Explanation

In the initial state of the wire will be,
$R = ρ \frac{L}{A}$
In elongation, the volume is the quantity that doesn't switch, but the density accomplishes. This indicates that the product of the length with the cross-section surface area is stable. To discover the area after the stretching as,
$L A = L^{'} A^{'} \Rightarrow A^{'} = \frac{L}{L^{'}} A$
The resistance of the elongated wire evolves:
$R^{'} = ρ \frac{L^{'}}{A^{'}} = \frac{A}{A^{'}} \frac{L^{'}}{L} R$

Find the ratio from previous term,
$\frac{A}{A^{'}} = \frac{L^{'}}{L}$

Applying,

$R^{'} = {(\frac{L^{'}}{L})}^{2} R$

$R^{'} = 2^{2} R$

$= 4 R .$

Therefore, The wire's resistance, if stretch to twice its initial length, is $4 R$

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71. A long, round wire has resistance $R$ . What will the wire's resistance be if you stretch it to twice its initial length?

Short Answer

Step by step solution

Given information

Explanation

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71. A long, round wire has resistanceR. What will the wire's resistance be if you stretch it to twice its initial length?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Measurements

Fundamentals of Physics

Further Mechanics and Thermal Physics

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Conservation of Energy and Momentum

Magnetism

Study anywhere. Anytime. Across all devices.

71. A long, round wire has resistance $R$ . What will the wire's resistance be if you stretch it to twice its initial length?