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Physics / Physics with MasteringPhysics 4 / Chapter 21 / Problem 113GP

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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A long, thin wire has a resistance R. The wire is now cut

Chapter 21, Problem 113GP

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QUESTION:

Problem 113GP

A long, thin wire has a resistance R. The wire is now cut into three segments of equal length, which are connected in parallel. In terms of R, what is the equivalent resistance of the three wire segments?

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QUESTION:

Problem 113GP

A long, thin wire has a resistance R. The wire is now cut into three segments of equal length, which are connected in parallel. In terms of R, what is the equivalent resistance of the three wire segments?

ANSWER:

Step 1 of 2

Here we need to find the equivalent resistance of the three wire segments which are connected in parallel. The segments are made from the wire with resistance $R$ . The wire is cut into three equal segments with equal lengths and they are connected in parallel configuration.

The resistance of the wire is given by,

$R=\rho{}\frac{L}{A}$

Where $\rho{}$ is resistivity of the wire, $L$ and $A$ are the length and area of the wire.

In the given case, for all the three wire segment the resistivity and area remains same so we have

$R\prec{}L$

Therefore, the resistance of the individual segments can be written as,

${R}_{1}={R}_{2}={R}_{3}=\frac{R}{3}$ …….1

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