Chapter 27: Q. 55 (page 764)

II You need to design a $1.0 A$ fuse that "blows" if the current exceeds $1.0 A$ . The fuse material in your stockroom melts at a current density of $500 A / {cm}^{2}$ . What diameter wire of this material will do the job?

Short Answer

Expert verified

The diameter wire of the material is find by the given current $1.0 A$ and density $500 A / {cm}^{2}$ by using current density formula $J = \frac{I}{A}$ and get the diameter of the wire as $0.5 m m$ .

Step by step solution

Given information

When the fuse "blows" if the current exceeds $1.0 A$ the fuse, material in the stockroom melts at a current density $500 A / {cm}^{2}$ .

Explanation

The wire will blow if the current reaches a density of $500 A / m^{2}$ .

The current density is role="math" localid="1648620008873" $J = \frac{I}{A} = \frac{4 I}{π D^{2}}$
To find the diameter for a provided current density and current by,
$D = \sqrt{\frac{4 I}{π J}}$
In numerical chance,
role="math" localid="1648620366993" $D = \sqrt{\frac{4 \times 1 A}{π \times 500 A / {cm}^{2}}}$

role="math" localid="1648620375079" $D = \sqrt{\frac{4 \times 1 A}{22 / 7 \times 500 A / {cm}^{2}}}$

$D = \sqrt{0.0025}$

role="math" localid="1648619723131" $D = 0.05 c m$

The diameter wire of the material is $0.5 m m$ .

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II You need to design a $1.0 A$ fuse that "blows" if the current exceeds $1.0 A$ . The fuse material in your stockroom melts at a current density of $500 A / {cm}^{2}$ . What diameter wire of this material will do the job?

Short Answer

Step by step solution

Given information

Explanation

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II You need to design a 1.0Afuse that "blows" if the current exceeds 1.0A. The fuse material in your stockroom melts at a current density of 500A/cm2. What diameter wire of this material will do the job?

Short Answer

Step by step solution

Given information

Explanation

One App. One Place for Learning.

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II You need to design a $1.0 A$ fuse that "blows" if the current exceeds $1.0 A$ . The fuse material in your stockroom melts at a current density of $500 A / {cm}^{2}$ . What diameter wire of this material will do the job?