Chapter 27: Q.22 (page 762)

22. A $3.0$ -mm-diameter wire carries a $12 A$ current when the electric field is $0.085 V / m$ . What is the wire's resistivity?

Short Answer

Expert verified

The wire's resistivity is $5 \times 10^{- 8} Ω m$ .

Step by step solution

Given information

A $3.0$ -mm-diameter wire carries a $12 A$ current when the electric field is $0.085 V / m$ .

Explanation

The current density is, $J = σ E$ ,
Rewrite as,

$J = \frac{E}{ρ}$

From this, the resistivity is, $ρ = \frac{E}{J}$

The current density by applying its definition:

$J = \frac{I}{A} = \frac{4 I}{π d^{2}}$

Substituting this expression in the one for the resistivity,
$ρ = \frac{π E d^{2}}{4 I}$
$ρ = \frac{π \times 0.085 V / m \times 0 . 003^{2} m}{4 \times 12 A}$

$= 5 \times 10^{- 8} Ω m$

Final answer

The wire's resistivity is $5 \times 10^{- 8} Ω m$ .

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22. A $3.0$ -mm-diameter wire carries a $12 A$ current when the electric field is $0.085 V / m$ . What is the wire's resistivity?

Short Answer

Step by step solution

Given information

Explanation

Final answer

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22. A 3.0-mm-diameter wire carries a 12A current when the electric field is 0.085V/m. What is the wire's resistivity?

Short Answer

Step by step solution

Given information

Explanation

Final answer

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Radiation

Torque and Rotational Motion

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Study anywhere. Anytime. Across all devices.

22. A $3.0$ -mm-diameter wire carries a $12 A$ current when the electric field is $0.085 V / m$ . What is the wire's resistivity?