Chapter 27: Q. 33 (page 763)

Pencil "lead" is actually carbon. What is the current if a $9.0 V$ potential difference is applied between the ends of a $0.70 mm$ diameter, $6.0 c m$ long lead from a mechanical pencil?

Short Answer

Expert verified

If $9.0 V$ potential difference is applied between the ends of a $0.70 mm$ diameter, $6.0 c m$ long lead from a mechanical pencil, then the current is $1.7 A$ .

Step by step solution

Given Information

Potential difference $= 9.0 V$

Pencil lead diameter $= 0.70 m m$

Pencil lead length $= 6.0 c m$

Explanation

Set $Δ V = 9.0 V, d = 0.70 mm$ and $l = 6.0 cm$ .

The electric field in the lead is given by

$E = \frac{Δ V}{l}$

So the current density is,

$J = σ E = σ \frac{Δ V}{l} .$

The current is given by

$I = J A,$

Where $A = \frac{1}{4} r^{2} π$ is the cross-section area of the wire,

$I = σ \frac{A}{l} Δ V$

Modify the expression,

$= σ \frac{d^{2} π}{4 l} Δ V$

From Table 27.2 in the book the conductivity of Carbon is $2.9 \times 10^{4} Ω^{- 1} m^{- 1}$ ,

$I = 1.7 A$

Final Answer

Hence, the current is $1.7 A$ .

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Pencil "lead" is actually carbon. What is the current if a $9.0 V$ potential difference is applied between the ends of a $0.70 mm$ diameter, $6.0 c m$ long lead from a mechanical pencil?

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Pencil "lead" is actually carbon. What is the current if a 9.0V potential difference is applied between the ends of a 0.70mm diameter, 6.0cmlong lead from a mechanical pencil?

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

Measurements

Turning Points in Physics

Mechanics and Materials

Electrostatics

Conservation of Energy and Momentum

Magnetism

Study anywhere. Anytime. Across all devices.

Pencil "lead" is actually carbon. What is the current if a $9.0 V$ potential difference is applied between the ends of a $0.70 mm$ diameter, $6.0 c m$ long lead from a mechanical pencil?