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Chapter 27: Q. 10 (page 762)

The current in a 100wattlightbulb is 0.85A. The filament inside the bulb is 0.25mmin diameter.

a. What is the current density in the filament?

b. What is the electron current in the filament?

Short Answer

Expert verified

a. The current density is 1.7·107A/m2.

b. The electron current in the filament islocalid="1648891656477" 5.3×1018electron/s.

Step by step solution

01

Given Information (Part a)

Lightbulb power=100watt

Current=0.85A

Filament diameter=0.25mm

02

Explanation (Part a) 

Let I=0.85Aand d=0.25mm,

The area of the wire is

A=d24π,

So the current density is

role="math" localid="1648891197210" j=IA=4Id2π

Substitute the values,

j=4(0.85A)(0.25mm)2×3.14

role="math" localid="1648891297578" =1.7·107A/m2

03

Final Answer (Part a)

Hence, the current density is=1.7·107A/m2

04

Given Information (Part b)

Lightbulb power=100watt

Current=0.85A

Filament diameter=0.25mm

05

Explanation (Part b)

The electron current is equal to the current divided by the magnitude of the charge of the electron,

Ie=Ie

Ie=0.85A1.6×10-19C

=5.3⋅1018electrons/s

06

Final Answer (Part b)

Hence, the electron current in the filament is5.3×1018electron/s.

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Most popular questions from this chapter

The resistivity of a metal increases slightly with increased temperature. This can be expressed as ρ=ρ01+αT-T0, where T0is a reference temperature, usually 20°C, and αis the temperature coefficient of resistivity. For copper, α=3.9×10-3C∘-1. Suppose a long. thin copper wire has a resistance of 0.25Ωat 20°C. At what temperature, in C∘, will its resistance be 0.30Ω?

The wires leading to and from a 0.12mmdiameter lightbulb filament are 1.5mm in diameter. The wire to the filament carries a current with a current density of role="math" localid="1648887651623" 4.5×105A/m2. What are (a) the current and (b) the current density in the filament?

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a. A battery supplies the energy to a circuit.

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c. A battery is a source of current; the current leaving the battery is always the same.

FIGURE P27.42 shows a 4.0cmwide plastic film being wrapped onto a 2.0cmdiameter roller that turns at 90rpm.The plastic has a uniform surface charge density of −2.0nC/cm2.

a. What is the current of the moving film?

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