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Chapter 27: Q. 10 (page 762)

The current in a $100 w a t t$ lightbulb is $0.85 A$ . The filament inside the bulb is $0.25 mm$ in 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 $1.7 路 10^{7} A / m^{2} .$

b. The electron current in the filament islocalid="1648891656477" $5.3 脳 10^{18} e l e c t r o n / s .$

Step by step solution

01

Given Information (Part a)

Lightbulb power $= 100 w a t t$

Current $= 0.85 A$

Filament diameter $= 0.25 m m$

02

Explanation (Part a)

Let $I = 0.85 A$ and $d = 0.25 mm$ ,

The area of the wire is

$A = \frac{d^{2}}{4} 蟺,$

So the current density is

role="math" localid="1648891197210" $j = \frac{I}{A} = \frac{4 I}{d^{2} 蟺}$

Substitute the values,

$j = (\frac{4 (0.85 A)}{{(0.25 m m)}^{2} 脳 3.14})$

role="math" localid="1648891297578" $= 1.7 路 10^{7} A / m^{2}$

03

Final Answer (Part a)

Hence, the current density is $= 1.7 路 10^{7} A / m^{2}$

04

Given Information (Part b)

Lightbulb power $= 100 w a t t$

Current $= 0.85 A$

Filament diameter $= 0.25 mm$

05

Explanation (Part b)

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

$I_{e} = \frac{I}{e}$

I_{e} = (\frac{0.85 A}{1.6 脳 10^{- 19} C})

$= 5.3 鈰� 10^{18} electrons / s$

06

Final Answer (Part b)

Hence, the electron current in the filament is $5.3 脳 10^{18} e l e c t r o n / s .$

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Most popular questions from this chapter

Suppose a time machine has just brought you forward from $1750$ (post-Newton but pre-electricity) and you've been shown the lightbulb demonstration of FIGURE Q27.1. Do observations or simple measurements you might make-measurements that must make sense to you with your $1700' s$ knowledge-prove that something is flowing through the wires? Or might you advance an alternative hypothesis for why the bulb is glowing? If your answer to the first question is yes, state what observations and/or measurements are relevant and the reasoning from which you can infer that something must be flowing. If not, can you offer an alternative hypothesis about why the bulb glows that could be tested?

The total amount of charge in coulombs that has entered a wire at time $t$ is given by the expression localid="1648639892228" $Q = 4 t - t^{2}$ , where $t$ is in seconds and $t 鈮� 0$ .
a. Find an expression for the current in the wire at time $t$ .
b. Graph $I$ versus $t$ for the interval $0 鈮� t 鈮� 4 s$ .

20. What electric field strength is needed to create a $5.0 A$ current in a $2.0$ -mm-diameter iron wire?

72. You've decided to protect your house by placing a $5.0$ -m-tall iron lightning rod next to the house. The top is sharpened to a point and the bottom is in good contact with the ground. From your research, you've learned that lightning bolts can carry up to $50 kA$ of current and last up to $50 渭 s$ .

a. How much charge is delivered by a lightning bolt with these parameters?
b. You don't want the potential difference between the top and bottom of the lightning rod to exceed $100 V$ . What minimum diameter must the rod have?.

$1.0 脳 10^{20}$ electrons flow through a cross-section of a $2.0 mm$ diameter iron wire in $5.0 s$ . What is the electron drift speed?

See all solutions

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