   Chapter 17, Problem 50P

Chapter
Section
Textbook Problem

A tungsten wire in a vacuum has length 15.0 cm and radius 1.00 mm. A potential difference is applied across it. (a) What is the resistance of the wire at 293 K? (b) Suppose the wire reaches an equilibrium temperature such that it emits 75.0 W in the form of radiation. Neglecting absorption of any radiation from its environment, what is the temperature of the wire? (Note: e = 0.320 for tungsten.) (c) What is the resistance of the wire at the temperature found in part (b)? Assume the temperature changes linearly over this temperature range. (d) What voltage drop is required across the wire? (e) Why are tungsten lightbulbs energetically inefficient as light sources?

(a)

To determine
The resistance of wire at 273K

Explanation

Given Info: The tungsten wire has length 15.0cm and radius is 1.00mm

Explanation:

Formula to calculate the resistance of wire A is,

R0=ρLA

• R is the resistance of tungsten wire,
• ρ is the resistivity of tungsten
• L is the length of the tungsten wire,
• A is the area of circular cross section of the wire,

Formula to find the area is ,

A=πr2

• r is the radius of circular cross section of the wire,

Substitute the above relation in the previous equation to rewrite R,

R0=ρLπr2

Substitute 5.6×108Ωm for ρ , 15.0cm for L , 3.14 for π and 1.00mm for r in the above equation to find R

R0=(5

(b)

To determine
The temperature of the wire

(c)

To determine
The resistance of wire at temperature 1445.68K

(d)

To determine
The voltage drop across the wire

(e)

To determine
The reason for inefficiency of tungsten bulb as a light source.

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