Question

A tungsten wire has a radius of 0.080 mm and is heated from 20.0 to 1392 oC. The temperature coefficient of resistivity is α = 4.5 x 10-3 (Co)-1. When 100 V is applied across the ends of the hot wire, a current of 1.5 A is produced. How long is the wire? Neglect any effects due to thermal expansion of the wire.

Answer 1

The length of the wire is 3.75 m

Step-by-step explanation:

Using ohm's law as:

Voltage = Current*Resistance

V = IR

So,

R = V/I = 100 / 1.5 = 66.6667 ohm

Using equation for temperature sensitivity for resistance as:

`R = R_0( 1 + \alpha \Delta T)`

Given,

α = 4.5 x 10⁻³ (Co)⁻¹

ΔT = (1392 - 20.0) °C = 1372 °C

So,

66.6667 = R₀ (1 + 0.0045*1372 )

R₀ = 9.2928 ohm

Resistivity of tungsten = 5.60 × 10⁻⁸ ohm.m

Considering,

R = pL/A

Where,

R is the resistance

p is the resistivity

L is the length

A is the area which is equal to πr²

Given,

r = 0.080 mm = 0.080*10⁻³ m

9.2928 = 5.6*10⁻⁸ *L / π*(0.080*10⁻³)^2

L = 3.33 m