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A 2.1 cm length of tungsten filament in a small lightbulb has a resistance of 0.067 ω. find its diameter. the resistivity of the filament is 5.6 × 10−8 ω · m. answer in units of mm.

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egenriether
The resistance of an ohmic material is given by 
[tex]R= \frac{ \rho l}{a} [/tex]
where l is the length and a is the cross sectional area.  For a circular wire, this area is that of a circle:
[tex]R= \frac{\rho l}{ {d^2} } \frac{4}{\pi}=\frac{5.6\times10^-8 \times0.021m\times4}{\pi d^2} = \frac{1.497\times 10^-9}{d^2} [/tex]
Then solving for diameter, d:
[tex]d^2=\frac{1.497\times 10^-9}{0.067}=2.235\times10^-8 [/tex]
[tex]d=0.1495mm[/tex]
shubhamchouhanvrVT

The diameter of the wire will be given as d=0.1495 mm

What is Resistance?

The resistance is defined as the obstruction in the flow of the charge or current.

The resistance of an ohmic material is given by

[tex]R=\dfrac{\rho d}{a}[/tex]

where l is the length and a is the cross-sectional area.For a circular wire, this area is that of a circle:

[tex]R=\dfrac{\rho l}{d^2}\dfrac{4}{\pi}[/tex]

[tex]R=\dfrac{5.6\times 10^{-8}\times 0.021\times 4}{\pi d^2}[/tex]

Then solving for diameter, d:

[tex]d^2=\dfrac{1.497\times 10^{-9}}{0.067}[/tex]

d=0.1495 mm

Hence the diameter of the wire will be given as d=0.1495 mm

To know more about Resistance follow

https://brainly.com/question/17563681

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