Question

What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.47ohms d=...

What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.47ohms


d= _________m

0 0
Add a comment Improve this question Transcribed image text
Answer #1
Concepts and reason

The concept used to solve this problem is resistance of the conductor.

Initially, use the expression in terms of resistance, resistivity, length of the wire, and area of cross section to find the area of cross section of the tungsten wire.

Then, use the value of area to find the diameter of the tungsten wire.

Fundamentals

The expression for resistance of the conducting wire is,

R=ρLAR = \frac{{\rho L}}{A}

Here, RR is the resistance, ρ\rho is the resistivity, LL is the length of the wire, and AA is the area of cross section.

The expression for area of cross section of the wire is,

A=πr2A = \pi {r^2}

Here, rr is the radius of the wire.

Expression for the diameter is,

d=2rd = 2r

Here, dd is the diameter.

The expression for resistance of the conducting wire is,

R=ρLAR = \frac{{\rho L}}{A}

Rearrange the above expression for AA.

A=ρLRA = \frac{{\rho L}}{R}

Substitute 5.6×108Ωm5.6 \times {10^{ - 8}}\,\Omega \cdot {\rm{m}} for ρ\rho , 1.00m1.00\,{\rm{m}} for LL, and 0.47Ω0.47\,\Omega for RR.

A=(5.6×108Ωm)(1.00m)(0.47Ω)=1.19×107m2\begin{array}{c}\\A = \frac{{\left( {5.6 \times {{10}^{ - 8}}\,\Omega \cdot {\rm{m}}} \right)\left( {1.00\,{\rm{m}}} \right)}}{{\left( {0.47\,\Omega } \right)}}\\\\ = 1.19 \times {10^{ - 7}}\,{{\rm{m}}^2}\\\end{array}

Therefore, the area of cross section of the wire is 1.19×107m21.19 \times {10^{ - 7}}\,{{\rm{m}}^2}.

The expression for area of cross section of the wire is,

A=πr2A = \pi {r^2}

Rearrange the above expression for rr.

r=Aπr = \sqrt {\frac{A}{\pi }}

Substitute 1.19×107m21.19 \times {10^{ - 7}}\,{{\rm{m}}^2} for AA and 3.143.14 for π\pi .

r=1.19×107m23.14=1.9467×104m1.95×104m\begin{array}{c}\\r = \sqrt {\frac{{1.19 \times {{10}^{ - 7}}\,{{\rm{m}}^2}}}{{3.14}}} \\\\ = 1.9467 \times {10^{ - 4}}\,{\rm{m}}\\\\ \approx 1.95 \times {10^{ - 4}}\,{\rm{m}}\\\end{array}

Expression for the diameter is,

d=2rd = 2r

Substitute 1.95×104m1.95 \times {10^{ - 4}}\,{\rm{m}} for r.

d=2(1.95×104m)=3.90×104m\begin{array}{c}\\d = 2\left( {1.95 \times {{10}^{ - 4}}\,{\rm{m}}} \right)\\\\ = 3.90 \times {10^{ - 4}}\,{\rm{m}}\\\end{array}

Therefore, the diameter of the tungsten wire is 3.90×104m3.90 \times {10^{ - 4}}\,{\rm{m}}.

Ans:

The diameter of the tungsten wire is 3.90×104m3.90 \times {10^{ - 4}}\,{\rm{m}}.

Add a comment
Know the answer?
Add Answer to:
What is the diameter of a 1.00-m length of tungsten wire whose resistance is 0.47ohms d=...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for? Ask your own homework help question. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT