Answer :
Final Answer:
The resistance of the 1.5 m length of tungsten wire with a radius of [tex]\(5.6 \times 10^{-12}\)[/tex] m is approximately 21.09 ohms.
Explanation:
The resistance [tex](\(R\))[/tex] of a wire can be calculated using the formula:
[tex]\[R = \frac{{\rho \cdot L}}{{A}}\][/tex]
Where:
[tex]- \(R\)[/tex] is the resistance.
[tex]- \(\rho\)[/tex]is the resistivity of the material (given for tungsten).
[tex]- \(L\)[/tex] is the length of the wire (given as 1.5 m).
[tex]- \(A\)[/tex] is the cross-sectional area of the wire.
The cross-sectional area [tex](\(A\))[/tex] of the wire can be calculated using the formula for the area of a circle [tex](\(\pi r^2\))[/tex], where [tex]\(r\)[/tex] is the radius of the wire.
Given the radius [tex](\(5.6 \times 10^{-12}\) m)[/tex], we can calculate \(A\):
[tex]\[A = \pi \cdot (5.6 \times 10^{-12})^2 = 9.86 \times 10^{-23} \, \text{m}^2\][/tex]
Now, we can calculate the resistance (\(R\)) using the resistivity of tungsten [tex](\(\rho\))[/tex]:
[tex]\[\rho = 5.6 \times 10^{-8} \, \Omega \cdot \text{m}\][/tex]
[tex]\[R = \frac{{(5.6 \times 10^{-8} \, \Omega \cdot \text{m}) \cdot (1.5 \, \text{m})}}{{9.86 \times 10^{-23} \, \text{m}^2}} \approx 21.09 \, \Omega\][/tex]
So, the resistance of the 1.5 m length of tungsten wire with a radius of [tex]\(5.6 \times 10^{-12}\)[/tex] m is approximately 21.09 ohms.
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