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Find the resistance whose length is 1 km , diameter is 0.5 mm and resistivity is 1.7*10↑-8?
Most Upvoted Answer
Find the resistance whose length is 1 km , diameter is 0.5 mm and resi...
Length=1 km=1000m
Radius=0.25 mm=0.25*10⁻³ m
Resistivity =1.72x10⁻⁸
Resistance=(Resistivity * Length)/(Area)
                  =(Resistivity * Length)/(πr²)
Resistance=[1.72*10⁻⁸*1000]/[22/7*(0.25*10⁻³)²
Resistance=22 ohm
Community Answer
Find the resistance whose length is 1 km , diameter is 0.5 mm and resi...
Understanding Resistance Calculation
To find the resistance of a conductor, we can use the formula:
R = ρ * (L/A)
where:
- R is the resistance in ohms (Ω)
- ρ (rho) is the resistivity of the material in ohm-meters (Ω·m)
- L is the length of the conductor in meters (m)
- A is the cross-sectional area in square meters (m²)
Given Values
- Length (L) = 1 km = 1000 m
- Diameter (d) = 0.5 mm = 0.0005 m
- Resistivity (ρ) = 1.7 × 10^-8 Ω·m
Calculating the Cross-Sectional Area (A)
- The formula for the area of a circle is: A = π * (r²)
- First, find the radius: r = d/2 = 0.0005 m / 2 = 0.00025 m
- Now, calculate A:
A = π * (0.00025 m)²
A ≈ 1.9635 × 10^-7 m²
Calculating the Resistance (R)
- Substitute the values into the resistance formula:
R = 1.7 × 10^-8 Ω·m * (1000 m / (1.9635 × 10^-7 m²))
R ≈ 86.5 Ω
Final Result
- The resistance of the conductor is approximately 86.5 ohms (Ω).
This calculation helps understand how the physical dimensions and material properties influence the resistance of electrical conductors.
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Find the resistance whose length is 1 km , diameter is 0.5 mm and resistivity is 1.7*10↑-8?
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