Resistivity of Copper Wire

In summary, the 12-gauge copper wire with a radius of 1.03×10−3 m has a resistivity of 1.7E-8 ohm meters. For part a, using the equation R=ρ(L/A) and A=∏r2, the resistance of 11.5 m of this wire at 20°C is 0.0587 ohms. For part b, a potential difference of 9.00 V applied across the wire results in a current of 1.54 A. The incorrect answer was due to incorrect usage of significant figures.
  • #1
Snape1830
65
0
12-gauge copper wire has a radius of 1.03×10−3 m. (a) What is the resistance of 11.5 m of this wire at 20°C. (b) How much current will pass through the wire if a potential difference of 9.00 V is applied across it?
The resistivity for copper is 1.7E-8 ohm meters
For part a:
The equation is R=ρ(L/A) and A=∏r2.
I solved for Area and got 3.33E-6 m2.
Then I did R=1.7E-8(11.5/3.33E-6)
R=.0587 ohms.

However, when I plug this into the system it says it's wrong. What did I do incorrectly? I double-checked my multiplication and everything.
 
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  • #2
Never mind, it was sig figs
 

1. What is the resistivity of copper wire?

The resistivity of copper wire is approximately 1.68 x 10^-8 ohm-meters at room temperature. This value may vary slightly depending on the purity and quality of the copper used.

2. How does the diameter of copper wire affect its resistivity?

The resistivity of copper wire is inversely proportional to its cross-sectional area. This means that as the diameter of the wire increases, the resistivity decreases. This is why thicker wires have lower resistance and are better for conducting electricity.

3. What factors can affect the resistivity of copper wire?

The resistivity of copper wire can be affected by factors such as temperature, impurities in the copper, and the composition of the wire's alloy. Higher temperatures and impurities can increase the resistivity, while a purer copper and specific alloy composition can decrease it.

4. How is the resistivity of copper wire measured?

The resistivity of copper wire is typically measured using a four-point probe method, where four evenly spaced probes are placed on the wire and a current is passed through it. The voltage drop across the probes is then measured and used to calculate the resistivity of the wire.

5. Why is copper a popular choice for electrical wiring?

Copper is a popular choice for electrical wiring due to its low resistivity, high conductivity, and ability to withstand high temperatures. It is also affordable, readily available, and has good corrosion resistance, making it a reliable choice for long-term use in electrical systems.

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