## Question

what length of copper wire, 0.462 mm in diameter, has a resistance of 1.00 ω?

**Answer:**

The task that we have at hand involves determining the length of a copper wire with a diameter of 0.462 mm that exhibits a resistance of 1.00 Ω. Therefore, the length of the copper wire can be ascertained by employing the formula that relates resistance, length, and the material’s resistivity. The given resistance, R = 1.00 Ω, and the diameter, d = 0.462 mm. Thus, the final answer to the above question is 9.98 m.

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### Image Explanation

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### Text **Explanation:**

**Data:** Information revealed from the question

- Resistance, R = 1.00 Ω
- Diameter, d = 0.462 mm

**Step 1: Convert Diameter to Radius**

The first step involves converting the diameter to the radius (r). Given that the diameter (d) = 0.462 mm, the radius (r) = d/2 = 0.462/2 = 0.231 mm.

**Step 2: Convert Radius to Meters**

For consistency in units, we will need to convert the radius which is in millimetres (mm) into meters (m) by dividing it by 1000. This is because 1 m equals 1000 mm.

Therefore, r = 0.231 mm / 1000 = 0.000231 m.

**Step 3: Calculate Cross-Sectional Area**

In addition to what we have done, we can now determine the cross-sectional area (A) of the wire by using the formula for the area of a circle, where A = πr^{2}.

**Step 4: Apply Ohm’s Law**

In this step, we will apply the formula for resistivity, which is ** ρ = RA/L**

We will need to rearrange the above formula to solve for length (L). Thus, **L = RA/ ρ**

However, * ρ* is the resistivity of copper, a constant (1.68 x 10

^{-8}Ωm)

**Solution:**

**Step 5: Substitute Values From Data and Solve for Length**

L = **RA/ ρ = (πr^{2} x 1Ω) / (1.68 x 10^{-8} Ωm)** [Remember that A = πr

^{2}]

Additionally, since r = 0.000231 m = 2.31 x 10^{-4} m

and π = 3.142

We can comfortably write:

L = **= (πr ^{2} x 1Ω) / (1.68 x 10^{-8} Ωm)**

**= (3.142 x (0.000231m)**

^{2}x 1Ω) / (1.68 x 10^{-8}Ωm)Therefore, L = 9.98 m

**Thus, upon solving for Length ( L ), the length of the copper wire is found to be approximately 9.98 meters.**

Therefore, a copper wire with a diameter of 0.462mm and a resistance of 1.00Ω has a length of approximately 9.98m.

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