Aluminum wire with a resistance of 25 ohms, is 10 m long. Determine the diameter of the wire.

1. Let’s write down the condition of the problem:

R = 25 Ohm

l = 10 m

ρ = 0.028 Ohm × mm2 / m

d -?

2. Formula of wire resistance:

R = ρ × l / A

Based on this, the cross-sectional area is equal to:

A = ρ × l / R

Substitute the numbers from the condition and calculate:

A = 0.028 Ohm × mm2 / m × 10 m / 25 Ohm

A = 0.0112 mm2

3. Formula for the area of a circle:

A = πr2

From this, the radius is:

r = √ A / p

Let’s calculate:

r = √ 0.0112 mm2 / 3.14

r = √ 0.0036 mm2

r = 0.06 mm

4. Formula of diameter:

d = 2r

Let’s calculate:

d = 2 × 0.06 mm

d = 0.12 mm

5. Let’s write down the answer:

Answer: d = 0.12 mm