Question

What is the potential difference across one wire of a 70 m extension cord made of 16 gauge copper wire carrying a current of 4 A at room temperature (20degrees Celsius)

Answer 1

V = 3.6 volts

Step-by-step explanation:

From Ohm's Law, we know that:

V = IR

but,

R = ρL/A

Therefore,

V = IρL/A

where,

V = Potential Difference = ?

I = Current = 4 A

ρ = resistivity of copper = 1.68 x 10⁻⁸ Ω.m

L = Length = 70 m

A = Cross-sectional Area = πd²/4 = π(1.29 x 10⁻³ m)²/4 [16 gauge wire has a diameter of 1.29 mm]

A = 1.31 x 10⁻⁶ m²

V = (4 A)(1.68 x 10⁻⁸ Ω.m)(70 m)/(1.31 x 10⁻⁶ m²)

V = 3.6 volts