Answer:
Step-by-step explanation:
Given that,
Gauge of copper is 24 or 26
The resistance of a wire is given as
R=ρl/A
Where R is resistance on ohms
ρ is resistivity in ohm•m
L is length of wire in m
A is area of cross sectional area m²
R/l = ρ/A
First wire
24 gauge wire has a R/l of 137Ω/mile
Second wire
26gauge wire has a R/l of 220Ω/mile
Both material are made of copper and they both have the same resistivity
R/l = ρ/A
Then,
ρ=RA/l
for 24 gauge
ρ=137A'
A' means area of 24 gauge wire
For 26 gauge
ρ=220A''
A'' means area of 26 gauge wire.
So, the resistivity are equal
Also, the cross section area is given as πr²= πd²/4
Resistivity 24 =Resistivity gauge 26
137A'=220A"
The ratio of diameter gauge 24 to 26 is what we want
137•πd'²/4 =220•πd"²/4
Then,
137•d'² =220•d"²
d'²/d"²=220/137
d'²/d"²=1.60584
Take square of both sides
d'/d"=1.267
the ratio of the diameter of 24-gauge wire to that of 26-gauge wire is 1.27 to 3s.f