What is the resistance of \"24-Gauge\" copper wire which has a diameter of 0.511

Question

What is the resistance of "24-Gauge" copper wire which has a diameter of 0.511 mm and a length of 10 cm? Copper has a resistivity of 1.68 times 10^8 Ohm m. If a 0.100 A current flows through the wire, what is the current density in the wire? A fuse in an electric circuit is a wire that is designed to melt, and thereby open the circuit if the current exceeds a predetermined value. Suppose that the material to be used in a fuse melts when the current density rises to 200 A/cm^2. What diameter of wire should be used to make a fuse that will limit the current to 0.50 A?

Explanation / Answer

a)
r = 0.511/2 mm = 0.2555 mm = 2.555*10^-4 m
A = pi*r^2
= pi*(2.555*10^-4)^2
=2.051*10^-7 m^2
  
R = rho*L/A
= 1.68*10^-8 * 0.1 / (2.051*10^-7)
=8.19*10^-3 ohm
  
b)
current density = current/ Area
=0.1/(2.051*10^-7)
               = 4.876*10^5 A/m^2
              
c)
200 A/cm^2 = current/ Area
200 = 0.50/(pi*r^2)
r= 0.0282 cm
=0.282 mm

diameter = 2r
= 2*0.282 mm
       = 0.564 mm

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.