What is the resistance of a 2.5 m length of copper wire 1.3 mm in diameter?
Given by,
lenth (L)=2.5mm,Diameter of copper wire =1.3mm,R=?,A=?
A=S=PIE(D/2)squre
s=3.14*(1.3/2)square
=3.14x0.65x0.65 mm
=3.14x0.4225 mm
=1.32665 mm
A=1.32665mm
R=l/A
=2.5/1.32665
=1.9x10-2 ohm
To calculate the resistance of a wire, we need two pieces of information: the resistivity of the material the wire is made of, and the dimensions of the wire. In this case, the wire is made of copper.
The resistivity of copper is typically given as 1.68 x 10^-8 Ω·m (ohm-meter). However, since we know the dimensions of the wire, we can also use a slightly simplified formula that accounts for the wire's length, cross-sectional area, and resistivity.
First, let's calculate the cross-sectional area of the wire. The formula for the area of a circle is A = πr^2, where A is the area and r is the radius of the circle. However, we are given the diameter of the wire, so we need to divide it by 2 to find the radius.
Given that the diameter is 1.3 mm, the radius is 0.65 mm or 0.65 x 10^-3 m.
Calculating the area using the formula:
A = π(0.65 x 10^-3 m)^2
Next, we need to calculate the resistance of a wire using the formula:
R = (ρ * L) / A
Where R is the resistance, ρ is the resistivity of copper (1.68 x 10^-8 Ω·m), L is the length of the wire, and A is the cross-sectional area of the wire.
Given that the length of the wire is 2.5 meters:
R = (1.68 x 10^-8 Ω·m * 2.5 m) / A
Now, we can substitute the value of A we calculated earlier:
R = (1.68 x 10^-8 Ω·m * 2.5 m) / [π(0.65 x 10^-3 m)^2]
Simplifying this equation will give us the resistance of the wire. Let's calculate it.