A piece of gold wire is used to form a circular loop of radius 12.3 cm. The wire has a cross-sectional area of 11.1 mm^2. Points A and B are 90.0° apart. Find the resistance between points A and B.
To find the resistance between points A and B, we need to use the formula for resistance:
R = (ρ * L) / A
where R is the resistance, ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.
The resistivity (ρ) of gold is a constant value, which is 2.44 x 10^(-8) ohm-meter.
First, let's find the length of the wire. The circumference of a circle is given by the formula:
C = 2 * π * r
where C is the circumference and r is the radius of the circle.
Substituting the given radius into the equation, we get:
C = 2 * π * 12.3 cm
Next, we need to convert the circumference from centimeters to meters:
C = 2 * π * 0.123 m
Now, using the formula for length:
L = C/2
L = (2 * π * 0.123 m) / 2
Next, we need to convert the cross-sectional area from mm^2 to m^2. Since 1 mm^2 = 10^(-6) m^2, we have:
A = 11.1 mm^2 * (10^(-6) m^2 / 1 mm^2)
Finally, we can substitute the values we found into the resistance formula:
R = (2.44 x 10^(-8) ohm-meter * (2 * π * 0.123 m)) / (11.1 mm^2 * (10^(-6) m^2))
Simplifying the equation gives you the resistance between points A and B.