A uniform stripe of eureka (resistivity 5-0 × 〖10〗^(-7) Ωm) has a resistance of 0.80 Ω per metre and is 0.25 cm wide. What is its thickness?
(show work)
0.025cm
We can use the following formula to solve for the thickness of the stripe:
Resistance = (resistivity x length) / area
We are given the resistance (0.80 Ω/m), resistivity (5.0 x 10^-7 Ωm), and width (0.25 cm) of the stripe. We need to solve for the area and then use that to find the thickness.
First, we need to convert the units to meters:
width = 0.25 cm = 0.0025 m
Next, we can rearrange the formula to solve for the area:
area = (resistivity x length) / resistance
area = (5.0 x 10^-7 Ωm) / (0.80 Ω/m)
area = 6.25 x 10^-7 m^2
Finally, we can use the formula for the area of a rectangle to solve for the thickness:
area = width x thickness
thickness = area / width
thickness = (6.25 x 10^-7 m^2) / (0.0025 m)
thickness = 0.00025 m = 0.025 cm
Therefore, the thickness of the eureka stripe is 0.025 cm.
To find the thickness of the uniform stripe of Eureka, we can use the formula for resistance:
Resistance = (Resistivity × Length) / Area
Given:
Resistance = 0.80 Ω/m
Resistivity = 5.0 × 10^(-7) Ωm
Width of the stripe = 0.25 cm = 0.0025 m
To find the thickness, we need to calculate the area of the stripe first. The area of a rectangle is given by:
Area = Length × Width
In this case, the width is given as 0.0025 m. However, we don't have the length of the stripe. However, we can rearrange the formula for resistance to solve for length:
Length = (Resistance × Area) / Resistivity
Plugging in the given values:
Length = (0.80 Ω/m × 0.0025 m) / (5.0 × 10^(-7) Ωm)
Simplifying the expression:
Length = 4.0 m
Now that we have the length, we can find the thickness using the formula:
Thickness = Area / Length
Plugging in the values:
Thickness = (0.0025 m) / (4.0 m)
Simplifying the expression:
Thickness = 0.000625 m
Therefore, the thickness of the uniform stripe of Eureka is 0.000625 meters.