A rectangular copper strip is 20cm long, 0.1cm wide and 0.4cm thick. Determine the resistance between (I) opposite ends (II) opposite sides. The resistivity of copper is 1.7 x 10-6ohm m
To determine the resistance between opposite ends of a rectangular copper strip, you can use the formula:
Resistance (R) = Resistivity (ρ) * Length (L) / Cross-sectional Area (A)
Where:
- Resistivity (ρ) is the resistivity of copper (1.7 x 10^-6 ohm m)
- Length (L) is the length of the strip (20 cm or 0.2 m)
- Cross-sectional Area (A) = Width (W) * Thickness (T)
Given that the width (W) of the strip is 0.1 cm (0.001 m) and the thickness (T) is 0.4 cm (0.004 m), we can calculate the cross-sectional area (A):
A = 0.001 m * 0.004 m
Now substitute the values into the formula:
R (opposite ends) = (1.7 x 10^-6 ohm m) * (0.2 m) / (0.001 m * 0.004 m)
Simplify the equation:
R (opposite ends) = (1.7 x 10^-6 ohm m) * (0.2 m) / (4 x 10^-6 m^2)
Cancel out units and multiply:
R (opposite ends) = (1.7 x 0.2) / 4 ohms
Solve for the resistance:
R (opposite ends) = 0.34 / 4 ohms
R (opposite ends) = 0.085 ohms
Therefore, the resistance between opposite ends of the rectangular copper strip is approximately 0.085 ohms.
To determine the resistance between opposite sides of the strip, we need to consider the new cross-sectional area, which is the product of the length (L) and width (W):
A (opposite sides) = 0.2 m * 0.001 m
Now substitute the new cross-sectional area into the formula:
R (opposite sides) = (1.7 x 10^-6 ohm m) * (0.2 m) / (0.001 m * 0.001 m)
Simplify the equation:
R (opposite sides) = (1.7 x 10^-6 ohm m) * (0.2 m) / (1 x 10^-6 m^2)
Cancel out units and multiply:
R (opposite sides) = (1.7 x 0.2) / 1 ohms
Solve for the resistance:
R (opposite sides) = 0.34 ohms
Therefore, the resistance between opposite sides of the rectangular copper strip is 0.34 ohms.