The specific resistance of manganin is 50 × 10^-8 ohm × m. The resistance of a cube of length 50 cm will be.

Understand the Problem

The question is asking to calculate the resistance of a cube of manganin given its specific resistance and length. The specific resistance is provided, and we need to apply the formula for resistance in terms of resistivity and dimensions to find the answer.

Answer

The resistance of the cube is $1 \times 10^{-6} \, \text{ohm}$.

Steps to Solve

Identify the variables
We have the specific resistance (resistivity) $\rho = 50 \times 10^{-8} , \text{ohm} \cdot \text{m}$ and the length of the cube $L = 50 , \text{cm} = 0.5 , \text{m}$.
Calculate the cross-sectional area of the cube
For a cube, the area ( A ) can be calculated as:
$$ A = \text{side}^2 $$ Since the cube's side is the same as the length, we have: $$ A = (0.5)^2 = 0.25 , \text{m}^2 $$
Use the resistance formula
The formula for resistance $ R $ in terms of resistivity is given by:
$$ R = \rho \frac{L}{A} $$ Substituting in the known values: $$ R = (50 \times 10^{-8}) \frac{0.5}{0.25} $$
Calculate the resistance
Calculating the fraction and multiplication:
$$ R = (50 \times 10^{-8}) \cdot 2 = 100 \times 10^{-8} = 1 \times 10^{-6} , \text{ohm} $$

The resistance of the cube is $R = 1 \times 10^{-6} , \text{ohm}$.

More Information

The resistivity of materials like manganin is often used in precision resistances due to their stable properties over varying temperatures. Manganin's specific resistance is very low, which makes it an ideal choice for applications requiring minimal fluctuation in resistance.

Tips

Forgetting to convert units from cm to m, which may lead to incorrect resistance calculations. It is crucial to keep units consistent.
Confusing the formulas; ensure to use the correct relationship for resistance involving resistivity, length, and cross-sectional area.

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