Question

Два алюминиевых провода имеют одинаковую массу. Диаметр первого провода в 2 раза больше, чем диаметр второго. Какой из проводов имеет большее сопротивление и во сколько раз? 15 баллов даю

Answer 1

Ответ:

В 16 раз

Объяснение:

Площадь сечения пропорциональна квадрату диаметра, значит площади различаются в 4 раза. Т. к. объемы равны, длины проводов также отличаются в 4 раза.

Из формулы R=p*L/S сопротивление второго провода R2= p*(4*L)/(S/4)=16R, т. е. в 16 раз больше.

Answer 2

Comparison of Two Aluminum Wires with Different Diameters

To determine which of the two aluminum wires has a greater resistance and by how much, we need to consider their diameters and the relationship between resistance and diameter.

Let's assume that the diameter of the first wire is 2x and the diameter of the second wire is x.

Relationship between Diameter and Resistance

The resistance of a wire is inversely proportional to its cross-sectional area. The cross-sectional area of a wire is directly proportional to the square of its diameter. Therefore, the resistance of a wire is inversely proportional to the square of its diameter.

Mathematically, the relationship can be expressed as:

Resistance ∝ 1 / (Diameter^2)

Comparing the Resistance of the Two Wires

Since the diameter of the first wire is twice that of the second wire, we can calculate the ratio of their resistances.

Let's denote the resistance of the first wire as R1 and the resistance of the second wire as R2.

According to the relationship mentioned above, we can write:

R1 ∝ 1 / (2x)^2 = 1 / (4x^2)

R2 ∝ 1 / x^2

To compare the resistances, we can calculate the ratio:

R1 / R2 = (1 / (4x^2)) / (1 / x^2) = 1 / 4

Therefore, the first wire has a resistance that is 1/4 times the resistance of the second wire.

Conclusion

In summary, the first wire, which has a diameter twice that of the second wire, has a resistance that is 1/4 times the resistance of the second wire.

Please note that the above explanation is based on the relationship between resistance and diameter. If there are any additional factors or specific conditions that need to be considered, please provide more information for a more accurate analysis.