Question

Во сколько раз увеличится/уменьшится сопротивление проводника: а)при уменьшении длины в два раза; б)при увеличении площади поперечного сечения в три раза?

Answer 1

R=rho*L/S
L в числителе, R ~ L. Если L уменьшается в 2 раза, то и R уменьшается в 2 раза.
S в знаменателе, R ~ 1/S. Если S увеличивается в 3 раза, то R уменьшается в 3 раза.

Answer 2

Calculating Change in Resistance

To calculate the change in resistance of a conductor, we can use the following formulas:

a) When the length is reduced by half: The resistance of a conductor is directly proportional to its length. Therefore, if the length is reduced by half, the resistance will also be halved.

b) When the cross-sectional area is increased threefold: The resistance of a conductor is inversely proportional to its cross-sectional area. When the cross-sectional area is increased threefold, the resistance will be reduced to one-third of its original value.

Let's cite the relevant search snippets to support these calculations:

a) When the length is reduced by half: According to Source "l" and "S" are mentioned in the context of resistance and length, indicating a direct relationship between length and resistance.

b) When the cross-sectional area is increased threefold: Source discusses the relationship between resistance and the cross-sectional area, indicating an inverse relationship. It mentions the factor "3" in relation to the change in resistance due to a change in the cross-sectional area.

These relationships align with the formulas and principles of resistance in conductors.