Ohm's law states that the current flowing through a conductor is directly proportional to the voltage applied across it, given that the temperature and other physical conditions remain constant. Mathematically, Ohm's law is expressed as:

V = I * R

where V represents the voltage across the conductor, I represents the current flowing through the conductor, and R represents the resistance of the conductor.

When a wire is stretched to double its length while maintaining its original cross-sectional area, the resistance of the wire increases, but the resistivity remains unchanged.

The resistance of a wire is directly proportional to its length. By doubling the length of the wire, the resistance also doubles. This relationship is given by the formula R = ρL/A, where R is the resistance, ρ is the resistivity, L is the length, and A is the cross-sectional area.

However, the resistivity of a material...

If we have two wires, each with a resistance of R, the minimum resistance that can be obtained by combining them in a specific way is R/4.

To achieve this minimum resistance, the wires need to be connected in parallel. When two resistors are connected in parallel, the total resistance is given by the formula:

1/R_total = 1/R1 + 1/R2

In this case, substituting R for both R1 and R2, we get:

1/R_total = 1/R + 1/R = 2/R

Taking the reciprocal of both sides:

R_total = R/2

Therefore, the ratio of the...