A 6m conductor has a resistance of 3 ohms. A conductor made of the same metal

A 6m conductor has a resistance of 3 ohms. A conductor made of the same metal, of the same cross-section and a length of 10m will have resistance?

Given:

l1 = 6 meters – the length of the first conductor;

R1 = 3 Ohm – resistance of the first conductor;

l2 = 10 meters – the length of the second conductor;

r1 = r2 – resistivity of both conductors are the same;

s1 = s2 – the cross-sectional areas of both conductors are the same.

It is required to determine R2 (Ohm) – the resistance of the second conductor.

The resistance of the first conductor will be equal to:

R1 = r1 * l1 / s1.

The resistance of the second conductor will be equal to:

R2 = r2 * l2 / s2.

Then the following equality will be true:

R1 / R2 = (r1 * l1 / s1) / (r2 * l2 / s2),

Taking into account that r1 = r2, and s1 = s2, we get:

R1 / R2 = l1 / l2, from here we find that:

R2 = R1 * l2 / l1 = 3 * 10/6 = 30/6 = 5 ohms.

Answer: the resistance of the second conductor will be 5 ohms