Question

The figure below shows three cylindrical copper conductors along with their face areas and
lengths. Discuss in which geometrical shape the resistance will be highest.

Answer 1

The geometry that has the highest resistance is 2.

Given:

Three cylindrical copper conductors along with their face areas and lengths.

To Find:

The geometry has the highest resistance.

Solution:

To find the geometry that has the highest resistance we will follow the following steps:

As we know,

Resistance is the property of conductors or wires that obstructs the flowing current.

The unit of resistance is the ohm.

The formula for finding resistance is

$ρ \frac{l}{a}$

Here, l is the length and a is the area.

So,

In-cylinder 1 resistance is given by:

Resistance in the cylinder of option 1 =

$r1 = ρ \frac{l}{a}$

Resistance in the cylinder - 2

$r2 = ρ \frac{2l}{ \frac{a}{2} } = ρ \frac{4l}{a} ohm$

Resistance in the cylinder - 3

$r3 = ρ \frac{ \frac{l}{2} }{2a} = ρ \frac{l}{4a} ohm$

Now, the order of resistance = r2 > r1 > r3

Henceforth, the geometry that has the highest resistance is 2.

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