A o.686-meter-long wire has a cross-sectional area of 8.23 ×10^-6 meter ^2 and a resistance of 0

A o.686-meter-long wire has a cross-sectional area of 8.23...

A o.686-meter-long wire has a cross-sectional area of $8.23 \times 10^{-6}$ meter $^{2}$ and a resistance of $0.125 \mathrm{ohm}$ at $20^{\circ}$ Celsius. This wire should be made of
(A) aluminum
(B) copper
(C) nichrome
(D) tungsten

Key Concepts

Electrical Resistance

Electrical resistance is a measure of how much a material opposes the flow of electric current. It depends on the inherent properties of the material as well as the geometric dimensions of the conductor, such as its length and cross-sectional area.

Resistivity

Resistivity is a fundamental material property that quantifies how strongly a given material opposes current flow. It is used to compare different materials and is determined by the specific atomic structure of the substance, with typical values varying significantly among conductors like copper, aluminum, tungsten, and alloys like nichrome.

Relationship Between Geometry and Resistance

The resistance of a conductor can be calculated using the formula R = ?(L/A), where R is the resistance, ? is the resistivity, L is the length of the conductor, and A is its cross-sectional area. This relationship shows that for a given material, longer conductors exhibit higher resistance while larger cross-sectional areas result in lower resistance.

Material Identification Based on Resistivity

In material science and electrical engineering, known resistivity values are used to identify unknown materials or confirm the suitability of a material for specific applications. By calculating the resistivity from measured resistance and known dimensions, one can compare the result with standard values to determine the likely material of a conductor.

Transcript

00:01 Question 37.

00:03 We have a wire that is 0 .686 meter long with a cross -sectional area of 8 .23 times 10 raised to negative 6 square meter and a resistance of 0 .125 oms at ambient temperature 20 degrees celsius.

00:19 We are to determine the identity of the said metal.

00:24 We are given four choices here.

00:26 So to help us answer the question, we recall the concept of resistance of a conductor in terms of its length and its area and its identity.

00:38 So this equation here is telling us that the resistance of a wire, of a conducting wire, is affected by its length, its cross -sectional area, and of course its resistivity.

00:53 So this resistivity, which is symbolized by greek letter rove, actually tells us of the identity of the material.

01:03 In other words, for us to answer the question here, we need to calculate the resistivity of this particular metal, and we compare it to the standard values of resistivity of the four metals, which i tabulated on the right side.

01:22 Okay, so manipulating this algebraically, the resistivity is just the ratio of the product.

01:30 Of the resistance and the cross -sectional area to the length.

01:36 Checking the units, everything is in the same system.

01:41 So that's there's no unit conversion needed.

01:45 So for the resistance, we have here 0 .125 oms.

01:50 And the cross -section area is 8 .23 times 10 to negative 6.

01:56 This is in square meter, divided by the length.

02:00 Of 0 .686 of a meter.

02:05 Okay.

02:06 So the resistivity here is 1 .5 times 10 to negative 6...