(a) Of what material is a wire made, if it is 25.0 m long with a 0.100 mm diameter and has a res

(a) Of what material is a wire made, if it is 25.0 m long...

Key Concepts

Resistivity

Resistivity is a fundamental property of a material that indicates how strongly it opposes current flow. It appears in the relation R = ?L/A, where R is the resistance, ? is the resistivity, L is the length, and A is the cross-sectional area. Knowing the resistivity helps in distinguishing between different conducting materials.

Cross?Sectional Area Calculation

For a wire with a circular cross section, the area is calculated using A = ?r². An accurate determination of the cross-sectional area is crucial because it directly influences the resistance according to the geometric factor in the resistance formula.

Temperature Dependence of Resistivity

The resistivity of most metals increases with temperature owing to increased atomic vibrations that scatter electrons. This change is typically described by the formula R = R?[1 + ?(T - T?)], where ? is the temperature coefficient of resistivity, highlighting the material’s change in resistance with temperature.

Material Identification via Resistivity

By computing the resistivity from the measured resistance, length, and area of the wire, and then comparing it with standard reference values, the material of the wire can be identified. This technique is a common method in both laboratory experiments and industrial applications to ascertain the type of metal used.

Transcript

00:01 In this particular problem we'll jot down the given data as wire length is given as l is equal to 25 meters at the same time its diameter is given as 0 .1 millimeter which we need to convert it into meter so we'll just divide by a thousand so we get down it as 0 .1 into 10 it is to my minus 3 meters.

00:48 Also its resistance is given as 77 .7 oms at 20 degrees celsius.

01:03 So we need to find the material of this particular wire.

01:06 At the same time in the next part we need to find the resistance of wire at 150 degrees celsius.

01:12 To start with this step a, we need to use the formula r is equal to row multiplied by l upon so therefore in order to find resistivity we just need to cross multiply so we'll get it as resistance multiplied by its area upon length now we'll first take care of the area part so here area that is cross -sectional area is given as pi r square so pi multiplied by d by two that is diameter divided by two the whole square which is equal to multiplied by 0 .1 into 10 to minus 3 upon 2 the whole square and we get this value as 7 .85 into 10 to minus 9 meter square so this is the area value that we get here therefore resistivity is equal to we'll substitute the values now 77 .7 that that is resistance multiplied by its area 7 .85 into 10res 2 minus 9 divided by 25.

02:46 So we get the resistivity value as 2 .44 into 10902 minus 8 oam meter.

02:58 So now from the table of resistivity of various materials at 20 degrees celsius, we can say that, we can can say that the wire is made up of cold as per the resistivity.

03:24 We'll start with the second part.

03:27 So step b, in order to find resistance of wire at 150 degrees celsius.

03:34 So the question is, resistance at 150 degrees celsius...

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