Select the best answer for items 1 through 10 to make each...

Select the best answer for items 1 through 10 to make each statement true, and place the letter for the answer in the space provided. The resistance of an aluminum wire is directly proportional to the___________________ a. CSA. d. number of circuit b. temperature of the wire. control components. c. circular mils. e. source voltage.

Select the best answer for items 1 through 10 to make each statement true, and place the letter for the answer in the space provided.
The resistance of an aluminum wire is directly proportional to the___________________
a. CSA.
d. number of circuit
b. temperature of the wire. control components.
c. circular mils.
e. source voltage.

Key Concepts

Electrical Resistance

Electrical resistance is the measure of how strongly a material opposes the flow of electric current. It depends on both the material properties and the geometry of the conductor, encapsulated in the formula R = ?L/A, where ? is the resistivity, L is the length, and A is the cross?sectional area.

Temperature Dependence of Resistivity

A key concept in understanding resistance in metals is that the resistivity of a metal like aluminum increases with temperature. This happens because rising temperature causes more vigorous atomic vibrations, which in turn increase electron scattering and result in higher resistance. Thus, for a given wire, resistance is directly affected by changes in temperature.

Conductors' Geometric Properties

The geometry of a conductor, including its length and cross-sectional area, plays a critical role in determining its resistance. Although the cross-sectional area (often expressed in terms of circular mils) inversely affects resistance, meaning that as cross-sectional area increases the resistance decreases, it is important to recognize that not all physical quantities (such as circular mils) are directly proportional to resistance.

Transcript

00:01 High in the given problem resistance of a copper conductor is given as 24 oom at a room temperature of t1 is equal to 20 degrees celsius.

00:15 Now we find the values of resistivities for copper which is 1 .68 into 10 dashper minus 8 oom into and that for aluminum which is 2 .65 into 10 dash per minus 8 oom meter now in the first part of the problem if we consider length of the copper wire to be l then according to the given problem length of aluminum conductor is three times to that of the copper conductor is 3l.

01:04 Similarly, if radius of copper wire is supposed to be r, then that of aluminum wire is twice to that of copper wire.

01:18 So now using the relation of resistance in terms of its resistivity, r is equal to row l by area of cross -section or we can say by r square resistance of copper wire divided by resistance of aluminum wire will be row of aluminum wire sorry row of copper wire divided by row of aluminum wire into length of copper wire and finally canceling pi it becomes radius of aluminum wire divided by radius of copper wire to the whole square so plugging in all known values here for copper wire the resistance is 24 om divided by resistance of aluminum wire which is missing we have to find it in this first part of the problem is equal to resistivity of copper which is 1 .68 into 10 dash to par minus 8 divided by resistivity of aluminum which is 2 .65 into 10 dash per minus 8 then this is l the length of copper wire this is 3l the length of aluminum wire then for r aluminum this is 2 r for copper this is r only having a whole square so canceling this 10 dash per minus 8 canceling this l canceling this r we get it to be 1 .68 into 1 into 4 divided by 2 .65 into 3 into 1.

03:11 So finally resistance of aluminum wire here comes out to be 28 .4 or approximately we can say 29 om means the resistance of aluminum wire is 20.

03:26 Which becomes the answer for the first part of this problem...

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