Concept explainers
The criterion for choosing the dimension of the lead wire so that it provides the same resistance of the gold wire.
Answer to Problem 72PQ
In order to result the same resistance as that of the gold wire, the lead wire should have dimensions such that the cross sectional area and the lengths of the wires are related as
Explanation of Solution
The resistivity of gold is
Write the expression for the resistance.
Here,
Analogous to equation (I), write the expression for the resistance of gold (Au) and lead (Pb) wires.
Since both wires has to have same resistance, equate the right-hand sides of equations (II) and (III) and reduce.
Conclusion:
Substitute
This expression is the most general statement about the dimensions with which the lead wire has to be made such that it offers same resistance as that of the gold wire. The ratio of the length to cross sectional area of the lead wire must be
Therefore, in order to result the same resistance as that of the gold wire, the lead wire should have dimensions such that the cross sectional area and the lengths of the wires are related as
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