Resistance and Resistivity: The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire?
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Resistance and Resistivity: The length of a certain wire is doubled while its radius is kept constant. What is the new resistance of this wire?
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Answer:
Explanation:
The formula for calculating the resistance of a material in terms of its resistivity is expressed as
where;
R is the resistance of the material
L is the length of the wire
A is the area = πr² with r being the radius
If the length of a certain wire is doubled while its radius is kept constant, then the new length of the wire L₁ = 2L
The new resistance of the wire R₁ will be expressed as
since the radius is constant, the area will also be the same i.e A = A₁ and the resistivity also will be constant. The new resistance will become
Taking the ratio of both resistances, we will have;
This shoes that the new resistance of the wire will be twice that of the original wire