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Question

If we double both the length and cross-sectional area of the wire, then its resistance will ____.

A
remain the same
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B
increase by two times
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C
reduce by two times
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D
increase by four times
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Solution

The correct option is A remain the same
Resistance is given by:
R=ρLA
where:
ρ: Resistivity
L: Length of the resistance
A: Area of cross-section

When length and area of cross-section is double, let the new resistance be R.
RR=ρ×2L/2Aρ×L/A
R=R
That is, the resistance will not change.

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